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Technology consulting

Thu, 26 Feb 2026 00:00:00 GMT

Who does what on the project

Project management is extremely important in consultanting as coordination costs are non-linear in the size of the team/projects.

Let’s take typical small project team

Grade	Time on project	Role
Associate Director	1 day/week	Navigate, keep client happy
Senior manager	Full time	Project manage, organise team, work if poss
Manager	Full time	Work, help to organise
Senior consultant	Full time	Work
Senior consultant	Full time	Work
Senior consultant	Full time	Work

Manger and SC work, Senior manager prioritises project managment, AD provides direction and trys to keep things on the rails, also providing a point of (more senior) contact for the client.

Project management

Stuff about project managment (TODO)

You’ll have to read emails and Teams messages and update accordingly
- If you’re a consultant for Globex Corp. and your client is Acme Inc., you’re potentially doubling up, with two sets of Microsoft Teams, two sets of Outlook, etc. to keep track of
- This is annoying however it is core to job role so not much that can be done — at least one perosn within the team needs to take lead in incorporating inbound client comms and this is usually the person wearing the project manager had in a small(er) team
- Teams will generally allow logins to multiple orgs which helps somewhat
It’s good to keep the Outlook calandar up to date
- If there’s a recurring meeting during e.g. a seasonal holiday period when everyone is away, cancel the meeting rather than leaving it in
- If someone is running e.g. 15 minutes late for a meeting and it involves three or more people, update the diary invite to make it start 15 minutes later

Various consulting tips

Teams status

A good Teams status when on a client machine

I am working on and off from a client device, please expect a delay in replying

OoO

Below are helpful instuctions about how to set Out of Office e.g. over leave periods in Outlook/Teams

Over your leave days please add an all-day meeting (not a teams call; for this reason best to do in Outlook) with ‘FS OoO’ where F = first name initiate, S = surname initial and send this to i) me ii) your line manager (if not me) and iii) anyone else you like (please do not set this to Out of office status otherwise those you share it will also show as out of office on Teams/Outlook) (for automagical Out of office status etc on Teams please then create a separate event over the span, just you no need to invite anyone else, and set the status to Out of office )

Appendices

Appendix: job grades

Grades are quite silly in technology consulting; we’ll use Accentures below as an example:

CL13 Analyst
CL12 Consultant
CL11 Senior Analyst / Senior Consultant (varies by practice)
CL10 Manager
CL9 Senior Manager
CL8 Associate Director (or “Associate Director/Associate Manager” in some groups; commonly treated as AD)
CL7 Director / Managing Director track begins to appear (titles vary)
CL6 Managing Director

Compare this to the simplicity of the US investment bank:

Analyst
Associate
VP
Director
Managaing director

Developing with agents

Sun, 08 Feb 2026 00:00:00 GMT

As of the time of writing the best offerings are:

Anthropic’s Claude Code (“CC”), using Opus 4.6
OpenAI’s Codex (“Codex”), using gpt-5.3-codex with thinking level set to xhigh (i.e. extra-high)

For the sake of brevity—at the risk of slightly wrong nomenclature—if I refer to CC or Codex, I mean specificially using the model mentioned above.

`AGENTS.md`/`CLAUDE.md`

If and only if you use both Codex and CC, it may make sense to symlink CLAUDE.md to AGENTS.md and add CLAUDE.md to .gitignore so you’re not duplicating the file in the repo.

Symlink creation and addition to .gitignore will need to be done after each clone; irrespective this feels more convenient that alternatives if you want to use Claude Code (which uses CLAUDE.md) and another model (which use AGENTS.md as a kind of industry standard) in the same repo.

# Note: AGENTS.md must exist
ln -s AGENTS.md CLAUDE.md

If such a file does not exist, you can create with /init within either CC or Codex. They provide helpful context for the agent and are read automatically on load if you launch within a directory which contains one.

At the top of such file you can add:

# AGENTS.md / CLAUDE.md

`CLAUDE.md` is a symlink to `AGENTS.md`, this is intentional.

Which is best?

As the time of writing, CC is strong than Codex IMHO. Opus 4.5 (re)set the bar for comprehension, taste, and ability to handle complex implimentations on large codebases. Codex will get it done, it just seems to have a lot less flair.

In terms of speed, they feel about the same to me.

The Codex TUI feels a bit snappier to me, no doubt as a result of beign developed in Rust rather than what looks like a combo of shell scripts, Python and Typescript.

The CC agent harness seems to be regarded as leading and I have no reason to doubt this, not least as Antrophic seemed to have cracked it first.

Using in combination

I get decent results having them both in the same repo, and having CC finnish up a feature and then having Codex review it.

Usage

Quite a good idea to keep an eye on token / usage limits if you’re using subscriptions, and especially important to keep an eye on usage if you’re using an API key and paying as you go.

/status in Codex
/usage in Claude

For Claude, I have also used claude-monitor (https://github.com/Maciek-roboblog/Claude-Code-Usage-Monitor) and ccusage (https://github.com/ryoppippi/ccusage)

MCP servers

For getting installation instructions, https://fastmcp.me/MCP/Explore is useful e.g. to install Brave search MCP server

codex mcp add brave-search --env BRAVE_API_KEY='xyz' -- npx -y @brave/brave-search-mcp-server

where xyz is API key

Playwright MCP is very handy as it allows the agent to have control of a web browser

codex mcp add playwright npx "@playwright/mcp@latest"

With a combination of Brave web search API (good enough to pay for IMHO) MCP, and Playwright MCP, and a database to write to (can be SQLite) Codex/CC can do desktop research nicely.

Favourite prompts

Codex seems particularly good at reviewing large codebases
- Please thoroughly review the entire codebase or
- Please review code this session (before a commit) seem to work well
Updating docs
- Please update CLAUDE.md as appropriate, including file maps
Before a commit
- Are we done here?

CC

You can turn on increase verbosity in CC in /settings which will provide more detailed output around what files are being edited etc.

`makefile`

I always add a makefile so I can easily run stuff and also as a reference to how to run things. CC/Codex can keep the makefile up to date which is very helpful

`AGENTS.md`

I tend to use somethign similar to the below preamble:

You have autonomy. Edit and run as needed. Do not commit. Say when done; I may ask you to run `make precommit`.

Do not use Docker unless explicitly asked. Use `make dev-local` for local development (requires PostgreSQL/Redis) or `make dev-sqlite` for standalone development (no external dependencies).

When the user doesn't specify "prod" or "production", assume they're talking about local dev.

For any new feature always implement the back-end first. The back-end api must be fully functioning. Then write and run comprehensive tests for the back-end. Only then go on to front end pages.

Windows 11 PIN change

Mon, 02 Feb 2026 00:00:00 GMT

Which version?

To check which version of Windows you have, hit Windows Key + R to open the run dialogue, type in winver and hit enter

How to change PIN

Settings -> Accounts -> Sign-in options -> PIN -> Change PIN

if you tick ‘Include letters and symbols’ you can then click again to see PIN requirements

Below are typical

$\geq$ 6 chars long
$\geq$ 1 upper case letter
$\geq$ 1 lower case letter
$\geq$ 1 digit

Auto log-out

Settings -> Accounts -> Sign-in options

“If you’ve been away, when should Windows require you to sign in again?” -> Never

Note that corporate policy may mean that e.g. 5 minutes is the longest option you can go with

Developer setup speedrun for Pop!_OS

Tue, 25 Nov 2025 00:00:00 GMT

Pop!_OS developer setup speedrun below.

Nodejs

# Grab the NodeSource setup script for Node 20.x (LTS)
curl -fsSL https://deb.nodesource.com/setup_20.x | sudo -E bash -

# Install Node.js + npm
sudo apt install -y nodejs

# Optional: install extra build tools for native npm modules
sudo apt install -y build-essential

Let’s make some tweaks so we can install globally in a cleaner way

# Create a directory named `.npm-global` in the user's home directory
mkdir ~/.npm-global
# Configure npm to use the newly created directory as the default location for globally installed packages
npm config set prefix '~/.npm-global'
# Add the `bin` directory inside `.npm-global` to the system's PATH environment variable
export PATH=~/.npm-global/bin:$PATH
# Note: Adopt the below for your shell
# Append the export command to the end of the `.profile` file to ensure the PATH update persists across sessions
echo 'export PATH=~/.npm-global/bin:$PATH' >> ~/.profile
# Refresh the current shell session to apply the changes made to the `.profile`
source ~/.profile

uv

curl -LsSf https://astral.sh/uv/install.sh | sh

Claude Code

# Deps
sudo apt install -y git ripgrep
# Note that we are not using sudo here deliberately
npm install -g @anthropic-ai/claude-code

OpenCode

npm install -g opencode-ai

ungoogled-chromium

sudo add-apt-repository ppa:xtradeb/apps
sudo apt update
sudo apt install ungoogled-chromium

zed

# - **`tar`** - Archive utility program
# - **`-C ~/bin`** - **Change directory** to `~/bin` before extracting (extracts files there instead of current directory)
# - **`-x`** - **Extract** files from the archive
# - **`-z`** - Decompress using **gzip** (handles `.gz` files)
# - **`-f`** - Specifies the **file** name that follows (`zed-linux-x86_64.tar.gz`)
# - **`zed-linux-x86_64.tar.gz`** - The archive file to extract

curl -LO https://github.com/zed-industries/zed/releases/download/v0.214.3-pre/zed-linux-x86_64.tar.gz
tar -C ~/bin -xzf zed-linux-x86_64.tar.gz
# Then want to link the binary so that zed is in ~/binary
cd ~/bin
ln -s ./zed-preview.app/bin/zed zed
cd

Go

sudo add-apt-repository ppa:longsleep/golang-backports
sudo apt remove golang
# 1.24 recent at the time of writing
sudo apt install golang-1.24
# then need to prepend /usr/lib/go-1.24/bin/ to $PATH
export PATH="/usr/lib/go-1.24/bin:$PATH"

gollm

Because you want to be able to ask questions on the shell

git clone https://github.com/algrt-hm/gollm.git
make build
cp ./bin/gollm-linux-amd64 ~/bin/gollm

Cursor

Download the .deb from: https://cursor.com/download

sudo dpkg -i ./cursor_2.1.26_amd64.deb

Beeper

https://www.beeper.com/download/linux

to get the AppImage … e.g. Beeper-4.2.229-x86_64.AppImage

chmod u+x ./Beeper-4.2.229-x86_64.AppImage
./Beeper-4.2.229-x86_64.AppImage

claude-monitor

# Install directly from PyPI with uv (easiest)
uv tool install claude-monitor

# Run from anywhere
claude-monitor  # or cmonitor, ccmonitor for short

How do I set the default browser?

Settings->Default applications

A plan for contacts

Sat, 27 Sep 2025 00:00:00 GMT

A table

The DDL required a couple of definitions:

an update_modified_column() trigger

CREATE OR REPLACE FUNCTION public.update_modified_column()
  RETURNS trigger
  LANGUAGE plpgsql
 AS $function$
     BEGIN
         NEW.updated_at = now();
         RETURN NEW;
     END;
 $function$

and a contact_status enum

CREATE TYPE public.contact_status
    AS ENUM ('active_colleague', 'former_colleague', 'client', 'vendor', 'contractor', 'candidate', 'personal');

And looks like this:


create table public.work_contacts
(
    id                     uuid
        default gen_random_uuid()
            not null primary key,
    full_name              text
        not null,
    primary_email          text
        unique,
    linkedin               text,
    pronouns               text,
    current_company        text,
    current_title          text,
    team_or_department     text,
    status                 contact_status
        default 'active_colleague'::contact_status
            not null,
    manager_id             uuid
        references public.work_contacts,
    tags_and_skills        text[]
        constraint work_contacts_tags_and_skills_check
            check (cardinality(tags_and_skills) < 100),
    contact_details        jsonb,
    employment_history     jsonb,
    how_we_met             text,
    first_interaction_date date,
    last_interaction_date  timestamp with time zone,
    general_notes          text,
    created_at             timestamp with time zone
        default now() not null,
    updated_at             timestamp with time zone
        default now() not null
);

alter table public.work_contacts
    owner to postgres;

create index idx_work_contacts_manager_id
    on public.work_contacts (manager_id);

create index idx_work_contacts_tags_and_skills
    on public.work_contacts using gin (tags_and_skills);

create index idx_work_contacts_contact_details
    on public.work_contacts using gin (contact_details);

create trigger update_work_contacts_modtime
    before update
    on public.work_contacts
    for each row
execute procedure public.update_modified_column();

Some commentary on the columns:

id — uuid, auto-generated if not provided
full_name
primary_email
linkedin — LinkdIn URL which is often useful for reference
pronouns
current_company
current_title
team_or_department — all self-explanatory text fields
status — using the contact_status enum to specify the status of the contact
manager_id — allows reference to another contact in order to be able to capture hierarchy
tags_and_skills — list of text tags i.e. free-form, schema not imposed
contact_details — free-form JSON blob to allow whatever extra contact details beyond primary_email
employment_history — free-form JSON blob which could be filled out with reference to e.g. LinkdIn or a CV
how_we_met — self-explanatory text field
first_interaction_date — self-explanatory date
general_notes — text field for anything else
created_at — date, automatically created
updated_at — date, updated automatically through the trigger

Example row:

SELECT to_jsonb(t)
FROM work_contacts t
WHERE full_name = 'Alice Smith';

{
  "id": "dd57ef33-2670-4246-b3a7-c4da34df2cdc",
  "status": "active_colleague",
  "linkedin": null,
  "pronouns": "she/her",
  "full_name": "Alice Smith",
  "created_at": "2025-07-30T12:13:19.853732+00:00",
  "how_we_met": "Hired her for the Analytics team in 2021.",
  "manager_id": null,
  "updated_at": "2025-09-27T15:26:56.339546+00:00",
  "current_title": "Lead Data Scientist",
  "general_notes": {
    "background": "Expert in time-series analysis. Big fan of strong coffee."
  },
  "primary_email": "alice.smith@example.com",
  "contact_details": {
    "phone": "555-0101",
    "github": "alicesmith-dev",
    "linkedin": "linkedin.com/in/alicesmith"
  },
  "current_company": "Innovate Corp",
  "tags_and_skills": [
    "Python",
    "PostgreSQL",
    "Machine Learning",
    "Data Visualization"
  ],
  "employment_history": [
    {
      "title": "Data Analyst",
      "years": "2019-2021",
      "company": "Data Solutions Inc"
    }
  ],
  "team_or_department": "Analytics",
  "last_interaction_date": null,
  "first_interaction_date": null
}

A handy shell function

Below a handy shell function. This is zsh but with small modifications would be fine in bash or similar.

# This assumes the user `postgres`, no password,
# a database called kpi and postgres host of 100.111.151.57

f-contacts () {
	if [[ $# -eq 2 ]]
	then
		echo "insert into work_contacts (full_name, primary_email) values ('$1', '$2')" | psql -U postgres -h 100.111.151.57 kpi
		q="select * from work_contacts where full_name='$1'"
		echo $q
		echo $q | psql -U postgres -h 100.111.151.57 kpi
	elif [[ $# -eq 3 ]]
	then
		echo "insert into work_contacts (full_name, primary_email, linkedin) values ('$1', '$2', '$3')" | psql -U postgres -h 100.111.151.57 kpi
		q="select * from work_contacts where full_name='$1'"
		echo $q
		echo $q | psql -U postgres -h 100.111.151.57 kpi
	else
		echo "Usage: $0 'full_name' 'primary_email' [linkedin_url]"
		echo "Adds to work_contacts table"
		q="select full_name, primary_email, linkedin, updated_at from work_contacts order by updated_at desc limit 10"
		echo $q
		echo $q | psql -U postgres -h 100.111.151.57 kpi
	fi
}

A sample note

Here is an example note, in markdown format. I use Bear which works very well across MacOS/iOS devices but convievably these could be kept anywhere.

# Alice Smith

#2025/September/27

- Alice is now at XYZ Corp and having a great time
- She recommended some meet-ups
  - Data Engineering Gurus and Sci-Pi Get Together, which I should have a look at
- Particular interest in data streaming pipelines as currently working on this

Some Python to extract bods from our notes

TBD

Updating the database

We have what we want from our notes, how do we update our database

Data taxonomy

Mon, 22 Sep 2025 00:00:00 GMT

Below a nice taxonomy of themes/areas in data, the ‘data landscape’ if you will:

AI, MLOps, machine learning
- Generative AI / LLMs
- MLOps
- Machine learning
Data engineering, platforms and architecture
- Architecture modernisation
- Customer data platform
- Data engineering
- Data observability
- Data platforms
- DataOps
- Event streaming
- Modern data stack
Data governance, management and privacy
- Data cataloguing
- Data governance
- Data literacy
- Data management
- Data marketplace
- Data privacy
Data science, analytics and insight
- Data workspaces
- Graph databases
- Modern analytics tools
- No-code/low-code
- Real-time analytics
- SQL databases
- Self-service analytics
- Visualisation
Leadership, culture and process
- Data culture
- Data democratisation
- Data fabric
- Data mesh
- Data strategy
- Data transformation
- Training and recruitment

Working with me guide

Thu, 18 Sep 2025 00:00:00 GMT

Template for a ‘working with me guide’ which can be useful to fill and out share with colleagues

Role and focus

What do I do?
Where can I add value?

Working style

How I prefer to work
Approach to
- decision making
- pace
- detail

Communication preferences

How to reach (medium/media of communication)
What works best in meetings/emails
Response time

What I value in others

Behaviours/qualities I appreciate in colleagues and teams

Things to avoid

What does not work well when working with me

How I will support you

What others can expect from me as a colleague/leader

Example: HR leader persona

Role and focus

I lead the HR function, focusing on strategy, culture, and building capability.

Working style

I like clear objectives upfront and prefer open, direct communication. I like time to reflect so I can give a well thought through opinion. I like to co-create things once I have had time to do my own thinking. I like scope to come up with my own way of doing things.

Communication preferences

Best way to reach me: Teams for quick questions, email for decisions.

What I value in others

Proactivity, transparency, and constructive challenge. Sharing the full picture and involving me in decision making.

Things to avoid

Last-minute surprises without context. Rushing me into giving a point of view on the spot. Only telling me half of the story. Being prescriptive on how something should be done.

How I will support you

I’ll give you honest feedback, advocate for your growth, and create clarity where possible.

Example: technology consultant persona

Role and focus

I am the capability lead for ML (machine learning) and GenAI, so I focus on this area in terms of technology. I work across sectors, with more experience in: finance, markets/banking, insurance and airlines

Working style

I like to find agreement on what we’re doing and then do it. I aim to — with others — monotonically deliver value

Communication preferences

I am in the office most days so available in person if you are also in the office. Otherwise Teams/email as required

What I value in others

Proactivity e.g. being able to do a bit of research when needed, competence and a willingness to get stuck in

Things to avoid

I particularly dislike having my time wasted — as Steve Jobs liked to say, time is the most important finite resource

How I will support you

If you work with me, I will aim to have one or both of us enhance our performance while we work towards a shared goal. I also try to maintain positive energy

Keeping credentials out of the repo

Thu, 11 Sep 2025 00:00:00 GMT

You use credentials in your (jupyter) notebook or python script and you are about to check it in to a (git) repository. What’s a quick and easy way to get the credentials into a separate file and load them? Use pydantic_settings.

Firstly, create a .env file with key value pairs in it in a similar way to a shell script

# Variables for config
API_KEY=your_super_secret_api_key_here_32_chars_minimum
DATABASE_URL=postgresql://username:password@localhost:5432/database_name

Secondly, add this to your .gitignore

echo .env >> .gitignore

Note that this assumes you are in the root of the repo so if not you will need to adjust the path to the .gitignore file

from typing import Annotated
from pydantic import Field, PostgresDsn
from pydantic_settings import BaseSettings, SettingsConfigDict


class AppSettings(BaseSettings):
    # Config variables saved in a .env in this folder
    model_config = SettingsConfigDict(env_file=".env", env_file_encoding="utf-8")

    # API key expected to be at least 32 chars
    api_key: Annotated[str, Field(min_length=32)]

    # Postgres connection string
    # We call this DATABASE_URL in our .env file
    pg_dsn: Annotated[PostgresDsn, Field(alias="DATABASE_URL")]


def main():
    settings = AppSettings()

    # Example of printing the various settings
    for k, v in settings.model_dump().items():
        print(f"{k}: {v}")


if __name__ == "__main__":
    main()

Data preparation

Wed, 27 Aug 2025 00:00:00 GMT

Some good pointers on data cleansing which also doubles as a good checklist of things to think about at the start of a data project, at least on the data engineering side.

Always Start With Understanding the Data

Know your source – Where is the data coming from? Internal database? Third-party API? Manual upload?
Understand its purpose – Why was this data collected? Who will use it?
Check data freshness – Is it near real-time, daily batch, or static historical data?
Understand scale – How many rows/records are we talking about? This will affect tooling and approach
Look for key business drivers – Which columns/fields matter most to the business use case?
Get context from stakeholders – Talk to PMs, analysts, or SMEs before you write a single cleaning script

Define the Schema Early

Choose correct data types – int, float, string, timestamp, boolean, pick precisely
Apply constraints – Not Null, Unique, Primary Key, Foreign Key where applicable
Default values – Decide defaults for missing fields only if business rules allow
Precision and scale – For decimals, know how many digits you need after the point
Data size control – Avoid VARCHAR(255) everywhere; optimize for reality
Match schema to usage – The schema should reflect how data will be queried and processed

Validate Data Types & Formats

Check for mismatches – Numeric columns containing strings (e.g., “N/A” in an int column)
Enforce formats – Dates should follow a standard (ISO 8601 or company format)
Parse complex types – JSON fields, arrays, structs, ensure they’re valid and parsable
Catch unit mismatches – e.g., “km” vs “miles” in the same column
Test with sampling – Randomly check 100–200 rows to spot patterns
Automate validation – Use scripts or frameworks like Great Expectations to enforce rules

Handle Missing Data Properly

Identify NULLs – Know exactly which fields are missing and how often
Decide on action – Drop, fill, or leave missing based on use case
Use domain logic – If birth_date is missing, you can’t just fill with 01-01-1900 without reason
Flag critical NULLs – Create alerts when important fields (like customer_id) are missing
Avoid blind imputation – Filling missing values can distort downstream analysis
Document decisions – Always record why you handled missing data a certain way

Detect & Remove Duplicates

Define uniqueness – What makes a record unique? Single field or combination?
Check both exact and fuzzy duplicates – E.g., same customer name with slightly different spelling
Decide on deduplication strategy – Keep first, keep last, or merge data
Flag potential duplicates – Don’t delete blindly; verify with business teams
Use hashing – Create hash keys for comparison when datasets are large
Automate dedup checks – Schedule scripts to run regularly for recurring data sources

Standardize Units & Formats

Pick one unit – Convert all weights, distances, currencies to a single standard
Use consistent casing – Lowercase or uppercase text fields consistently
Normalize whitespace – Trim spaces before/after values
Standardize date formats – Pick one and stick to it (e.g., YYYY-MM-DD)
Apply consistent naming – “US”, “USA”, and “United States” should be unified
Automate standardization – Use mapping tables or scripts to enforce rules

Identify & Fix Outliers

Define valid ranges – Age can’t be 250, salary can’t be -5000
Use statistical methods – Z-score, IQR to detect anomalies
Validate with domain experts – Sometimes “outliers” are actually correct
Flag for review – Never delete unusual values without business sign-off
Track frequency – Recurrent outliers may mean an upstream issue
Document everything – If you remove or alter data, log it

Enforce Referential Integrity

Check foreign keys – Ensure referenced IDs exist in parent tables
Avoid orphan records – A transaction without a valid customer should be flagged
Validate join keys – Ensure keys are consistent in type and format across tables
Cascade rules – Decide how deletes/updates propagate across related tables
Regular audits – Schedule scripts to check integrity at intervals
Collaborate with upstream teams – Fix issues at the source if possible

Track Data Lineage

Know the source – Where each field came from
Document transformations – Every cleaning step should be traceable
Map dependencies – Know which downstream systems use your cleaned data
Use versioning – Keep snapshots of data and schemas over time
Audit regularly – Compare current and historical data for unexpected changes
Adopt a lineage tool – Like OpenLineage or DataHub for visibility

Build Automated Data Quality Checks

Threshold alerts – E.g., alert if NULL rate exceeds 5%
Schema drift detection – Notify if schema changes unexpectedly
Volume checks – Alert if record count deviates drastically
Value checks – Alert on unexpected category values
Freshness checks – Alert if data hasn’t been updated in X hours
Integrate into pipelines – Make quality checks a default pipeline step

Work Closely With Domain Experts

Clarify ambiguous fields – Ask if “status” means order status or payment status
Verify assumptions – Don’t assume “active” means the same to every team
Review sample records together – See if values match expectations
Learn business rules – Data cleaning without business rules is guesswork
Get sign-offs – Before making irreversible changes
Educate non-technical teams – Help them understand why cleaning matters
Review sample records together – See if values match expectations.
Learn business rules – Data cleaning without business rules is guesswork.
Get sign-offs – Before making irreversible changes.
Educate non-technical teams – Help them understand why cleaning matters.

Optimize for Performance

Filter early – Remove irrelevant data as soon as possible.
Use efficient joins – Avoid cartesian products.
Index where needed – Speeds up lookups during cleaning.
Batch processing – For large datasets, break into chunks.
Push down operations – Do cleaning in the database when possible.
Test scalability – Will your cleaning process handle 10x more data?

Build for Repeatability

Script everything – Avoid manual cleaning in Excel.
Use parameterized scripts – Makes them reusable across datasets.
Store scripts in version control – Git it or regret it.
Automate schedules – So cleaning runs on time without human intervention.
Document every step – Future you will thank present you.
Create modular functions – For common cleaning tasks like trimming text or removing duplicates.

Monitor Post-Cleaning Quality

Re-run checks after cleaning – Did the changes actually improve quality?
Validate downstream outputs – Reports/dashboards should reflect expected changes.
Watch for regressions – Sometimes cleaning breaks something else.
Track KPIs – e.g., error rate, completeness score.
Share results with stakeholders – Show the value of your work.
Iterate – Data cleaning is never truly “done.”

Keep a Data Quality Mindset Always

Don’t chase perfection – Focus on what matters most for the use case.
Think prevention – Fix issues at the source, not just downstream.
Stay curious – Ask why an issue exists, not just how to fix it.
Balance speed vs accuracy – Sometimes “good enough” is enough to move forward.
Document lessons learned – Every dataset teaches you something.
Be the advocate – If you don’t care about data quality, no one else will.

Source: Shubham Srivastava, Amazon Data Engineer

Meeting quality

Wed, 06 Aug 2025 00:00:00 GMT

Rough model for meeting quality:

$\frac{\bar q}{n^{k}}$

where $k>1$ , $\bar q$ is mean quality of meeting participants and $n$ is the number of participants in the meeting

uv to manage packages

Sun, 25 May 2025 00:00:00 GMT

I have replaced poetry in enough projects now to be able to cover off uv

Generally speaking I will have already set up a git repo so I use the following to get started

# No git repo req'd hence the vcs flag

uv init \
--name $PROJECT_NAME \
--vcs none \ 
--python 3.13.2 \
.

Once that is done we then need to ask uv to set up a venv in .venv for us with e.g.

uv venv \
--python 3.13.2 \
".venv"

To run anything within your project, automatically making use of the venv, you can use

uv run python src/main.py

where src/main.py is the path of the python script you want to run

To add new packages is as simple as:

uv add package-name

where package-name is the name of the package

My vanilla makefile is below:

.POSIX:

# To install uv: 
# curl -LsSf https://astral.sh/uv/install.sh | sh

NAME = project_name
PYTHON = 3.13.2
PREPEND = uv run
VENV = .venv

run:
	$(PREPEND) python src/main.py

modules:
	uv pip list

format:
	$(PREPEND) python -m black ./src/*.py ./tests/*.py
	$(PREPEND) python -m isort ./src/*.py ./tests/*.py

test:
	$(PREPEND) pytest

cursor:
	uv run cursor .

bootstrap:
	@printf "uv init \\ \n \
	--name $(NAME) \\ \n \
	--vcs none \\ \n \
	--python $(PYTHON) \\ \n \
	. \n"

venv:
	uv venv \
	--python $(PYTHON) \
	$(VENV)

install:
	uv pip install .

activate:
	@echo source $(VENV)/bin/activate

Setting up uv where pyproject.toml already exists

If you’re not setting up a new project and are e.g. cloning a repo to a machine fresh

(here assuming python version is 3.13.3)

# if 3.13.3 not yet installed
# uv python install 3.13.3
uv venv --python 3.13.3 ".venv"
source .venv/bin/activate
uv pip install -r pyproject.toml

Consultancy B

Tue, 29 Apr 2025 00:00:00 GMT

I spoke to someone who left the commencial team and he said that there were two problems

Half the team are ‘leaders’, which means they have a tendancy to think that work is for others

A lot of activity and energy is devoted to intra-company activities. Everyone is looking around them; inside and not out

New project considerations

Fri, 25 Apr 2025 00:00:00 GMT

You are a consultant starting a new project. What do you need to think about?

Overall objectives

The primary goals of the engagement mobilization and initiation process are to:

Ensure everyone understands the engagement’s purpose, deliverables, and intended business value
Clarify the roles of all team members and associated personnel
- Delivery Lead
- Team Lead
- Account Manager (i.e. sales/commercial function)
Prepare consultants for client site work, including behavioral expectations and first-day logistics
Guide the Team Lead on effectively utilizing the initial days on site

Pre-engagement: alignment & readiness

This phase focuses on preparing for the engagement start:

Notice period: A minimum one-week notice (ideally two) is needed from client commitment to the start date for preparation
Roles & responsibilities: Clearly define and assign roles internally before the start date, covering proposal context, contracts, client communication, resource logistics, tools/access, and scope communication. Build strong relationships with the Account Manager, involving the Account Manager in role definition and key task completion
Contracts & governance: Finalize all contracts and commercial agreements before the start date. Establish internal governance structures, reporting cadences, and escalation paths
Communicate needs: The delivery lead should brief the Team Lead on business objectives, metrics, and deliverables. The Team Lead should review and conduct a playback session for alignment
Onboard team: Provide consultants clarity on objectives, client expectations, timelines, roles, working hours, office etiquette, and administrative processes. Ensure necessary tools, systems, and access are available before the start date, as delivery cannot commence without them. Address training needs and how to use time effectively while awaiting access
Schedule kick-off: Arrange the client-delivery team kick-off meeting for the first day

Start of engagement

Kick-off meeting with stakeholders: This crucial meeting should cover:
- Introductions of key team members (client and consulting company side)
- Clarification of roles and responsibilities on both sides
- Recap of project background, business objectives, and success criteria
- Verification of scope and dependency resolution (with mitigation plans if needed)
- Establishing communication channels and ways of working
- Defining reporting, tracking, and review mechanisms
- Confirming decision-making authority and escalation paths
- Identifying any additional stakeholders
- Agreeing on next steps and priorities
- Ensuring notes are captured and shared
Work backlog development: Define initial activities to progress towards the first milestone
Risk & issue management: Identify potential risks and existing issues, establish a logging process (e.g., RAID log), and define escalation paths

Ongoing processes & governance

Several key areas need to be defined, often during the kick-off or shortly after:

Ways of working: Agree on communication tools, check-in frequency/format, meeting attendees, handling urgent issues, action tracking, decision approvals, milestone alignment, and working hours
Governance structures: Define key stakeholders, decision-making authority (scope, budget, timelines), approval processes for changes, priority setting, team expectations, risk/compliance ownership, and issue escalation paths (internal and client). Note that some aspects may need finalization post-kick-off
Reporting cadence: Determine frequency, format, recipients, KPIs, and level of detail for both internal and client reporting
Tracking mechanisms: Choose tools (e.g., Jira, Trello) for progress tracking, define monitoring responsibilities, document risks/blockers, establish escalation processes, and identify KPIs for success measurement
Review mechanisms: Set frequency and structure for formal reviews (e.g., retrospectives), determine necessary participants, and establish how feedback on processes will be gathered

Proposal context

The Business Context, Problem Statement, Business Objectives, Value Outcomes, High-Level Plan, Assumptions, Dependencies, and Risks are typically defined during the proposal stage and should be reused for guidance and completeness during the kick-off.

UBS dresscode from 2010

Tue, 15 Apr 2025 00:00:00 GMT

Around 2010 UBS released a somewhat hardcore dresscode in Switzerland, for members of the private bank. The tone may be somewhat prim but it is extremely thorough and therefore qualifies as edutainment.

I am sans Français so the below is a machine translation.

UBS Dress Code

For the attention of PKB employees

Introduction
- The Purpose of the Dress Code
- Clothing as an Essential Vector of Non-Verbal Communication
The UBS Dress Code
- What Does the Dress Code Consist Of?
- Guidelines
The UBS Dress Code for Women
- The Suit and Trouser Suit
- The Blouse
- UBS Accessories for Women
  - The Scarf and Nicky/Tying Techniques
- Shoes and Belt
- The Personal Touch
  - Jewellery
  - Neat Make-up
  - Hands
  - Hair
  - Use of Perfume and Deodorant
  - Fresh Breath
  - Underwear and Tights
- Clothing Care
The UBS Dress Code for Men
- The Suit
- The Shirt
- UBS Accessories for Men
  - The Tie/Tying Technique
- Shoes and Belt
  - The Belt
  - Shoes
  - Socks
  - Jewellery
  - Underwear
- A Neat and Stylish Appearance
  - Shaving
  - Facial Care
  - Hands
  - Hairstyle
  - Other Facial Hair
  - Use of Perfume and Deodorant
- Clothing Care
Check Your Look!

Introduction

The Purpose of the Dress Code

Our business essentially aims to establish solid relationships with our clients, shareholders, and environment based on mutual respect. Meeting our clients’ needs and establishing lasting relationships are central to our business. By behaving impeccably in our daily interactions with all our stakeholders, we directly contribute to strengthening UBS’s image as an upright and responsible company. UBS’s reputation is our most precious asset. Adopting impeccable behaviour also implies having an impeccable presentation. Client advisors are very often the first point of contact for our clients and are perceived as representatives of UBS.

Clothing as an Essential Vector of Non-Verbal Communication

Respecting the Dress Code, which dictates a neat appearance and correct presentation, helps communicate our values and culture. Through this, we convey what we concretely mean by the notions of truth, clarity, and performance: respectful, responsible, and upright management, a conscientious, reliable, and constant attitude, as well as respect for the most demanding professional standards. Our clothing style often reflects our way of acting. Individuals are primarily judged on their appearance. Dark grey, black, and dark blue colours symbolise competence, formality, and seriousness. An impeccable appearance can provide inner peace and a sense of security. It is by taking into account that the first impression constitutes a decisive factor that the Dress Code proposed today has been developed. This underlines the professionalism of our bank.

The UBS Dress Code

What Does the Dress Code Consist Of?

The Dress Code is an integral part of UBS’s brand image and supports our efforts to be considered a first-rate financial institution. By UBS Dress Code, we mean a collection of clothing intended to give our staff a professional and stylish look while highlighting their skills and personality.

Guidelines

These guidelines are intended for all PKB employees and their observance is mandatory. Senior managers are required to guarantee and monitor compliance with this Dress Code and ensure that staff display a neat appearance.

The “UBS Dress Code for PKB Employees” is an integral part of the guidelines applicable to all PKB employees.
UBS accessories must under no circumstances be worn privately.
Each PKB employee is personally responsible for the proper maintenance and cleaning of their clothes.
Obsolete UBS accessories must be destroyed or discarded.
The terms used to refer to individuals also apply to female persons.

The UBS Dress Code for Women

The Dress Code for Women:

Plain suit or trouser suit in dark grey, black, or dark blue
White blouse, preferably a shirt
UBS accessory: nicky or scarf
Closed, black, classic shoes
Black belt

The Suit and Trouser Suit

Classic plain professional attire in dark grey, black, or dark blue. These pieces are very flattering, have a light cut, and offer a high level of comfort. The resulting silhouette is elegant and slender without any feeling of tightness. The jacket must remain smooth, even when buttoned, and must not be tight. Skirts and trousers must (both when standing and sitting) offer sufficient room and be able to return to shape on their own. The skirt must not ride up when you walk.

The ideal skirt length is mid-knee and can go down to five centimetres below the knee (measured from the middle of the knee).

Tips and Advice

Although blazers have pockets, they were not designed to hold a large number of personal effects or accessories (keys, tools, etc.). Preferably leave these pockets empty so they do not deform unattractively.
The jacket is worn with buttons fastened. When sitting, they must always be unfastened.

The Blouse

The basic element of our professional clothing collection: the plain white shirt with a classic collar.

Tips and Advice

The blouse is generally worn tucked into the trousers or skirt, and its neckline must be appropriate for the rest of the Dress Code (a hand’s width below the collarbone).
The blouse must neither be tight across the chest nor gape, as this contributes to a sloppy appearance.
The blouse collar should preferably be worn inside the lapel. However, wearing it over the lapel can soften features.
Wear flesh-coloured underwear under white blouses. Furthermore, we recommend, as far as possible, not applying make-up to your neck. Make-up stains on collars look bad.
Generally, a blouse is worn with a jacket. When it is very hot, and after validation from your line manager, it is possible to wear only the blouse with trousers or a skirt.

UBS Accessories for Women

The Scarf and the Nicky

Wearing a UBS scarf or nicky is mandatory. Properly tied, a scarf or nicky can highlight your professionalism and style. As such, you will find, opposite, some examples of possible tying techniques.

The nicky must always be folded then tied with a knot oriented, not downwards, but as far as possible, top left. The “boy scout” style (nicky with a gusset at the nape) is to be rejected in all cases.
Knots should be undone after use to allow the fabric to rest. You can optionally lightly steam your accessories on setting 1.
Position your badge on the left side, horizontally on the upper third of the garment. The pocket square can help with positioning.

Shoes and Belt

Shoes should be closed, black, and classic.

Without suitable, quality shoes, even the most beautiful suit lacks style. Only appropriate shoes will advantageously complete a correctly observed Dress Code, confer style and elegance, and contribute positively to the overall impression. If your outfit is dark grey, black, or dark blue, closed black shiny leather shoes in a classic or trendy style will be perfect. The heel height must not exceed 7 cm; wearing open shoes is prohibited. When choosing shoes, it is important to consider that they will be worn all day. Therefore, you must absolutely be vigilant, when purchasing, about their shape and the comfort they provide. Absolutely avoid wearing painful new shoes that prevent you from being comfortable, considerate, and attentive when interacting with clients.

Tips and Advice

To improve your comfort, you can wear silicone insoles, for example, when walking on hard floor coverings.
Regularly check if your soles or heels need replacing, in addition to the normal care of your shoes, as worn heels can detract from your appearance.
It is important to regularly clean and polish your shoes and use shoe trees or stuff them with paper to maintain their shape.
Give your shoes a break time equivalent to double their wearing time so that the leather can dry and rest.
Change shoes once a day: with “fresh” shoes, you will feel better and improve your work performance.
Never wear shoes that are too small for you: there is nothing worse than a forced smile.

The Belt

When the skirt or trousers have belt loops, wearing a black belt is mandatory.

The Personal Touch

Jewellery

Jewellery should serve to add a personal touch to your style, complement your outfit, and enhance your personality. The colour of the jewellery worn must match the Dress Code. Indeed, attention is generally drawn to what appears elegant and discreet. Earrings, hoops, rings, and chains whose colours match your outfit will suit best. For work safety reasons, but not only, it is inadvisable to wear more than seven pieces of jewellery, as well as any overly flashy jewellery. Finally, there is no obligation to wear any.

Tips and Advice

Here is an example of seven pieces of jewellery you can wear so that your overall appearance is coherent:
- Simple wedding ring (1)
- Discreet watch (1)
- Subtle glasses (1)
- Earrings (2)
- Ring, chain, or bracelet to attract attention (2)
Tattoos, piercings, or ankle chains are outdated and do not reflect a professional appearance. Therefore, wearing them is not permitted.
Glasses: Wearing ultra-trendy glasses or lenses in overly bright colours is not permitted. Also ensure that your jewellery matches the metallic colour of your glasses frame.
Glasses ensure good vision. Therefore, they must always be clean.
Wearing sunglasses is permitted outdoors. However, rules of etiquette require that you remove them during meetings with clients or other people so that eye contact can be established. Sunglasses should not be worn on the head.
Out of consideration for our foreign clientele, avoid wearing overly conspicuous religious symbols.

Neat Make-up

An impeccable appearance involves not only the well-matched wearing of accessories, shoes, and jewellery, but also the care of your hair and skin. An elegant appearance is only achieved if you devote sufficient attention to these last two points. The use of make-up gives women a more professional touch. Light daytime make-up consisting of foundation, mascara, and a discreet lipstick matching the Dress Code will enhance your personality.

Hands

Having clean and neat hands as well as maintained nails goes without saying. Your nail varnish and lipstick must correspond to the Dress Code. Flashy trend colours, such as green, blue, dark brown, or black, etc., as well as nail decorations are not permitted.

Tips and Advice

Poorly cared-for hands and chipped nail varnish give an extremely neglected appearance.
No need for overly beautiful and very long nails! Many elegant women have short nails, and if they are neat, your appearance will only be more beautiful and natural!

Hair

A suitable hairstyle is essential for pleasing others and oneself and also contributes decisively to your well-being. Studies have shown that neat hair and a stylish and impeccable cut significantly increase individuals’ likeability and help enhance their personality.

Tips and Advice

Your hairstyle is worth asking yourself the following questions: Is this a cut that suits my age? How much time am I willing to spend every morning doing my hair? What result do the quality and volume of my hair give? What are my general proportions? What is the shape of my face and my features?
Anything unnatural (when you want, for example, to have straight hair and are constantly forced to iron it to achieve this effect) generates a lot of stress. Besides, a look requiring a lot of effort shows.
Long hair (below the shoulders) must be tied back. If you wear hair clips, they must be discreet and the same colour as your hair. The use of scrunchies or elastic bands is also possible.
Very brightly coloured hair or highlights are not permitted; furthermore, they require significant maintenance.
If you colour your hair, you must ensure that your roots are always impeccable.

Use of Perfume and Deodorant

As most of us think, smells and colours play an important role in our external appearance. And as with make-up, your perfume should enhance your personality. A scent should first be perceptible at arm’s length and discreetly. Perfume, as well as deodorants, should not be too strong. You should also change them often because the nose eventually stops smelling their strength. Therefore, changing them regularly can help you dose them better.

Tips and Advice

Applying perfume well: perfume is applied where the pulse is perceptible: on the wrist, in the crook of the elbow, or on the neck. Never rub the spot where you have applied perfume drops, as this can destroy its molecules.
The ideal time to apply perfume is immediately after taking a hot shower when the skin pores are still open. Thus, the scents will last longer. Furthermore, your skin should not be dry. Therefore, you should always apply a body lotion to your skin beforehand. It is important that this lotion is fragrance-free or has a neutral smell, because even if it is pleasant, it would quickly result in an unharmonious and overpowering mixture of smells. Another solution: use the care line corresponding to the perfume worn.
The amount of perfume used varies completely depending on its character. Generally: spray a very small amount of perfume on your skin then wait 15 minutes until it has deployed all its scents. Only then should you judge if it is necessary to reapply.
Persistent scents are not recommended in daily work. Therefore, avoid reapplying perfume during the second half of the day and trying new perfumes during your lunch break.

Fresh Breath

Parallel to the pleasant smell given off by discreetly worn perfume, other clearly discernible smells prove rather annoying. For example garlic, onion, or cigarette smoke.

Tips and Advice

Avoid smoking when in contact with clients. Likewise, frequenting smoky establishments during the lunch break should be avoided.
Avoid dishes based on garlic and onion and consume chlorophyll chewing gum sparingly.
Chewing gum has the advantage of having a cleansing effect on the teeth. But, during a discussion, it proves rather unpleasant.

Underwear and Tights

Underwear is among the most intimate items of our clothing. They should not, however, be neglected and, on the contrary, they must fit you perfectly, never be tight, nor dig into the skin, and naturally not be visible through your clothes, nor stand out or be seen over your suit. Your silhouette should not suffer from wearing your undergarments. The colour of your tights, strictly plain, must correspond to the Dress Code. Tights or stockings in a darker colour than your skirt or trousers slim the legs. During the summer months, if you wear a skirt, you can absolutely wear thin, flesh-coloured stockings. You must always wear dark stockings with trousers. If you wear a skirt, wearing tights remains mandatory even in hot weather. Wearing opaque tights, fishnet stockings, patterned stockings, or overly shiny tights is prohibited.

Tips and Advice

Microfibre is an ideal fabric for undergarments: it is light, thin, sporty, thermoactive, and unlike cotton, it does not wrinkle.
Accepted colours for tights and knee-highs:
- Grey
- Black
- Anthracite
Always carry a spare pair of stockings with you: laddered tights can be temporarily repaired with clear nail varnish and a bit of luck. Nevertheless, the damage remains visible and the tights should be changed as soon as possible.
You will extend the life of your stockings and tights if your toenails are well-trimmed and filed. Likewise, overly long or brittle nails are detrimental to your tights as they can snag the threads unattractively.

Clothing Care

You are responsible for the proper maintenance and cleaning of your clothes.

Tips and Advice

If possible, leave your outfit hanging in the open air for two days after wearing it. The fabric fibres can thus rest, and you will extend the life of your clothes.
Trousers and skirts should be regularly steam-ironed, and trouser creases regularly refreshed.
Ensure you regularly take your clothes to the dry cleaner so they benefit from professional cleaning.
After being worn once, blouses should be washed and ironed appropriately. Follow the care instructions. It is preferable to iron them when the fabric is still slightly damp.
Scarves and nickys must also be regularly washed following their care instructions.
Dirty outfits must be washed immediately and no longer worn: stains could become ingrained and more difficult to remove.

The UBS Dress Code for Men

The Dress Code for men:

Plain two-piece suit in dark grey, black, or dark blue
White long-sleeved shirt without cufflinks
UBS accessory: the tie
Black, classic shoes
Black belt

The Suit

Classic plain professional attire in dark grey, black, or dark blue. The single-breasted two-button jacket and trousers are the main components of a classic professional suit. The jacket must be fastened up to (but not including) the bottom button when standing or moving. The bottom button must always remain unfastened. When sitting, the blazer must remain open. The garment must always be buttoned so as not to feel constricted, and the back vent must not open. The collar must fit your morphology correctly, and no folds should form under the nape. The shoulders have natural proportions: shoulders that are too wide make a suit look too big and the head too small. Conversely, shoulders that are too narrow constrict and make the head appear exaggeratedly large. The jacket must completely cover your posterior. Ensure that the bottom of your trousers forms a slight break just above the shoe.

Tips and Advice

In hot weather, it is possible not to wear the jacket provided you wear a long-sleeved shirt.
Only well-pressed creases give a neat appearance; therefore, ensure they are regularly refreshed.
Generally, it is not recommended to wear a jacket with pockets that are too full, as this disrupts the look.
Likewise, refrain from storing an overly bulky wallet in your trouser pockets.
Store your jacket appropriately on a hanger with a wide, rounded shoulder shape. This will preserve the shape of your garment.

The Shirt

The basic element of our professional clothing collection: the plain white long-sleeved shirt without cufflinks. The modern cut is now light and rather fitted, and shirts thus offer improved comfort. At the collar, the shirt must be loose enough to leave a space of at least one finger. Shirt cuffs should not be too wide compared to the wrist. The sleeve length is correct when, with the arm bent, the cuff extends about 1.5 to 2.5 centimetres below the jacket sleeve and is clearly visible. The shirt collar should extend about 1 to 1.5 centimetres above the jacket collar and should not ripple under the tie. The points of the shirt collar should sit under the jacket lapel. Wearing short-sleeved shirts and cufflinks is prohibited.

Tips and Advice

The breast pocket of shirts should remain empty, except for storing a pen or your badge.
The top button of shirts must always remain fastened.

UBS Accessories for Men

The Tie

Wearing the UBS tie is absolutely imperative. There are several tying techniques, and a correctly tied tie should touch the top of the belt buckle.

Tips and Advice

Each time you take off your suit, untie your tie and hang or roll it up. Give your tie at least a day’s rest before wearing it again so that the fabric and lining can rest.
Preferably leave the removal of any stains to professionals. The fresher the stains, the better the result obtained.
Never wash or iron your ties yourself.
The tie pin is rather outdated today but is considered useful and decorative by many tie wearers.
The point of your tie must under no circumstances go into your trousers.

Tying Techniques

Simple or Four-in-Hand Knot: The simple tie knot has a slight asymmetry. It is slim and therefore suits spread, button-down, and classic collars better.
Simple Windsor Knot: This slim knot suits the spread collar, also called the Kent collar, the button-down collar, and the classic collar. It is suitable for all types of events. Also consider your height and build. A slim knot gives a disproportionate look on a stout individual. In this case, a bulkier knot is more indicated.
Double Windsor Knot: This knot, when bulky, gives the look a somewhat dramatic touch. It suits the cutaway or spread collar. The further apart the collar points are, the bulkier the knot can be. Tie your tie every morning. Loosening it and hanging it in the wardrobe is not enough.

Shoes and Belt

Belt

Wearing a black belt is always mandatory.

Shoes

Black and classic shoes. An outfit without adequate shoes lacks coherence: shoes are, indeed, the foundation of your presentation. Black lace-up shoes with leather soles should be worn with the mandatory grey, black, or dark blue suit. Models that have proven themselves are classic “brogues” with holes, elegant “Oxfords”, or “Derbys”, with a slender and distinguished line. Slip-on models, as well as shoes with decorations or coarse buckles, should be avoided. Likewise, western boots and ankle boots are not permitted. The shoe must fit you perfectly.

Tips and Advice

Well-maintained shoes give a better impression than neglected ones. Maintenance is not just a matter of external appearance.
Proper repair extends the life of shoes. We recommend replacing heels early enough. Likewise, consider having a new outsole fitted before it is worn through.
Always put on your shoes using a shoehorn. This helps preserve the counters. Furthermore, socks can slip or wrinkle. Completely unlace your shoes after use.
After wearing them, let your shoes rest for at least one day, allowing the leather to dry and rest. Stretch your shoes using shoe trees, preferably wooden ones. It is also possible to stuff the shoes with paper and store them on their side.
Change shoes once a day: with “fresh” shoes, you will feel better and improve your work performance.

Socks

As with shoes, only wearing black socks without patterns is permitted. Preferably choose knee-high socks to ensure your legs remain invisible in all sitting positions. Short socks, as well as ankle socks, are not compatible with correct attire.

Tips and Advice

Finely ribbed socks have the advantage of slimming the leg and drawing attention to the shoes.
In summer, light cotton or silk socks are perfectly suitable. In winter, thicker cotton or wool socks will be ideal.

Jewellery

No need to wear much, but rather choose a few colourful and elegant matching accessories to add a final touch to your look. The rule is not to exceed three accessories, including sober-coloured glasses; the wedding ring does not count among these three items. The Dress Code requires foregoing bracelets and earrings. Piercings and tattoos are forbidden. Wearing ultra-trendy glasses or lenses in overly bright colours is also not tolerated. Wearing a watch should be done insofar as it does not threaten work safety.

Tips and Advice

Glasses must always be kept clean. This allows, on the one hand, to permanently guarantee optimal vision and, on the other hand, dirty spectacle lenses create a neglected appearance.
During meetings with clients or other third parties, it is essential that you remove your glasses so that eye contact can be established. Sunglasses should not be worn on the head.
Wearing a watch suggests reliability and great concern for punctuality.

Underwear

For aesthetic and hygiene reasons, as well as for general well-being, we recommend wearing an undershirt. Choose your underwear so that it is functional, not visible over your clothes, nor discernible underneath.

Tips and Advice

The ideal is to choose a thin and fitted (cotton) t-shirt.
Underwear should exclusively be made from high-quality fabrics, be easily washable, but also remain in good condition after several washes.

A Neat and Stylish Appearance

Body and facial care are an integral part of a neat overall presentation. Gone are the days when facial care was limited to the morning shave and the use of a little aftershave.

Shaving

Even if you do not wear a beard but only a moustache, daily shaving is a necessity. Three-day stubble is not permitted. Whether you wet shave or dry shave matters little, it’s your choice. For those who wear a beard, it must be short and neat. The same applies to those who wear a moustache. An untidy beard gives a neglected appearance. If in doubt, speak to your line manager who will decide.

Facial Care

Skin pollution factors are increasingly numerous. Consequently, requirements for skin protection and care must also increase. Since the skin is practically our first garment, we recommend protecting it by applying a care cream composed of nourishing and soothing active ingredients. Thus, your skin will appear beautiful and neat, and your radiance will only be more manifest!

Hands

Having clean and neat hands, without broken or dirty nails, goes without saying. Tip: never let your nails exceed 1.5 mm and round their corners using a nail file.

Hairstyle

We recommend a visit to the hairdresser approximately every four weeks to maintain your hairstyle. During this period, hair grows on average one centimetre, which is especially visible at the nape and around the ears. A regularly maintained hairstyle constitutes a minimum requirement in terms of hygiene! The most important thing in this regard remains simplicity. If you have to spend half an hour every morning doing your hair, it means something is wrong. Coloured hair or highlights prove unconvincing when the artificial colour contrasts excessively with the objective age of your skin. Likewise, a grey or white beard can clash with the retouched colour of your hair.

Other Facial Hair

Every little hair that grows on the body has a function. Eyebrows protect the eyes from sweat, and eyelashes protect from dust and small insects. Nose hairs, meanwhile, retain dust and foreign bodies, clean, warm, and humidify the inhaled air, making it tolerable for the lungs. Proliferating facial hair, however, disturbs the overall appearance and should be avoided.

Use of Perfume and Deodorant

It is not only what we see, but also what we smell that influences our perception of things and our communication. With our nose as the organ of smell, we intercept, thanks to its sensors, odours and scents, however tiny, which we judge as pleasant or repulsive. A pleasant encounter can only take place if we “smell good” to our interlocutor. Our body odour cannot be changed. However, we can ensure that it only produces pleasant scents:

By using an effective deodorant, you will maintain, for several hours, the freshness with which you will feel confident and full of vitality. In case of excessive sweating, your deodorant should also be able to be reapplied during the day.
Whether you are a smoker or not, the smell of cold smoke pleases no one. If you smoke, regularly air your clothes and clean them more frequently. Try to limit your consumption during work and use a spray or mouth drops after each smoked cigarette.
A pronounced breath (garlic, onions, etc.) can also have considerable repercussions on communication. It is nevertheless possible to combat bad breath by avoiding these substances during the week.
If you like to wear perfume or aftershave, remember that here too, tastes vary. Smelling hints of perfume is often more pleasant than being invaded by a fragrant cloud.

Clothing Care

You are responsible for the proper maintenance and cleaning of your clothes.

Tips and Advice

If possible, leave your outfit hanging in the open air for two days after wearing it. The fabric fibres can thus rest, and you will extend the life of your clothes.
Trousers should be regularly steam-ironed, and trouser creases should be frequently refreshed.
Ensure you regularly take your suit to the dry cleaner, so it benefits from professional cleaning.
Shirts should be washed and ironed appropriately each time they have been worn. Follow the care instructions. It is preferable to iron them when the fabric is still slightly damp.
Dirty outfits must be washed immediately and no longer worn: stains could become ingrained and more difficult to remove.

Check Your Look!

Our external appearance acts as non-verbal communication and says a lot about our personality. The list on the following page indicates what we frequently judge as lacking style in our interlocutor. Check your look before “going on stage” to avoid the worst mistakes.

Don’ts

Shoes

Dirty and unmaintained shoes or worn heels
Cotton socks with court shoes
Plastic shoes with crepe soles

Socks

Socks that are too short where the skin is visible
Laddered or holey tights
Patterned socks or socks decorated with cartoon images
Wool or cotton socks for women
Nylon stockings for men

Trousers

Trousers with an unsuitable leg length, too tight at the waist or seat
Trousers without a belt
Trousers with incorrect creases

Skirt

Too tight at the waist and seat
Too short
With a visible lining

Shirt and Blouse

Dirty collar and cuffs
Sleeves too short
Too tight across the chest or stomach
Wearing short-sleeved shirts and cufflinks is prohibited.

Tie

Tied too short or too long
Knot unsuitable for the shirt
Knot unsuitable for the face shape

Jacket/Blazer

Sleeves too short/long
Unsuitable cut at the shoulders
Too tight across the chest or stomach
Rolled-up sleeves
Jacket worn open

Jewellery

Disproportionate jewellery in size and quantity
Flashy jewellery
Neck chains/identity bracelets for men
Visible piercings and tattoos

Hands

Dirty and unmaintained nails
Coloured and fancy false nails
Rough or cracked skin

Hair

Dirty and unmaintained hair
Unshaved nape for short haircuts
Colouring too old showing roots
Damaged ends

Underwear

Underwear visible through clothes/showing over clothes

We wish you great success!

Leaked 2018 Tesla email

Thu, 03 Apr 2025 00:00:00 GMT

‘Leaked’ email from Musk to Tesla employees in 2018. This could be apocryphal but leaving an unnecessary meeting if it’s not a good use of time is also a house rule at Goldman, so it feels plausible.

From: Elon Musk
Sent: 17 April 2018
To: All Tesla employees

Btw, are a few productivity recommendations:

Excessive meetings are the blight of big companies and almost always get worse over time. Please get rid of all large meetings, unless you’re certain they are providing value to the whole audience, in which case keep them very short.
Also get rid of frequent meetings, unless you are dealing with an extremely urgent matter. Meeting frequency should drop rapidly once the urgent matter is resolved.
Walk out of a meeting or drop off a call as soon as it is obvious you aren’t adding value. It is not rude to leave, it is rude to make someone stay and waste their time.
Don’t use acronyms or nonsense words for objects, software, or processes at Tesla. In general, anything that requires an explanation inhibits communication. We don’t want people to have to memorize a glossary just to function at Tesla.
Communication should travel via the shortest path necessary to get the job done, not through the “chain of command.” Any manager who attempts to enforce chain of command communication will soon find themselves working elsewhere.
A major source of issues is poor communication between departments. The way to solve this is to allow the free flow of information between all levels. If, in order to get something done between departments, an individual contributor has to talk to their manager, who talks to a director, who talks to a VP, who talks to another VP, who talks to a director, who talks to a manager, who talks to someone doing the actual work, then super dumb things will happen. It must be ok for people to talk directly and just make the right thing happen.
In general, always pick common sense as your guide. If following a “company rule” is obviously ridiculous in a particular situation, such that it would make for a great Dilbert cartoon, then the rule should change.

If there is something you think should be done to make Tesla execute better or allow you to look forward to coming to work more (same thing in the long term), please send a note to [redacted].

Thanks for being such a kickass team and accomplishing miracles every day. It matters. We are burning the midnight oil to burn the midnight oil.

Elon

Advice for IBD interns from 2010

Wed, 02 Apr 2025 00:00:00 GMT

I include the below—with redaction to protect the innocent—for nostalgia value and also by way of reference. This email went around most of the IBD team at a leading European investment bank in 2010.

From: [redacted]
Sent: 06 July 2010 16:52
To: [redacted]
Cc: [redacted]
Subject: RE: Interns - how to get a job…

Thanks all for your responses.

I’ve tried to collate into 3 brackets of ‘Etiquette’, ‘General’ and ‘Practical’. Any further comments let me know, otherwise I’ll turn this into a slide.

(‘Washing’ was removed from the list as I think we are all hopeful that basic hygiene, the use of knives & forks vs hands and refraining from licking plates @ restaurants w/colleagues is a given…)

Etiquette

Be on your desk at 8am - this is best practise and will be noted by senior bankers
Chaps wear a tie

General

Deadline management
- With every project ask for a deadline
- Any conflict in delivery, talk to the principals to work out whose work has to take priority; Person A’s “urgent” might be less important than Person B’s
- Let the team know in a timely manner if you do not think you will hit your deadline
- If you do finish your work ahead of the deadline let your team know and send to them for review - don’t just sit on the work
Be prepared to juggle several pieces of work / tasks at once. This is usual.
If you have urgent work to do don’t go AWOL (or at least let your associate / analyst know you’ll be gone)
Ask around the team before leaving for the evening if anyone would like any help
Learn the names of everyone around you quickly - especially the seniors - it will help!
Be team-players - ability to work with each other as interns will be noted
No matter how menial or time-consuming the task is, remember that everyone in the office around you had to do those tasks too when they started

Practical work

Takes notes in meetings
Bring calculator / WGL / other materials relevant to the project to meetings
Be first to offer to handle simple tasks like getting books printed / organizing courier etc
If you have sensible reason to disagree with the path a piece of work is taking (commercial / intellectual / practical disagreements), be grown up in fashion in which you voice any concern. Challenging the ways things are done is not taboo
If in doubt, ask potentially silly questions up front i.e. whilst being briefed at the beginning of a task/project - far better than making up your own potentially silly answers
There are no silly questions, except ones you have asked already
Offer to print documents ahead of internal meetings
Offer to set up meeting invites / dial ins
Print out work, proof read it and check your numbers before you hand it back
Always save ALL your back up in the client files / other companies folder. Keep the folders tidy!

The only way to be seen as trustworthy, competent, hard-working and responsible is to be those things throughout your time here - there are no shortcuts

Stop AirPods from switching connection from iPhone to Mac

Mon, 24 Mar 2025 00:00:00 GMT

To stop your AirPods from automatically switching from your iPhone to your Mac, you can follow these steps:

On iPhone:
- Go to Settings > Bluetooth
- Tap the (i) icon next to your AirPods
- Tap “Connect to This iPhone”
- Select “When Last Connected to This iPhone”
On Mac:
- Go to  (Apple) menu > System Settings > Bluetooth
- Click the (i) icon next to your AirPods
- Under “Connect to This Mac”, choose “When Last Connected to This Mac”

Python on Windows

Fri, 21 Mar 2025 00:00:00 GMT

Python on Windows is something that doesn’t really make sense.¹

However you may wish to do it anyway; perhaps you want to use Chrome webdriver in non-headless mode, in which can you can’t then run in in Linux in WSL, which is the sensible way to run Python on Windows.

For Python on Windows:

Install the Python from python.org
- If you’re not sure which version you want to download, it’s likely ‘Windows installer (64-bit)’
Run cmd
Run py --list-paths

You will get something like the below most likely

 -V:3.13 *        C:\Users\UserName\AppData\Local\Programs\Python\Python313\python.exe

To run a specific version of python on windows you can use e.g. py -V:3.13
You can run this to check you get python and then type exit when you are done
We can use this to get a venv in the current folder: py -V:3.13 -m venv venv
Activate the venv and you’re off to the races: .\venv\Scripts\activate.bat

(venv) C:\Users\UserName\wherever>python
Python 3.13.2 (tags/v3.13.2:4f8bb39, Feb  4 2025, 15:23:48) [MSC v.1942 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>>

With apologies to Dr. Johnson: “Installing Python on Windows is like a dog’s walking on his hind legs. It is not done well; but you are surprised to find it done at all.”↩

Comparisons which may not make sense

Wed, 19 Mar 2025 00:00:00 GMT

Somethimes when trying to get one’s arms around a technology, you can see A and B pop up from time to time and be curious about how they compare. It is only after a bit more research that one finds out that A and B may really be quite distinct, to the extend that such a comparison would likely only be made by someone new to the domain.

In this spirit I here collect some technology comparisons that do not make sense, made by yours truely.

RocksDB versus Redis

RocksDB and Redis are both key-value stores but are really quite different.

Redis is primarily an in-memory data store that keeps the entire working dataset in RAM for fast access, with optional persistence through snapshots or logs. RocksDB, by contrast, is an on-disk data store optimized for storage on SSDs and flash devices, offering stronger durability guarantees by writing data to disk.

Redis is ideal for:

Caching and session management
Real-time analytics requiring rapid data retrieval
Applications with smaller datasets and low-latency requirements

RocksDB is better suited for:

High write workloads
Large-scale data persistence
Applications requiring durable storage with efficient point lookups

Important differences:

Scalability: Redis is primarily a single-node database but provides replication and clustering for horizontal scaling. However, users rate it as “very scalable”. RocksDB lacks built-in scalability features and doesn’t scale well beyond a few threads, showing significant performance degradation when scaled to multiple threads.
Data Size Limitations: Redis is limited by available RAM, which can become expensive for large datasets. RocksDB has no strict limitation on dataset size since it stores data on disk, making it more suitable for multi-terabyte datasets.
Data Structures: Redis provides rich data structures (strings, hashes, lists, sets, sorted sets), while RocksDB offers a simpler key-value interface with operations like Get, Put, Delete, and NewIterator.
Memory Usage: Redis requires substantial memory, which can be expensive. RocksDB uses disk storage more efficiently, potentially saving infrastructure costs for large datasets.
Data Durability: Redis risks potential data loss during server crashes as it primarily keeps data in RAM. RocksDB provides stronger durability guarantees with its disk-based storage approach.
Integration: Both systems have wide language support. Redis has clients for almost every programming language, while RocksDB offers bindings for C++, C, and Java.

Team check-in

Wed, 19 Mar 2025 00:00:00 GMT

Atlassian suggest quite a useful process for team check-ins which they call a “health monitor”.¹

I’m not a big fan of the nomenclature, but the process itself makes a lot of sense and feels like it could be a good occasional replacement for the traditional end-of-sprint retrospective.²

In terms of tooling, one of the many SaaS tools which provide a ‘collaborative whiteboard’ e.g. Miro, could be used to allow individuals to vote and provide feedback.

Step 1: vote and feedback

For the following:

Team Cohesion: We have the mutual trust and respect necessary to be an effective team for healthy collaboration. We have a strong sense of connectedness between members
Balanced Team: We have a well-rounded team with the right mix of skills, experience and perspectives. Each member contributes meaningfully and responsibilities are distributed effectively
Encouraging Difference: We embrace diverse viewpoints and create a safe space for open discussions. We recognise that different perspectives strengthen our team and lead to better outcomes
Shared Understanding: We have a clear and common understanding of our goals, roles and expectations. Our communication ensures alignment and minimises misunderstandings
Value and Metrics: We define success through measurable outcomes that reflect our impact. We regularly assess our progress and ensure our work delivers real value
Suitable Ways of Working: We adapt our processes and tools to fit our needs, ensuring efficiency and effectiveness. Our ways of working support collaboration and continuous delivery
Engagement and Support: We foster an environment where everyone feels heard, valued and supported. We actively engage with each other and provide the help needed to succeed
Continuous Improvement: We are committed to learning and evolving as a team. We regularly reflect on our work, identify areas for growth and take action to improve

Vote on the above, on an individual basis, which can be non-attributed

Reading the statement, where do you feel the team is at? Do you agree, disagree or somewhere in the middle?
- Options are: agree, not sure, disagree

After voting, provide feedback on an individual basis, which would be attributed

What specific feedback would you like to share? What caused you to vote the way you did?

Step 2: brainstorm

Brainstorm on three items from the above, using the feedback from the previous step.

Criteria around which to choose could be: the ones people disagree with; those with disparity across the three options; or even consider solidly green ones, considering how we might maintain those in the green.

What is the problem?
- Summarise the feedback into a problem statement
What does success look like in 1 month?
- If this attribute was in a great state, how would it benefit the team? Brainstorm what success could look like if the problem is resolved
What actions could we take to reach that outcome?
- Brainstorm potential solutions to the problem. Identify the ideal solution to the problem to experiment with
What action will we take NOW?
- Identify one action to take leaving the session. Ensure there is an owner for that action and a due date

https://www.atlassian.com/team-playbook/health-monitor?tab=instructions ↩
A high quality colleague who is much more of an Agile-respecter than I am had following comment: “I think this is in addition to or supplementary to a retro, which I consider a non-negotiable and more specific to the sprint, whereas I see this as slightly more ‘team holistic’ - which could be monthly, 6 weekly or even quarterly on longer projects”↩

A very efficient turmeric latte

Tue, 18 Mar 2025 00:00:00 GMT

This below is an efficient proxy for the ‘Golden spiced milk (warm)’—a.k.a. spicy turmeric latte—at Caravan.

Minor Figures do “Barista Chai Concentrate” which has all the spices already. You can then just add some turmeric and whisk it all together. Quantities are for one mug:

Ingredients

4 tablespoons Minor Figures Barista Chai Concentrate
1/4 teaspoon turmeric
Oat milk

Method

Heat oat milk
Combine

Cursor in WSL2 on Windows

Tue, 11 Mar 2025 00:00:00 GMT

Cursor in WSL2 on Windows is a pain: neither the latest version of Cursor nor the latest version of WSL extension will actually work. As such I cannot recommend this because it is so fiddly. With that disclaimer; this is how I got it working:

Using

Windows 11 and WSL2¹
Cursor Setup 0.45.8 - Build 250201b44xw1x2k-x64.exe
- Note as of 11 March 2025 the latest version of Cursor seems to try to download a version of WSL that doesn’t seem to exist—404 error when running ../bin/cursor within WSL—which is why we use a different version
WSL extension version 0.88.3, which can be downloaded from here: https://marketplace.visualstudio.com/_apis/public/gallery/publishers/ms-vscode-remote/vsextensions/remote-wsl/0.88.3/vspackage and which will download as ms-vscode-remote.remote-wsl-0.88.3.vsix

Steps

Install Cursor
Run Cursor from within Windows, select Extensions, and drag and drop in ms-vscode-remote.remote-wsl-0.88.3.vsix, which will install the extension
Close Cursor in Windows
Within WSL, run /mnt/c/Users/$WIN_USERNAME/AppData/Local/Programs/cursor/resources/app/bin/cursor to launch Cursor, where $WIN_USERNAME is your username in Windows

Cursor should then open in Windows and connect to the WSL environment

Further

The Cursor Extensions tab doesn’t seem to work in WSL so any extensions need to be downloaded manually and dropped in e.g. https://marketplace.visualstudio.com/_apis/public/gallery/publishers/vscodevim/vsextensions/vim/1.29.0/vspackage for Vim keybindings

By WSL I mean the latest version of WSL, being WSL2, so here I use WSL and WSL2 interchangeably. For more on WSL and its versions see Microsoft documentation here.↩

Innovation

Tue, 04 Mar 2025 00:00:00 GMT

Ideas

Industrial revolution
- Labour is expensive
  - Urbanisation: labour shortages in some industries
- Tinkering
  - Continued improvements due to inveterate tinkerer/inventor/business-person combo
  - James Watt: steam engine
  - Richard Arkwright: textile machinary
  - Henry Cort: iron production
- Mechanization: economic returns to innovation
  - Potential for massive reduction in per-unit labour costs
  - Lower production costs $\rightarrow$ wider markets
- Infrastructure
Skunkworks⁰
- wiki: engineering independence, elitism and secrecy - Warren M. Bodie
- dedicated time and space: ‘Kelly Johnson set them apart from the rest of the factory in a walled-off section of one building, off limits to all but those involved directly’¹
- Mary Golda Ross
- P-38 Lightning
  - aluminum skin joggled (?), fitted and flush-riveted: $\downarrow$ aerodynamic drag $\uparrow$ strength: result: first 400+ mph
  - drop tank system for range: initial R&D w/o contract
- P-80
  - first jet used operationally by the US military: 143 days from start to finish
- A-12
  - made out of titanium, became SR-71
Elon
- has done
  - First private company to send a spacecraft to the International Space Station (Dragon)
  - Developed Falcon 9, the first reusable orbital rocket, significantly reducing launch costs
- principles
  - a priori thinking
  - vertical integration
  - iterative development and rapid prototyping
  - interdisciplinary knowledge and talent recruitment
  - mission (‘colonise Mars’)
Google 20% time
- Not an official rule, more informal/cultural
- Early Google ~ smart kids
- IP belongs to Google ~ what interesting stuff will people come up with?
- Gmail started by Paul Buchheit, who worked on it during his 20% Time before it became a full Google project
- Google maps early development
Bill Janeway, VC and Economist
- ‘cash and control’ ~ for startups, meaning they need financial backing but also autonomy to experiment and learn
ARPA under J Licklider
- high-risk high-EV projects (‘moonshots’)
  - Google X now called ‘The Moonshot Factory’
- low-bureaucracy, high-trust environment
- leadership and talent … assembly and deft management of exceptional teams

A reference to comic-book Prohibition: “In Al Capp’s comic strip Li’l Abner, Big Barnsmell’s Skonk Works — spelled with an “o” — was where Kickapoo Joy Juice was brewed from skunks, old shoes, kerosene, anvils, and other strange ingredients. When the name leaked out, Lockheed ordered it changed to “Skunk Works” to avoid potential legal trouble over use of a copyrighted term. The term rapidly circulated throughout the aerospace community, and became a common nickname for research and development offices” https://en.wikipedia.org/wiki/Skunk_Works ↩
https://en.wikipedia.org/wiki/Skunk_Works ↩

Presentation pointers

Tue, 04 Mar 2025 00:00:00 GMT

Titles

In the US, titles are indeed ‘title-case’ i.e. the initial letter of each word is capitalised: This Is A Title
In Europe, this is not the case: This is a title
Titles do not have full-stops (periods in American English)¹

Underlining

Underlining should not be used for emphasis in electronic documents/slides; italics and bold should be used instead
Underlining is for hyperlinks or emphasis in a hand-written document

Block capitals

Block capitals should not be used

Bullet points

Bullet points do not have full-stops (periods in American English)

Dashes

En dash (the short one: -) is used for number ranges (1990-2000) and compound adjectives (New York-London flight)
Em dash (the longer one: —) is used for parenthetical phrases—like this

Fonts

In general it is a good idea to only have a few different fonts or font sizes on a single slide

The front page

If you’re not sure of a title, just go with ‘Client name’ and ‘Discussion materials’²
We’re assuming a business context here; if it’s not a business context, you can replace the client name with whatever you audience is called
There should be a date on the front page. If the exact date e.g. 3 March 2025 is too specific, just use the month and the year

Footnotes

A footnote should be in very small font at the bottom of the relevant slide³
Footnotes are in prose and so they should have a full-stop at the end (period in American English)

Brevity and detail

Quality beats quantity in the same sense as ‘if I had more time I would have written you a shorter letter’⁴
Detail is usually dependent on context e.g. an RfP response or a presentation which is likely to be forwarded on and read as a document—rather than presented—lacks a voice-over and so the required contents has to be covered in the slides

Review

Run spellcheck
If you have sufficient time, going away and doing something else and then coming back to the presentation to review it may help you to review it with fresh eyes
When reviewing documents of any kind it is best to do so somewhere free of distractions where you can focus on the document at hand, if possible. Within an office environment an unused meeting room or call booth is ideal for this
If the presentation is particularly important, e.g. an RfP response, there is no substitute IMHO for printing off a hard copy and carefully reading it line by line, making corrections in ink or pencil
- See here for a good guide to copy editing marks: https://www.csuchico.edu/style-guide/guidelines/copy-editing-marks.shtml

The exception to this is the New York Times style title: ‘A happened. Then B happened’. As that would not make much sense in a presentation, we can ignore this edge case.↩
And if you are not discussing the slides with anyone, slides may not be necessary?↩
My preferred way to do footnotes is to have a superscript number between brackets in the text like this: $^{(1)}$ . Then at the bottom of the slide in very small font: ‘(1): This is the related note text.’↩
Apparently in “Lettres Provinciales” (Provincial Letters) in 1657, Pascal wrote: “Je n’ai fait celle-ci plus longue que parce que je n’ai pas eu le loisir de la faire plus courte” which translates to “I have made this longer than usual because I have not had time to make it shorter”.↩

Calculating value for business cases

Wed, 26 Feb 2025 00:00:00 GMT

If we consider a taxonomy of business cases we might include:

a technology element
a sector or industry
particular use case(s)

The particular use case is likely to be conditional on both the technology element and the sector/industry.

Examples:

PowerBI, (in) Insurance, (for) Financial Reporting
Neo4J graph database, (in) Pharmaceuticals, (for) R&D: Compound Synthesis Management

The core of a business case is often quantifying the financial value of the work, which is what is discussed here.

Calculating value

tl;dr: We can find value by estimating annual cost savings and capitalising by a suitable cost of capital.

Example 1: Financial reporting at an insurer

Here value derives from time savings. We assume our financial reporting solution saves an estimated 10 senior financial full-time employees (FTEs) a fifth of their time.

Line	Label	Unit	Value	Note
a	Senior finance FTE cost (all in)	£	140,000
b	Working hours per day	Hours	8
c	Working days per year	Days	260
d	Working hours per annum	Hours	2,080	$b \times c$
e	Cost per hour	£	67.3	$a \div d$
f	Time saving	%	20%
g	Value of time saving per person per day	£	107.7	$b \times e \times f$
h	Value per person per year	£	28,000	$c \times g$
i	Number of people in finance team	#	10
j	Total annual saving	£	280,000	$h \times i$
k	Cost of capital	%	8%
l	Capitalised value	£m	3.5	$j \div k$

Example 2: Enhanced drug discovery in pharmaceuticals

This is a more complex example which is broken down into several sections, reflecting the different workstreams within the project.

Assumptions

As a shortcut to enable us to think about the value generated by the drug discovery, we use the fact that the client has told us that a blockbuster drug can deliver $13 billion of revenue in a year, and estimate that 1/1000 drugs being worked on will be blockbuster drugs.

Line	Label	Unit	Value	Note
a	Blockbuster drug annual revenue ($m)	$m	13,000
b	Blockbuster drug daily revenue ($m)	$m	35.6	$a \div 365.25$
c	Proportion of drugs which are blockbuster	#	0.001	1/1000
d	Daily drug revenue expectation ($)	$	35,592

Every day lost therefore has an expected value of $36k.

Pipeline for Compound Synthesis Management logistics graph

Here value derives from reliability and we assume that when the graph database is down, the drug discovery process is halted, affecting the time to market for our expected (i.e. mean-average-value) new drug. Our improved ETL/ELT pipelines materially reduce downtime by improving robustness, reporting and observability such that when issues do occur, they can be dealt with — i.e. fixed and re-run — more quickly.

Line	Label	Unit	Value	Note
e	GraphDB is out of action before our work	#	0.14	$2/14$ weeks
f	GraphDB is out of action after our work	#	0.036	$0.5/14$ weeks
g	Work days in year	Days	260
h	Delta as work days in year	Days	27.9	$(e - f) \times g$
i	Value based on assumptions	$	991,493	$d \times h$

The reduction in downtime of around 75% has a value associated with it of $991k.

Dashboards for management reporting

Here value derives from time savings across both producers and consumers of management information. The assumption here is that self-service elements of the dashboard allow consumers of management information to answer questions through their own investigation, without sending the preparer queries on an ad hoc basis. Furthermore, much of the production of management information is now automated. We assume that both producers and consumers of management information have time costed at $2k per day and that there is one producer and ten consumers. Reporting is approximately monthly with different reports being used at the half-year end, such that the report in question is produced ten times over the course of a year.

Line	Label $^{(1)}$	Unit	Value	Note
j	TS: KPI/reporting preparation time	$	20,000	$10 \times$ $2k/day
k	TS: directors, recipients of KPI/reporting	$	60,000	3 days $\times$ 10 directors
l	Value attributed to time saving	$	80,000	$j + k$

(1): TS is time saving.

Our dashboards save $80k-worth of time.

Robotic laboratory machines log files

Here value derives from higher utilisation of robotic laboratory machines. This higher utilisation is achieved through the ingestion and analysis of log files which are generated on the machines themselves. We assume that inefficiencies such as the machines not working properly — improper de-capping of the acoustic tubes — can be reduced. Robotic laboratory machines are very expensive, and so $500k per year reflects both running cost and depreciation.

Line	Label	Unit	Value	Note
m	Assumed cost of machine per year	$	500,000
n	Number of machines	#	5
o	Improved efficiency	#	0.02
p	Value attributed to improved efficiency	$	50,000	$m \times n \times o$

We assume 2% efficiency improvement, with an associated saving of $50k.

Capitalised savings

Line	Label	Unit	Value	Note
q	Total ($m)	$m	1.12	$i+l+p$
r	Cost of capital	%	8%
s	Capitalised	$m	14.0	$q \div r$

The sum of annual savings capitalised comes out at $14m.

Safari downloads

Wed, 19 Feb 2025 00:00:00 GMT

Safari will automatically unzip zip archives that are downloaded, which is quite annoying.

To stop Safari from automatically e.g. unzipping downloaded files, follow these steps:

Click on “Safari” in the top menu bar, then select “Preferences” or “Settings” (depending on your Safari version).
In the Preferences/Settings window, go to the “General” tab.
Scroll down to the bottom of the General tab.
Uncheck the box next to “Open ‘safe’ files after downloading”.

After completing these steps, Safari will no longer automatically unzip downloaded files. Instead, it will save them as compressed .zip files, allowing you to manage them manually.

Getting started in your own wood

Sun, 26 Jan 2025 00:00:00 GMT

Getting started in your own wood by Julian Evans and Will Rolls is often recommended as the first book to read for the novice to silviculture. Below are the bits I found useful — the book also contains a lot of other useful information about establishing woodland which I have not included here.

Wood Management Practices

Cleaning: Removal of unwanted growth in young trees past the establishment phase, but not yet 3-7m tall
Pruning: Side branches pruned from lower trunk up to 4-6m, preferably in late spring due to sap
Thinning: Removing about 1/3 of trees, leaving best examples, starts when trees are 10-12m tall, initially every 3-5 years, reducing to 8-10 years

Animals and Wildlife

Deer Culling: For experts; make local enquiries
Pheasants: If present in your wood, they belong to you
Protected Species: 17 species of bats, dormouse, great crested newt, otter, sand lizard, smooth snake, natterjack toad, and some plants like marsh saxifrage
Rabbit and Squirrel Control: Can be controlled at any time; deer best controlled in winter, specific rules apply

Timber and Firewood

License Requirement: Needed for felling more than 5m^2 timber in 3 months or selling 2m^2
Firewood Sources: Obtained from thinning, debris or coppicing
Seasoning:
- Green: 50% water, 0.28 tonnes/kW stove output/year
- 1 year: 35-30% water, 0.19 tonnes/kW
- 2 years: 25-20% water, 0.165 tonnes/kW
Burning Technique:
- Best done using seasoned wood, hot and fast in an enclosed stove
- use Defra approved appliance and have a CO_2 alarm

Measurement and Yields

Tree Trunk Size: 1m^3 of wood is considered large
Wood Weight by Diameter:
- 10 cm = 0.03 tons
- 20 cm = 0.25 tons
- 30 cm = 0.7 tons
- 40 cm = 1.2 tons
- 50 cm = 2.1 tons
Conifer Yield: Around 8 m^3/ha/year for established woodland
Timber-to-Log Conversion:
- 1m^3 solid timber = 1.5m^3 neatly stocked logs
- 1m^3 solid timber = 2.5m^3 loosely stocked logs

Professional Assistance

Contact: Forestry Commission for a woodland officer, or use Confor for forestry contractors
Professional Forester: Consult when unsure about management practices

Matcha

Sat, 04 Jan 2025 00:00:00 GMT

Matcha is a fantastic substance.

Don’t make tea with it, ingest it. Dosage:¹

Typical ‘dose’ is 1/4 of a teaspoon in e.g. the morning smoothie
1/2 a teaspoon is a strong dose
1 teaspoon is, for me, too much i.e. enough to introduce behavioural changes and feels to me to be about equivalent to 150mg of modafinil

This is based on my own experience i.e. that of a healthy adult male↩

Cursor aide-mémoire

Wed, 04 Dec 2024 00:00:00 GMT

Cursor is essentially VSCode with additional LLM functionality which seems to be better than Copilot.

Turn off phone-home a.k.a. telemetry

Settings (icon top right) > General > Privacy Mode

Using LLM within the IDE

Prompt to edit: select code/text for context then ⌘ + k
Ask a question: select code/text for context then ⌘ + l
Retrieval Augmented Generation over codebase: ⌘ + enter

Turning off AI-powered completions etc

There’s a ‘Cursor Tab’ menu / toolbar in the bottom right of the IDE:

To temporarily turn off AI assistance in Cursor completely via the command palette:

Press cmd + shift + p (on Mac) or ctrl + shift + p (on Windows/Linux) to open the command palette.
Type disable cursor tab in the command palette.
Press Enter to apply the change.

This will disable the AI auto-completion feature temporarily. To re-enable it, follow the same steps but type enable cursor tab instead.

You can also set up custom hotkeys for quick toggling:

Press cmd/ctrl + shift + p.
Go to preferences: open keyboard shortcuts.
Search for cursor tab.
Set an enable hotkey and a disable hotkey.

A plan for fat

Sun, 24 Nov 2024 00:00:00 GMT

A pattern of facts that many of us will recognise once we are through our twenties;¹

one’s trousers become tighter
in the shower, one notices a bit more mass on the torso than there was previously

i.e. you have noticed you have more adipose tissue than before.

Don’t panic, we can come up with a plan. First let us remind ourselves:

stress and lack of sleep reduces insulin sensitivity, increasing the propensity to store fat²
the human body obeys the laws of physics: mass will reduce when more energy is consumed then supplied

Trying to chill out and sleep more is easier said than done. We do know though that physical exercise is likely to help with both, so we can just concentrate on the second of those points. There are two ways we can do this:

reduce energy in — i.e. consume fewer calories
increase energy out — i.e. exercise

Taking these in turn:

My answer to the first is to have a light supper where vegetables feature. If we consider simple dishes along these lines e.g. tricolor salad³, good quality ingredients will go a long way in terms of satisfaction.

On exercise, my suggestion would be to establish a baseline of aerobic exercise, in minutes per day, which corresponds to the current level.

People who know about these things seem to suggest that increasing volume of exercise by about 10% week-on-week is appropriate. Say we currently do 15 minutes of aerobic exercise per day and we wish to hit a target of 30. Using these values as examples, we then wish to find out how many weeks $w$ this will take:

$(30 \times 7) = (15 \times 7) \times 1.1^w \\ 2 = 1.1^w \\ \ln 2 = w \ln 1.1 \\ \ln 2 / \ln 1.1 = w \approx 7.3$

So if we increase the volume of exercise by 10% week-on-week, in 7-8 weeks we will reach our target.

This plan is for the author.↩
Insulin is an anabolic hormone and inhibits lipolysis.↩
Tricolor salad being tomato, avocado and mozzarella, some basil leaves and a bit of salt and olive oil.↩

D/l from YouTube for smartphone use

Sun, 27 Oct 2024 00:00:00 GMT

To download video from YouTube in small format / file size suitable for e.g. copying into Dropbox and watching on e.g. an iPhone

yt-dlp \
-f 'bestvideo[height<=360]+bestaudio/best[height<=360]' \
--write-sub \
--write-auto-sub \
--sub-lang 'en.*' \
--embed-metadata \
--merge-output-format mkv \
$URL

where $URL is the URL of the YouTube video

Recent go on Pop!_OS

Sun, 29 Sep 2024 00:00:00 GMT

Below are instructions for obtaining a recent version of go on Pop!_OS 22.04 LTS. At the time of writing the default version is 1.18 which is quite a few versions behind the latest version of go.

sudo add-apt-repository ppa:longsleep/golang-backports
sudo apt remove golang
sudo apt install golang-go

Let’s check it

go version

go version go1.23.1 linux/amd64

… which is recent at the time of writing

References

https://go.dev/wiki/Ubuntu

Cloud explainer

Sun, 25 Aug 2024 00:00:00 GMT

Minimal definition: computers somewhere else which are always on and which can be accessed over the internet.

What it is (physically)

Computers in data centres

How many are there?
- Approx. 12k datacenters worldwide
- Datacenters can include a lot of servers e.g. CERN’s data centre contains around 10k servers
Where are they?
- The US has the most datacenters with around 2,500 facilities
- In Europe, Germany, the UK and France have 300-600 each
- In general, infrastructure/connectively and cheaper power support datacenter development
These require cooling and are power-hungry
Some regulatory arbitrage e.g. George Hotz (‘we have a lot of a computers and v high power draw but we are certainly not a data centre’)

Precursors: what makes it possible

Internet connectivity
- Generally better commercial and residential bandwidth (FTTC/FTTP etc.)
- Phones/4G
- IoT
Data centres
- Virtualisation — instead of a computer (server) running one operating system, it runs a hypervisor which allows many operating systems to be run at one. Different users can then operate and manage these operating systems as though they have their own computer.
- Containerisation — containerisation is a type of virtualization in which all the components of an application are bundled into a single container image and can be run in isolated user space on the same shared operating system. Containers are lightweight, portable, and highly conducive to automation. The key technologies for automation are Docker and Kubernetes
Reliability — once you have virtualisation/containerisation and you spread the workload across many servers, if one of them falls over, another can take over, leading to ‘fault tolerance’
e.g. Amazon realising it can rent its APIs/services
- Jeff Bezos’ API mandate memo
- this is still happening see e.g. FT: How Lidl accidentally took on the big guns of cloud computing
Extremely high-speed networking within a given data centre and also between data centres from a given cloud provider within a given region (e.g. AWS within Western Europe)

Kubernetes

What it is (more abstractly)

Largest providers
- Amazon Web Services (AWS)
- Microsoft Azure
- Google Cloud Platform (GCP)
- Oracle Cloud Platform
- Alibaba Cloud (China)
Core/typical cloud offerings (below I use AWS examples)
- Storage — e.g. Simple Storage Service (S3) ‘storage buckets’, Elastic Block Store (EBS) storage that attaches to EC2
- Compute — virtual machines e.g. Elastic Cloud Compute (EC2)
- Databases e.g. Redshift (columnar postgres), Relational Database Service (RDS; Postgres, MySQL, Oracle etc flavours)
- Various other bits
  - Message queues e.g. Simple Queue Service (SQS)
  - Streaming e.g. something like Kafka
  - Serverless e.g. Lambda
  - Container registry e.g. Elastic Container Registry (ECS)
  - Container running i.e. managed Kubernetes e.g. EKS (Elastic Kubernetes Service)
  - Specific to data — ML/AI e.g. SageMaker — ETL e.g. AWS Glue

Pros and cons

Pros

Potentially lower costs as costs are in operating expenditure and you ‘pay as you go’
Certain services scale automatically with the workload, such that computational/storage resources are increased or decreased as required automatically
High availability i.e. very low to practically no downtime
Workers can access cloud resources wherever they are in the world, subject to good internet connection and authentication / security privileges
Server/low level software maintenance — cloud providers usually handle routine maintenance, updates, and security patches, reducing the need for IT staff

Cons

Data security: cannot reduce the risk of a breach on someone else’s infrastructure to 0
Use of multiple geographical locations, which the cloud can make quite straight forwards, can make it difficult to comply with relevant laws and regulations e.g. Germany is often a default data centre choice for those in Europe as Germany has the most stringent laws around this sort of thing as I understand it
Vendor dependency: big cos may have a multi-cloud strategy but this is likely to reduce benefits around cost and efficiency (e.g. consider egress fees between different cloud providers)
Cost management: a spike in activity could cause a material increase in resources being used, which you will then pay for; in addition because the cost calculations are complex it can be very hard to estimate costs ahead of time
Latency / speed: particularly when connecting to data centres e.g. on a different continent. Further, the exact location, hardware, and usage patterns of other users will impact on the performance of e.g. your virtual machine / EC2 instance

Relating our other practices

Cloud platforms have revolutionised the way data is stored, processed, and analysed. They offer scalable, flexible, and cost-effective solutions for handling large volumes of data.

Cloud Engineers play a crucial role in leveraging cloud platforms to build and manage data infrastructure. Examples of what they are responsible for:

Data Warehousing and Data Lakes: Provisioning data warehouses and data lakes to store and organise data.
ML Infrastructure: Setting up cloud-based infrastructure for machine learning model development and deployment.
Model Management: Managing machine learning models, including version control, deployment, and monitoring.
Cost Optimisation: Implementing strategies to reduce cloud infrastructure costs while maintaining performance.
High Availability: Ensuring data redundancy and fault tolerance to minimise downtime.
Monitoring & Alerting: Tracking the health and performance of cloud resources, data pipelines and applications.
Access Controls: Managing access controls to ensure data security and compliance.

Mindset of a Cloud Engineer

Cloud Engineers possess a mindset that is characterised by a strong focus on efficiency, reliability, and cost-optimisation. Here are some key aspects of their mindset:

Automation-First Approach:

Efficiency: Cloud Engineers strive to automate as many tasks as possible to reduce manual effort and errors.
Consistency: Automation ensures that infrastructure and processes are deployed and managed consistently.
Scalability: Automated provisioning makes it easier to scale resources up or down based on demand.

Security and Compliance:

Risk Mitigation: Cloud Engineers prioritise security measures to protect sensitive data and prevent unauthorised access.
Compliance Adherence: They ensure that cloud infrastructure and processes comply with relevant industry standards (e.g., GDPR, HIPAA).
Continuous Improvement: Security is an ongoing process, and Cloud Engineers continually evaluate and update security measures.

Cost Optimisation:

Resource Efficiency: Cloud Engineers seek to optimise resource utilisation to minimise costs.
Cost-Effective Solutions: They explore and implement cost-saving strategies, such as reserved instances, spot instances, and serverless computing.
Cost Monitoring: Regular monitoring and analysis of cloud spending helps identify areas for optimisation.

Reliability and High Availability:

Redundancy: Cloud Engineers design infrastructure with redundancy to ensure high availability and minimise downtime.
Disaster Recovery: They implement disaster recovery plans to protect against data loss and service disruptions.
Monitoring and Alerting: Robust monitoring and alerting systems help identify and address issues promptly.

Continuous Improvement:

Learning and Adapting: Cloud Engineers stay up-to-date with the latest cloud technologies and best practices.
Experimentation: They are open to experimenting with new tools and techniques to improve efficiency and performance.
Feedback Loops: Cloud Engineers actively seek feedback from stakeholders to identify areas for improvement.

Other things to know about

Often the typical cloud offering is some combination of some open source software running on the required building blocks e.g.
- Amazon Managed Workflows for Apache Airflow (Amazon MWAA) is literally Airflow running on AWS
- At some point ‘the cloud’ just becomes more and more abstracted services
  - pay money (increased with use usually), get API to use
  - e.g. Supabase – database platform with extra bits so app builders can not worry about databases, where to store user into etc
Typical things to know about if you are on the cloud
- It can get complex pretty quickly
Kinesis Data Streams and Amazon MSK can often be used interchangeably in streaming data workflow
Understanding common cloud migration strategies can help you effectively engage with potential clients and address their specific needs. Here are some key strategies to be familiar with:
- Lift and Shift involves moving existing applications and data to the cloud without making significant changes to the architecture.
  - Benefits: Quick and cost-effective for applications that are well-suited to cloud environments.
  - Considerations: May not fully leverage cloud benefits like scalability and elasticity.
- Re-platforming is similar to lift and shift, but involves making minor modifications to the application to optimise it for the cloud environment.
  - Benefits: Can improve performance and reduce costs compared to lift and shift.
  - Considerations: Requires some technical expertise and may not fully realize cloud benefits.
- Refactoring involves re-architecting applications to take full advantage of cloud-native capabilities like microservices, serverless computing, and containers.
  - Benefits: Can significantly improve performance, scalability, and cost-efficiency.
  - Considerations: Requires significant technical expertise and may involve a lengthy migration process.
DevOps is a cultural and technical approach that aims to break down silos between development and operations teams. It emphasises collaboration, automation, and continuous delivery to deliver software faster and more reliably.
Infrastructure as Code (IaC) is a methodology that treats infrastructure resources (like servers, networks, and storage) as code. This means you can manage and provision infrastructure using the same version control systems, automation tools, and testing practices used for application code.
- Common examples of this include AWS CloudFormation, Terraform & ARM Templates
Microservices architecture breaks down large applications into smaller, independent services that communicate with each other via APIs.
Hybrid Cloud: Combining on-premises and cloud infrastructure to meet specific business needs.
Key things to know about when using the cloud / three very basic things to take away:
- Computation, storage, etc can be separated out as long as computers can communicate with each other e.g. via APIs
- The cloud shifts expenditure
  - From: capital expenditure (buying on-prem servers) and having specific expertise within the company (e.g. database administrators)
  - To: operating expenditure (paying $$$ to AWS/Azure/GCP every month) and having specific expertise within the company (people with cloud understanding)
  - The server maintenance piece being outsourced is very helpful, because clearly this is an area of competitive advantage for the cloud provider and they are very, very good at maintaining vast numbers of servers in the data centre given that it is core to their business
- Although in theory it makes things easier, two things that can easily go awry in the cloud without the right expertise and decision making
  - Security
  - Architecture/complexity
  - People forgetting to turn off resources after they spin them up

Reading from DVDs in linux

Thu, 01 Aug 2024 00:00:00 GMT

tl;dr: If you don’t need or care about subs, mkvtoolnix-gui is probably the way to go. If you do, worth using makemkv

makemkv

For the linux version, available for free, there are some steps to follow at https://forum.makemkv.com/forum/viewtopic.php?f=3&t=224. These instructions have worked well for me on on Ubuntu-based systems previously

Once installed makemkv from the shell

File -> Open Files -> find the VIDEO_TS folder from the vobcopy rip

To check the subs have worked I then watch the output mkv quickly in VLC as it’s easy to work out how to turn the subs on from the GUI

mkvtoolnix-gui

Libraries to read/decss

sudo apt install libdvd-pkg && sudo dpkg-reconfigure libdvd-pkg

Vobcopy

sudo apt install vobcopy

cd to a fresh folder and then run

sudo vobcopy -m

mkvtoolnix

sudo apt install mkvtoolnix-gui

You can watch the .vobs to see which ones you want

In the case of my example I want

ls VTS_01*vob

VTS_01_0.VOB  VTS_01_1.VOB  VTS_01_2.VOB  VTS_01_3.VOB  VTS_01_4.VOB  VTS_01_5.VOB

If you drag in the first one, MKVToolNix GUI will realise you want the others too

You can then hit ‘Start multiplexing’

References

What is a data warehouse

Thu, 01 Aug 2024 00:00:00 GMT

What is the data warehouse?

Quick and dirty LaTeX/Pandoc setup

Mon, 22 Jul 2024 00:00:00 GMT

Quick instructions for getting LaTeX and Pandoc set up on MacOS with enough of the bells and whistles to be useful.

We use brew to install Pandoc and BasicTex and then use ‘the native TeX Live Manager’ i.e. the package management system that comes with BasicTex to install various core packages after that.

# brew
brew install basictex pandoc

# Note that you need to add the below to your .bashrc or similar
eval "$(/usr/libexec/path_helper)"

# tex bits
sudo tlmgr update --self
sudo tlmgr install texliveonfly
sudo tlmgr install adjustbox
sudo tlmgr install tcolorbox
sudo tlmgr install collectbox
sudo tlmgr install ucs
sudo tlmgr install environ
sudo tlmgr install trimspaces
sudo tlmgr install titling
sudo tlmgr install enumitem
sudo tlmgr install rsfs

You should then be able to:

pandoc input.md \
	--from markdown \
	--to pdf \
	--output output.pdf \
	--pdf-engine=xelatex

How to turn off mobile alerts for Outlook and Teams

Mon, 22 Jul 2024 00:00:00 GMT

How to turn off mobile alerts

Outlook mobile

Open and go to Inbox
Click the menu in the top left — look for a coloured circle with an initial in it (e.g. ‘F’ if your name is Freda)
Click the alarm icon … this will give various options about how long to keep do not disturb on for

Teams mobile

Open and go to Chat
Click the menu in the top left — look for a coloured circle with an initial in it (e.g. ‘FK’ if your name is Frida Kahlo)
Click ‘Notifications’ and select an option e.g. ‘Only calls’

References:

How to turn on Out of Office

Teams desktop

Click the initials in the top right
Click ‘Set status message’ -> ‘Schedule Out of Office’

Outlook desktop

Click tools -> ‘Automatic Replies’

References:

Retro questions

Tue, 16 Jul 2024 00:00:00 GMT

Traditional questions for the end of Sprint Retro, per Agile:

What went well?
What did not go well?
What did we learn?
What changes can we make?

mods for LLM interface in the shell

Thu, 28 Mar 2024 00:00:00 GMT

mods from Charm_ is a very cozy way to use LLMs (ChatGPT and the like) in the shell — just make sure your API key is set as an environment variable (e.g. OPENAI_API_KEY) and the prompt is the first argument e.g.

mods 'Please suggest some popular films from the 1980s'

Why bother? It looks nice, it keeps your history with hashes (like a git commit log), and it’s extremely handy to ask programming queries/for examples directly in the shell. mods -l to show history, mods -s='hash' to view from the hash.

Mods can also have input piped in which means we can also do prompt-stuffing with pbpaste / pbcopy.

Note: on MacOS pbpaste / pbcopy are build-in. On Linux the below aliases can be used for the same effect:

alias pbcopy='xclip -selection clipboard'
alias pbpaste='xclip -selection clipboard -o'

Syntax for combining on the shell:

echo 'This is the string to stuff' | pbcopy
(echo 'Prompt'; pbpaste)

Prompt
This is the string to stuff

Actually mods makes it even easier than this because it will append anything piped in to the prompt provided as the first argument.

e.g. if you want a portion of a webpage summarising and you have just copied the text you want:

pbpaste | mods 'Please summarise the below\n---\n'

How to install

To install in Debian/Ubuntu/Pop!_OS

sudo mkdir -p /etc/apt/keyrings
curl -fsSL https://repo.charm.sh/apt/gpg.key | sudo gpg --dearmor -o /etc/apt/keyrings/charm.gpg
echo "deb [signed-by=/etc/apt/keyrings/charm.gpg] https://repo.charm.sh/apt/ * *" | sudo tee /etc/apt/sources.list.d/charm.list
sudo apt update && sudo apt install mods

To install on MacOS

brew install charmbracelet/tap/mods

Refs

mods on github: https://github.com/charmbracelet/mods
… features page: https://github.com/charmbracelet/mods/blob/main/features.md
charm http://charm.sh/

Investing

Mon, 18 Mar 2024 00:00:00 GMT

Investing

Ask someone who knows a bit about finance what you should invest in and they will say ‘a low-cost tracker fund’. Before piling in even to one of these it’s a good idea to know about the following.

A tracker fund is a fund which tracks — hence the name — the value of some index. By way of example VUSA tracks the S&P 500, which is a US stock market index. A stock market index tracks the value of an investment accross multiple companies; in the case of the S&P 500, this tracks the 500 largest US companies by market capitalisation.

Asset class

The most common asset classes are equity, debt, real estate. A tracker fund is a collection of equity investments. It’s a good idea to know the characteristics of equity investment generally. Some salient characteristics: some pay a dividend, some don’t, different equities have different volatilities and levels of correlation with other equities in their price, the minimum value of an equity is 0 (so you can only lose what you have put in, unless you add leverage).

Geography

Which geographies do you want exposure to? VUSA covers US equities but trackers are available to cover various geographies (e.g. Japanese equities), and groups of geographies (e.g. developed markets).

Volatility

It’s good to have an idea of how much the value of the tracker fund goes up and down.

Timing

It’s good to at least look at a chart before piling in. Timing is also related to ‘is the market cheap or expensive compared to previous periods’? Two examples of this are the Shiller PE ratio or the ratio of total market capitalisation to GDP also called the Buffett Indicator.

Beginner to intermediate tips

Sat, 17 Feb 2024 00:00:00 GMT

After a bootcamp or formal study and a thorough introduction to Python, there are some profitable avenues to pursue which, it seems, are often overlooked. Here I outline a handful of things in which I regard as being worth consideration, as they make it much easier to get useful work done with Python. These are:

venv
makefile
pytest
pydantic
SQLAlchemy

venv

A venv is a handy place where you can pip install to your heart’s content while leaving your system python installation unaffected.

It is good practice to use a venv, not least as if you run into conflicting module version issues, which are thankfully less frequent than they used to be, you can always delete the venv and start again. For anything hardcore/production-y you may wish to consider pyenv virtualenv, but for hobby projects/just getting code running, getting a venv set up is very quick and easy.

In the folder you want to have the venv in, just run python -m venv venv and a folder will be created called venv which constitutes your venv.

Once your have created it you can just run (with bash or zsh) source ./venv/bin/activate to activate it. Once activated, any Python source code you run and any modules you install will use the venv rather than the system Python. To deactivate you can use deactivate; after the venv has been deactivated, running Python will run the Python on your system rather than the venv.

One thing to bear in mind with a venv is that it is path dependent, so you can’t move it once it has been created. If you need the venv to then be in a different place, you will want to delete it and create a new one.

makefile

Makefiles are a seriously old but useful technology and offer two things:

a more convenient way to run commands
a simple DAG

Crucially they offer a nice handy place to put commands, and they can be very simple. Here is one for a dashboard written in python which uses streamlit. Typing make run is more convenient than typing python -m streamlit run dashboard.py.

.POSIX:

# Used to activate pyenv-virtualenv
project_name = kpis-dashboard
# Not used in makefile but handy for documentation purposes
python_version = 3.12.1

help:
	@echo "help here"

test:
	python -m pytest -s

activate:
	@echo pyenv activate $(project_name)

run:
	python -m streamlit run dashboard.py

format:
	find . -name '[a-z]*.py' | xargs python -m black -l 140
	find . -name '[a-z]*.ipynb' | xargs python -m black -l 140

requirements:
	pip freeze > requirements.txt

The combination makes the makefile particularly well suited to running commands that manipulate files in a chain. This combination is ideal where you might want to compile something before you run it, which is the original purpose of the makefile from the days where the majority of software in UNIX-land was written in C. Here is an example for a very simple HTTP server (which I call netpage) used on a local network. This example requires a compiled language and so go is shown:

# If run with no arguments it will build and then run

.POSIX:

# Define the name of the go binary here
GO = go
TARGET = netpage

# Run server with low priority; we use sudo so we can listen on port 80
run: $(TARGET)
	sudo nice -n 20 ./$(TARGET)

# Build if cmd/netpage/netpage.go is newer than ./netpage
netpage: cmd/$(TARGET)/$(TARGET).go
	$(GO) build cmd/$(TARGET)/$(TARGET).go

In the example above, on make run, if netpage.go is more recent than the netpage binary, it will be recompiled before it is run.

pytest

Testing with pytest is extremely easy and allows you to arbitrarily call functions, which is handy in development.

If you are testing mypythonfile.py, create a new file called test_mypythonfile.py like so:

from mypythonfile import *

# To test some_function which is defined in my_python_file
# for the sake of exposition we assume some_function(s: str) -> str
def test_some_function() -> None:
    input_ = "Input passed to function"
    expectaton = "Value I expect to return"
    assert some_function(input_) == expectation

Then just run python -m pytest -s, or, even easier, add a test makefile rule to your makefile to run this for you whenever you run make test.

pydantic

Pydantic is a way to enforce types within classes within Python. Python famously employs duck-typing i.e. generally makes types as unobtrusive as possible, as part of the design of the language. Sometimes it is highly beneficial to have certainty about what types are being used, and pydantic can be used for this. I find pydantic particularly useful when dealing with databases/ORMs, as in this case you do need to care about types.

import pydantic
from datetime import date

class Person(pydantic.BaseModel):
    model_config = pydantic.ConfigDict(arbitrary_types_allowed=True)

    name: str
    title: str
    date_of_birth: date

bob = Person(name='Bob', title='Mr.', date_of_birth=date.today())

Using SQLAlchemy as an ORM

An ORM is essentially a way to abstract away a database—meaning a standard RDBMS like PostgreSQL, MySQL, MS SQL Server, and the like—and interact with it as though it were a standard Python object.

SQLAlchemy with vanilla SQL, which is what you want when you want to get data out of the db for use in a Jupyter notebook or similar:

import pandas as pd
import sqlalchemy
import os
from sqlalchemy.orm import sessionmaker

user = os.environ["USER"]
password = os.environ["PASS"]
host = os.environ["HOST"]
db = os.environ["DB"]

engine = sqlalchemy.create_engine(f"postgresql://{user}:{password}@{host}/{db}")

def q(s: str, engine: sqlalchemy.engine.base.Engine=engine):
    with engine.connect() as con:
        ret = con.execute(sqlalchemy.text(s)).fetchone()[0]
    return ret

max_date = q("select max(date) from table_name")

SQLAlchemy used as an ORM looks like this:

import sqlalchemy
import datetime
import pydantic
import sqlalchemy.orm
import functools
from typing import Any, Final

default_db_name: Final[str] = "punch-card"
default_db_url: Final[str] = f"sqlite:///{default_db_name}.sqlite3"

# Metadata for sqlalchemy tables
metadata = sqlalchemy.MetaData()

# Delcarative base class for sqlalchmey
Base = sqlalchemy.orm.declarative_base()


class TimerLogPydantic(pydantic.BaseModel):
    label: str
    state: str
    date: datetime.date
    ts: datetime.datetime


timer_log_table = sqlalchemy.Table(
    "timer_log",
    metadata,
    sqlalchemy.Column("label", sqlalchemy.Text, nullable=False),
    sqlalchemy.Column("state", sqlalchemy.Text, nullable=False),
    sqlalchemy.Column("date", sqlalchemy.Date, nullable=False),
    sqlalchemy.Column("ts", sqlalchemy.DateTime(timezone=True), primary_key=True),
)


class TimerLogBase(Base):
    __tablename__ = "timer_log"

    label = sqlalchemy.Column(sqlalchemy.Text, nullable=False)
    state = sqlalchemy.Column(sqlalchemy.Text, nullable=False)
    date = sqlalchemy.Column(sqlalchemy.Date, nullable=False)
    ts = sqlalchemy.Column(sqlalchemy.DateTime(timezone=True), primary_key=True)

    def __repr__(self) -> str:
        return f"TimerLogDB(label={self.label!r}, state={self.state!r}), date={self.date!r}), ts={self.ts!r})"


def get_engine_and_ddl(conn_str: str) -> sqlalchemy.engine.base.Engine:
    engine = sqlalchemy.create_engine(conn_str)

    # Check we have what we expect from the matadata, otherwise create
    expected_tables = metadata.tables.keys()
    inspector = sqlalchemy.inspect(engine)
    have_tables = inspector.get_table_names()

    if set(have_tables) == set(expected_tables):
        # Expected tables are the same as existing tables"
        pass
    else:
        # Have {have_tables} tables, expect {expected_tables} tables, will create
        metadata.create_all(engine)

    return engine


def get_session(conn_str: str) -> sqlalchemy.orm.session.Session:
    engine = get_engine_and_ddl(conn_str=conn_str)
    Session = sqlalchemy.orm.sessionmaker(engine)
    return Session()


def write_timer_log(row: dict[Any], conn_str: str = default_db_url) -> None:
    # Put into pydantic class first so we catch any issues
    stg = TimerLogPydantic(**row)
    insert_data = TimerLogBase(label=stg.label, state=stg.state, date=stg.date, ts=stg.ts)
    with get_session(conn_str=conn_str) as session:
        session.add(insert_data)
        session.commit()


def read_timer_log(conn_str: str = default_db_url) -> list[TimerLogBase]:
    with get_session(conn_str=conn_str) as session:
        statement = sqlalchemy.select(TimerLogBase).order_by(TimerLogBase.ts)
        ret = session.scalars(statement).all()
    return ret

Conveniently query db from the shell

Thu, 08 Feb 2024 00:00:00 GMT

Sometimes you want to use a database (e.g. postgres) to hold personal data that you would like to be able to query quickly and easily.

A nice way to do this and to keep it very simple is to keep a shell function in your .bashrc/.zshrc which you can then query on the terminal.

By way of example, let’s assume that you need help remembering the birthdays of your family and friends. You could just put a recurring event into your digital calendar, but you want to use a database, which is something I can entirely understand.

select person, birthday.birthday from birthday;

person	birthday
Jill	1988-04-06
Frodo	1985-09-28
Bob	1989-09-11
Bill	1956-06-01

You want output that looks like this, and tells you which birthdays are coming up:

person	birthday	days
Jill	Saturday 06 April	58
Bill	Saturday 01 June	114
Bob	Wednesday 11 September	216
Frodo	Saturday 28 September	233

With this function in you .zshrc or similar, you can just run f-birthdays and have that output in your shell whenever you want it:


f-birthdays () {
	cat <<EOF | psql -U postgres -h dbhostname personal
with cte_a as (select person,
                      make_date(
                              extract(year from current_date)::int,
                              extract(month from birthday)::int,
                              extract(day from birthday)::int) as bday
               from birthday
               where birthday is not null),
     cte_b as (select *,
                      bday - current_date as day_delta
               from cte_a),
     cte_c as (select person,
                      to_char(bday, 'Day DD Month') as birthday,
                      case
                          when day_delta < 0
                              then day_delta + 365
                          else day_delta end as days
               from cte_b)
select *
from cte_c
order by days;
EOF
}

(Note that this assumes a table called birthday in a database called personal on the hostname dbhostname, and we query with the user postgres)

To summarise:

Speeding up a Youtube demonstration video

Tue, 06 Feb 2024 00:00:00 GMT

It’s not uncommon for coursework involving technology to be graded via the inclusion of a Youtube video, which the student (learner) uploads to show their work. Timestamps can be included in the description which makes it very easy for the person who is marking (grading) the work to see whereabouts in the video the different required features/parts of the specification are shown. By way of example, this is the approach taken by Harvard’s CS50W, where both a code submission and video upload is required for submission of coursework.

Often it is specified that a video cannot exceed a certain length. What if your video is too long though, and you already generated your timestamps? In this case you would want to do two things

Speed up the video
Update the timestamps that you have already generated

Speeding up the video

This can be done with the open source video editing software Shotcut

To install: brew install shotcut—this assumes MacOS, adjust as approprate for your OS and package manager
Launch shotcut and open your video—you can adjust the speed using Properties and then export the video after that

Updating the timestamps

Assuming you have timestamps in a file like this timestamps.md:

0:00 Models: Your application should have at least three models in addition to the User model: one for auction listings, one for bids, and one for comments made on auction listings
0:28 Create Listing: Users should be able to visit a page to create a new listing
1:30 Active Listings Page: The default route of your web application should let users view all of the currently active auction listings
1:51 Listing Page: Clicking on a listing should take users to a page specific to that listing

etc.

Something similar to the below (youtube_speedup.py) can be used to update the timestamps:

# Description:
#   A tool to update the timestamps of a video to reflect a given speed-up factor
# Usage:
#   cat timestamps.md | python youtube_speedup.py -s 1.5 -t 6:35

import sys
import argparse
import re


def validate_input(input_: str) -> None:
    len_acceptable = sum([1 for c in input_ if c.isdigit() or c == ":"])
    assert len(input_) == len_acceptable, f"{input_} is not a valid input (digits, colon)"


def round_int(real: float) -> int:
    return int(round(real, 0))


def timestamp_line_split(input_: str) -> tuple[int, int, str]:
    splits = re.split(r"\s+", input_.strip())
    time = splits[0]
    rest = " ".join(splits[1:])
    assert ":" in time, f"Invalid time format: {time} (should contain a colon e.g. MM:SS)"
    mins_s, secs_s = time.split(":")
    return (int(mins_s), int(secs_s), rest)


def speed_up_transform(mins: int, secs: int, speed_up: float) -> tuple[int, int]:
    length_in_secs = mins * 60 + secs
    new_length_in_secs = length_in_secs / speed_up
    new_mins = new_length_in_secs // 60
    new_secs = new_length_in_secs % 60
    return (round_int(new_mins), round_int(new_secs))


def parse_timestamps(input_: str, speed_up: float) -> list[str]:
    buffer = []

    # Firstly let's isolate the timestamps and the descriptions
    for timestamp_raw in input_.split("\n"):
        timestamp = timestamp_raw.strip()
        if timestamp:
            mins, secs, description = timestamp_line_split(timestamp)
            new_mins, new_secs = speed_up_transform(mins, secs, speed_up)
            new_timestamp = f"{new_mins}:{new_secs} {description}"
            buffer.append(new_timestamp)

    return "\n".join(buffer)


def main():
    # Create the parser
    parser = argparse.ArgumentParser("Update the timestamp timestamps of a video to reflect a given speed-up. Pipe in the timestamp text")

    # Add arguments
    parser.add_argument("-s", "--speedup", type=float, help="speed-up factor as a float e.g. 1.5")
    parser.add_argument("-t", "--time", type=str, help="Existing time e.g. 5:00")

    # Parse the arguments
    args = parser.parse_args()

    # Probably a better way to do this
    assert args.speedup, "A speed-up factor is required"
    assert args.time, "A time is required"

    # Calculate the new total time
    validate_input(args.time)
    mins, secs = args.time.split(":")
    mins, secs = int(mins), int(secs)
    new_mins, new_secs = speed_up_transform(mins, secs, args.speedup)

    # Print the updated timestamps
    input_ = sys.stdin.read()
    print(parse_timestamps(input_, args.speedup))

    # Print the new total time
    print(f"{mins}:{secs} -> {new_mins}:{new_secs}")


if __name__ == "__main__":
    main()

Maths notes

Sun, 24 Dec 2023 00:00:00 GMT

Pure Mathematics Year 1/AS

1. Algebraic expressions

Can use laws of indicies to simplify powers of the same base
- $a^m \times x^n = a^{m+n}$
- $(a^m)^n = a^{mn}$
- $(a^m) / (a^n) = a^{m-n}$
- $(ab)^n = a^n b^n$
Factorising is the opposite of expanding brackets
A quadratic expression has the form

$ax^2+bx+c$ where $a,b,c \in \text{R}$ are real numbers $a \ne 0$

$x^2-y^2 = (x+y)(x-y)$
Can use laws of indicies with any rational power
- $a^{1/m} = ^m \sqrt a$
- $a^{n/m} = ^m \sqrt{a^n}$
- $a^{-m} = \frac{1}{a^m}$
- $a^0 = 1$
Can manipulate surds using these rules
- $\sqrt{ab} = \sqrt a \times \sqrt b$
- $\sqrt{a/b} = \frac{\sqrt a}{\sqrt b}$
The rules to rationalise denominators are
- Fractions in the form $\frac{1}{\sqrt{a}}$ , multiply by $\frac{\sqrt a}{\sqrt a}$
- Fractions in the form $\frac{1}{a+\sqrt{b}}$ , multiply by $\frac{a-\sqrt b}{a-\sqrt b}$
- Fractions in the form $\frac{1}{a-\sqrt{b}}$ , multiply by $\frac{a+\sqrt b}{a+\sqrt b}$

2. Quadratics

To solve a quadratic by factorising
- Write in form $ax^2+bx+c=0$
- Factorise LHS i.e. quadratic
- Set each factor equal to $0$ and solve to find the values of $x$
Solutions of the equation $ax^2+bx+c=0$ where $a \ne 0$ are given by $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$ax^2+bx+c = a(x+\frac{b}{2a})^2 + (c - \frac{b^2}{4a})$
The set of possible inputs for a function is called the domain, the set of possible outputs the range
The roots of a function are the values of $x$ for which $f(x)=0$
You can find the coordinates of a turning point of a quadratic graph by completing the square
- If $f(x) = a(x+p)^2 + q$ the graph of $y=f(x)$ has a turning point at $(-p, q)$
For the quadratic function $f(x)=ax^2+bx+c=0$ the expressions $b^2-4ac$ is called the discriminant
- $b^2-4ac > 0$ two distinct real roots
- $b^2-4ac = 0$ one repeated real root
- $b^2-4ac < 0$ no real roots

3. Equations and inequalities

Linear simultaneous equations can be solved using elimination or substitution
Simultaneous equations with one linear and one quadratic equation can have up to two pairs of solutions, should make sure that solutions are correctly paired
Solutions of a pair of simultaneous equations represent the points of intersection of their graphs
For a pair of simultaneous equations that produce a quadratic equation of the form $ax^2+bx+c=0$
- Rules for discriminant have roots per above on quadratics
Solution of an inequality is the set of all real number e.g. $x$ that make the inequality true
To solve a quadratic inequality
- Re-arrange so RHS = 0
- Solve the corresponding quadratic equation to find the critical values
- Sketch the graph of the quadratic function
- Use your sketch to find the required set of rules
The values of $x$ for which the curve $y = f(x)$ is above the curve $y = g(x)$ satisfy $f(x) > g(x)$
The values of $x$ for which the curve $y = f(x)$ is below the curve $y = g(x)$ satisfy $f(x) < g(x)$
If $y > f(x)$ or $y < f(x)$ then the curve $y=f(x)$ is not included in the region and is represented by a dotted line
If $y \geq f(x)$ or $y \leq f(x)$ then the curve is included in the region and it represented by a solid line

4. Graph and transformations

If $p$ a root of $f(x)$ then the graph of $y=f(x)$ touches or crosses the x-axis at $(p,0)$
Graphs of $h=\frac kx$ and $y=\frac{k}{x^2}$ where $k$ is a real constant have asymptotes at $x=0$ and $y=0$
The x-coordinates at the points of intersection of the curves with equations $y=f(x)$ and $y=g(x)$ are the solutions to the equation $f(x)=g(x)$
The graph of $y=f(x)+a$ is a translation of the graph $y=f(x)$ by $\begin{pmatrix} 0 \\ a \end{pmatrix}$
The graph of $y=f(x+a)$ is a translation of the graph $y=f(x)$ by $\begin{pmatrix} -a \\ 0 \end{pmatrix}$
When a function is translated any asymptotes are also translated
Graph of $y=af(x)$ is a stretch of $y=f(x)$ by scale factor $a$ in the vertical direction
Graph of $y=f(ax)$ is a stretch of $y=f(x)$ by scale factor $\frac 1a$ in the vertical direction
Graph of $y=-f(x)$ is a reflection of $y=f(x)$ in the x-axis
Graph of $y=f(-x)$ is a reflection of $y=f(x)$ in the y-axis

5. Straight line graphs

The gradient $m$ of the line joining the point with coordinates $(x_1,y_1)$ to the point with coordinates $(x_2, y_2)$ can be calculated using the formula $m=\frac{y_2-y_1}{x_2-x_1}$
The equation of a straight line can be written in the form $y=mx+c$ where $m$ the gradient and $(0,c)$ the y-intercept
The equation of a straight line can also be written in the form $ax+by+c=0$ where a,b,c integers i.e. $a,b,c \in \mathbb{Z}$
The equation of a line with gradient $m$ that passes through the points with coordinates $(x_1,y_1)$ can be written as $y-y_1=m(x-x_1)$
Parallel lines have the same gradient by definition
If a line has a gradient $m$ a line perpendicular to it has a gradient of $-\frac 1m$ i.e. the product of both is $-1$
Can find the distance $d$ between $(x_1,y_1)$ and $(x_2,y_2)$ by using the formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
The point of intersections of two lines can found using simultaneous equations
Two quantities are in direct proportion when they increase at the same rate. Graph of these quantities is a straight line through the origin
A mathematical model is an attempt to represent a real-life situation using mathematic concepts. It is often necessary to make assumptions about the real-life problems in order to create a model

6. Circles

The midpoint of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
The perpendicular bisector of a line segment $AB$ is the straight line that is perpendicular to $AB$ and passes through the midpoint of $AB$ . If the gradient of $AB$ is $m$ then the gradient of its perpendicular bisector $l$ will be $-\frac 1m$
The equation of a circle with centre $(0,0)$ and radius $r$ is $x^2+y^2=r^2$
Given the equation of a circle $x^2+y^2+2fx+2gy+c=0$ : this circle has centre $(-f,-g)$ and radius $\sqrt{f^2+g^2-c}$
A straight line can intersect a circle once, by just touching the circle, or twice. Not all straight lines will intersect a given circle
A tangent to a circle is perpendicular to the radius of the circle at the point of intersection
The perpendicular bisector of a chord will go through the centre of a circle
If $\angle PRQ = 90 \degree$ then $R$ lies on the circle with diameter $PQ$ . The angle in a semi-circle is always a right-angle
To find the centre of a circle given any three points
- Find the equations of the perpendicular bisectors of two different chords
- Find the coordinates of intersection of the perpendicular bisectors

7. Algebraic methods

When simplifying algebraic fraction, factorise the numerators and denominator where possible and then cancel common factors
Can use long division to divide a polynomial by $(x \pm p)$ where $p$ and constant
The factor theorem states that if $f(x)$ is a polynomial then if $f(p)=0$ then $(x-p)$ a factor of $f(x)$ and vice versa
Can prove a mathematical statement is true by deduction. This means starting from known facts or definitions and then using logical steps to reach the desired conclusion
In a mathematical proof one must:
- State any information of assumptions that are being used
- Show every step of proof clearly
- Make sure that every step follows logically from the previous step
- Make sure you have covered all possible cases
- Write a statement of proof at the end of your working
To prove an identity:
- Start with the expression on the side of the identity
- Manipulate that expression algebraically until it matches the other side
- Show every step of algebraic working
Can prove a mathematical statement is true by exhaustion. This means breaking the statement into smaller cases and proving each case separately
Can prove a mathematical statement is not true by counter-example. A counter-examples is one example that does not work for the statement; one is sufficient to disprove

8. The binomial expansion

Pascal’s triangle is formed by adding adjacent pairs of numbers to find the numbers on the next row
The $(n+1)$ row of Pascal’s triangle gives the coefficients in the expansion of $(a+b)^n$
$n! = n \times (n-1) \times (n-2) \times \ldots \times 2 \times 1$
$^nC_r = \binom{n}{r} = \frac{n!}{r!(n-r)!}$
$r$ th entry $n$ th row of Pascal’s triangle is $^{n-1}C_{r-1}$
Binomial expansion is $(a+b)^n=a^n + \binom n1 a^{n-1}b + \binom n2 a^{n-2}b^2 + \ldots + \binom nr a^{n-r}b^r + \ldots b^n$ where $\binom nr a^{n-r}b^r$ is the general term
If $x$ is the small the first few terms in the binomial expansion can be used to find an approximate value for a complicated expression

9. Trigonometric ratios

Cosine rule to find a missing side if know two sides and the angle betwixt $a^2=b^2+c^2-2bc \cos A$
Cosine rule to find an angle if you know all three sides $\cos A = \frac{b^2+c^2-a^2}{2bc}$
Sine rule to find length of missing side $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Sine rule to find missing angle $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$
The sine rule sometimes produces two possible solutions for a missing angle; one $< 180\degree$ , one $> 180\degree$ ; can use: $\sin \theta = \sin (180\degree-\theta)$
Area of triangle is $\frac 12 ab \sin C$
Graphs of $\sin, \cos, \tan$ are periodic
- $y=\sin \theta$ repeats every $360 \degree$ and crosses the x-axis at $\ldots -180 \degree, 0 \degree, 180 \degree, 360 \degree \ldots$ and has maximum and minimum values of $1$ and $-1$
- $y=\cos \theta$ repeats every $360 \degree$ and crosses the x-axis at $\ldots -90 \degree, 90 \degree, 270 \degree, 450 \degree \ldots$ and has maximum and minimum values of $1$ and $-1$
- $y=\tan \theta$ repeats every $180 \degree$ and crosses the x-axis at $\ldots -180 \degree, 0 \degree, 180 \degree, 360 \degree \ldots$ , has no maximum or minimum values and has vertical asymptotes at $\ldots -90 \degree, 90 \degree, 270 \degree \ldots$

10. Trigonometric identities and equations

For a point $P(x,y)$ on a unit circle such that $OP$ makes an angle $\theta$ which the positive x-axis
- $\cos \theta = x$ i.e. x-coordinate of $P$
- $\sin \theta = y$ i.e. y-coordinate of $P$
- $\tan \theta = \frac yx$ i.e. gradient of $OP$
Can use the quadrants (CAST) to determine whether each of the trigonometric ratios is positive; only $\cos \theta$ positive in the C quadrant for instance
Can use these rules to find $\sin, \cos, \tan$ of any positive or negative angle using the corresponding acute angle made with the x-axis, $\theta$
Angles
- $\sin 30 \degree = \frac 12$
- $\sin 45 \degree = \frac {1}{\sqrt2}$
- $\sin 60 \degree = \frac {\sqrt 3}{2}$
- $\cos 30 \degree = \frac {\sqrt 3}{2}$
- $\cos 45 \degree = \frac {1}{\sqrt2}$
- $\cos 60 \degree = \frac 12$
- $\tan 30 \degree = \frac {1}{\sqrt 3}$
- $\tan 45 \degree = 1$
- $\tan 60 \degree = \sqrt 3$
$\sin^2 \theta + \cos^2 \theta \equiv 1$
Calculator gives principal values in the following ranges
- $\cos^{-1}$ in range $0 \leq \theta \leq 180 \degree$
- $\sin^{-1}$ in range $-90 \leq \theta \leq 90 \degree$
- $\tan^{-1}$ in range $-90 \leq \theta \leq 90 \degree$

11. Vectors

If $\vec{PQ} = \vec{RS}$ then line segments are equal in length and are parallel
$\vec{AB} = - \vec{BA}$ as the line segment $AB$ is equal in length parallel and in the opposite direction to $BA$
The triangle law for vector addition is $\vec{AB}+\vec{BC}=\vec{AC}$
Any vector parallel to $\mathbf a$ may be written as $\lambda \mathbf a$ where $\lambda$ a non-zero scalar
Unit vector has length $1$ . Unit vectors along x- and y-axis usually denoted by $\newcommand{\cvec}{\binom} \mathbf i = \cvec 10$ , and $\mathbf j = \binom 01$ . It follows that $\binom{p}{q} = p \mathbf i + q \mathbf j$
For vector $\mathbf = x \mathbf i + y \mathbf j = \binom xy$ the magitude of the vector is given by $| \mathbf a | = \sqrt{x^2+y^2}$
A unit vector in the direction of $\mathbf a$ is $\frac{\mathbf a}{| \mathbf a |}$
In general a point $P$ with coordinates $(p,q)$ has position vector $\vec{OP} = p \mathbf i + q \mathbf j$
$\vec{AB}=\vec{OB}-\vec{OA}$ where $\vec{OB}, \vec{OA}$ are position vectors
If the point $P$ divides the line segment in the ratio $\lambda : \mu$ then $\\ \vec{OP}=\vec{OA} + \frac{\lambda}{\lambda + \mu} \vec{AB} = \vec{OA} + \frac{\lambda}{\lambda + \mu} (\vec{OB} - \vec{OA})$

12. Differentiation

The gradient of a curve at a given point is defined as the gradient of the tangent to the curve at that point
The gradient function or derivative of the curve $y=f(x)$ is written as $f'(x)$ or $\frac{dy}{dx} \\ f'(x) = \lim_{h \to 0} \frac{(x+h)-f(x)}{h}$
- This can be used to find the gradient for any value of $x$
For $a,n \in R$ where $a$ a constant
- $f(x)=ax^n$ then $f'(x) = anx^{n-1}$
- $y=ax^n$ then $\frac{dy}{dx} = anx^{n-1}$
If $y=f(x) \pm g(x)$ then $\frac{dy}{dx}=f'(x) \pm g'(x)$
The tangent to the curve $y=f(x)$ at $(a,f(a))$ has equation $y-y(a)=f'(a)(x-a)$ as implied by $y-y_1=m(x-x_1)$
Equation of normal to $y=f(x)$ at $(a, f(a))$ therefore $y-f(a) = - \frac{1}{f'(a)}(x-a)$
Function $f(x)$ is increasing on the interval $[a,b]$ if $f'(x) \ge 0$ for all values of $x$ such that $a < x < b$
Function $f(x)$ is decreasing on the interval $[a,b]$ if $f'(x) \le 0$ for all values of $x$ such that $a < x < b$
Differentiating $y=f(x)$ twice gives second order derivative $f''(x)$ or $\frac{d^2y}{dx^2}$
Any point on the curve $y=f(x)$ where $f'(x)=0$ is called a stationary point. For a small positive value $h$ :

Type	$f'(x-h)$	$f'(x+h)$
Local maximum	$> 0$ +ve	$< 0$ -ve
Local minimum	$< 0$ -ve	$> 0$ +ve
Point of inflection	$< 0$ -ve	$< 0$ -ve
Point of inflection	$> 0$ +ve	$> 0$ +ve

If a function $f(x)$ has a stationary point when $x=a$ then
- if $f''(a) > 0$ the point is a local minimum
- if $f''(a) < 0$ the point is a local maximum
- if $f''(a) = 0$ it could be local min, local max, or a point of inflection. Need to look at points either side of determine its nature

13. Integration

If $\frac{dy}{dx}=kx^n$ then $y=\frac{k}{n+1}x^{n+1}+c, n \ne 1$
When integrating polynomials, apply the rules of integration separately to each term
$\int f'(x) \,dx = f(x)+c$
$\int (f(x)+g(x)) \,dx = \int f(x) \,dx + \int g(x) \,dx$
To find the constant of integration $c$
- Integrate the function
- Substitute the values $(x,y)$ of a point on the curve or the value of a function at a given point $f(x)=k$ into the integrated function
- Solve the equation to find $c$
If $f'(x)$ is the derivative of $f(x)$ for all $x$ in the interval $[a,b]$ then the definite integral is defined as $\int_a^b f'(x) \,dx = [f(x)]_a^b = f(b) - f(a)$
Area between a positive curve, the x-axis and the lines $x=a$ and $x=b$ is given by $\text{Area}=\int_a^b y \,dx$ where $y=f(x)$ is the equation of the curve
When the area bounded by a curve and the x-axis is below the x-axis, $\int y \,dx$ gives a negative answer
Can use definite integration together with areas of trapezia and triangles to find more complicated areas on graphs

14. Exponentials and logarithms

For all $x \in \R$ and constant $k$
- If $f(x)=e^{kx}$ then $f'(x)=ke^{kx}$
- If $y=e^{kx}$ then $\frac{dy}{dx}=ke^{kx}$
$\log_a n = x$ is equivalent to $a^x=n$
Laws of logarithms
- $\log_a x + \log_a y = \log_a xy$ (multiplication)
- $\log_a x - \log_a y = \log_a (\frac xy)$ (division)
- $\log_x (x^k) = k \log_a x$ (power)
Following special case should be remembered
- $\log_a (\frac 1x) = \log_a (x^{-1}) = - \log_a x$ (power law when $k=-1$ )
- $\log_a a=1$ as $a^1 = a$ $(a > 0, a \ne 1)$
- $\log_a 1=0$ as $a^0 = 1$ $(a > 0, a \ne 1)$
If $f(x)=g(x)$ then $\log_a f(x) = \log_a g(x)$
Graph of $y=\ln x$ is a reflection of the graph $y=e^x$ in the line $y=x$
$e^{\ln x} = \ln (e^x) = x$
If $y=ax^n$ then the graph of $\log y$ against $\log x$ will be a straight line with gradient $n$ and intercept $\log a$
- $y=ax^n \implies \log y = \log (ax^n) = \log a + \log (x^n) = \log a + n \log x$
If $y=ab^x$ then the graph of $\log y$ against $x$ will be a straight line with gradient $\log b$ and intercept $\log a$
- $y=ab^x \implies \log y = \log (ab^x) = \log a + \log (b^x) = \log a + x \log b$

Pure Mathematics Year 2

1. Algebraic methods

To prove a statement by contradiction you start by assuming it is not true. You then use logical steps to show that this assumption leads to something impossible (either a contradiction of the assumption or a contradiction of a fact that is known to be true). Can conclude that if assumption is incorrect the original statement was true
A rational number can be written as $\frac ab$ where $a$ and $b$ are integers i.e. $a,c \in \Z$ . An irrational number cannot be written in the form $\frac ab$ where $a,c \in \Z$
To multiply fractions, cancel any common factors, then multiply numerators and denominators
To divide two fractions multiply the first fraction by the reciprocal of the second fraction
To add or subtract two fractions, find a common denominator
A single fraction with two distinct linear factors in the denominator can be split into two separate fractions with linear denominators. This is called splitting it into partial fractions e.g. $\frac{5}{(x+1)(x-4)} = \frac{A}{x+1} + \frac{B}{x-4}$
The method of partial fractions can also be used when there are more than two distinct linear factors in the denominator e.g. $\frac{7}{(x-2)(x+6)(x+3)} = \frac{A}{x-2} + \frac{B}{x+6} + \frac{C}{x+3}$
A single fraction with a repeated linear factor in the denominator can be split into two or more separate fractions e.g. $\frac{2x+9}{(x-5)(x+3)^2} = \frac{A}{x-5} + \frac{B}{x+3} + \frac{C}{(x+3)^2}$
An improper algebraic fraction is one whose numerator has a degree equal to or larger than the denominator. An improper fraction must be converted into a mixed fraction before it can be expressed in partial fractions
Can either use
- algebraic division
- or relationship $G(x)=G(x)\times\text{divisor}+\text{remainder}$ to convert an improper fraction into a mixed fraction

2. Functions and graphs

A modulus function is in general a function of the type $y=|f(x)|$
- When $f(x) \ge 0$ , $|f(x)|=f(x)$
- When $f(x) < 0$ , $|f(x)|=-f(x)$
To sketch the graph of $y=|ax+b|$ sketch $y=ax+b$ then reflect the section of the graph below the x-axis in the x-axis
A mapping is a function if every input has a distinct output. Functions can either be one-to-one or many-to-one
$fg(x)$ means apply $g$ then $f$ i.e. $fg(x)=f(g(x))$
Functions $f(x)$ and $f^{-1}(x)$ are inverses of each other so $ff^{-1}(x)=x$ and $f^{-1}f(x)=x$
Graphs of $y=f(x)$ and $y=f^{-1}(x)$ are reflections of each other in the line $y=x$
The domain of $f(x)$ is the range of $f^{-1}(x)$
The range of $f(x)$ is the domain of $f^{-1}(x)$
To sketch the graph of $y=|f(x)|$
- Sketch the graph of $y=f(x)$
- Reflect any parts where $f(x) < 0$ (parts below x-axis) in the x-axis
- Delete the parts below the x-axis
To sketch graph of $y=f(|x|)$
- Sketch the graph of $y=f(x)$ for $x \ge 0$
- Reflect this in the y-axis
$f(x+a)$ is a horizontal translation of $-a$ i.e. $\binom{-a}{0}$
$f(x)+a$ is a vertical translation of $+a$ i.e. $\binom{0}{a}$
$f(ax)$ is a horizontal stretch of scale factor $\frac 1a$
$af(x)$ is a vertical stretch of scale factor $a$
$f(-x)$ reflects $f(x)$ in the y-axis
$-f(x)$ reflects $f(x)$ in the x-axis

3. Sequences and series

In an arithmetic sequence the difference between consecutive terms is a constant
The formula for the nth term of an arithmetic sequence is $U_n=a+(n-1)d$ where $a$ is the first term and $d$ the common difference
An arithmetic series is the sum of the terms of an arithmetic sequence
The sum of the first $n$ terms of an arithmetic series is given by $S_n=\frac n2 (2a+(n-1)d)$ where $a$ is the first term and $d$ is the common difference, which can also be written as $S_n=\frac n2 (a+l)$ where $l$ is the last term
A geographic sequence has a common ratio between consecutive terms
The formula for the $n$ th term of a geometric sequence is $U_n=ar^{n-1}$ where $a$ is the first term and $r$ is the common ratio
The sum of the first $n$ terms of a geometric series is given by $S_n=\frac{a(1-r^n)}{1-r}, r \ne 1$ or $S_n=\frac{a(r^n-1)}{r-1}, r \ne 1$ where $a$ is the first term and $r$ is the common ratio
A geometric series is convergent if and only if $|r| < 1$ where $r$ is the common ratio
The sum to infinity of a convergent geometric series is given by $S_ \infty = \frac{a}{1-r}$
Sigma $\Sigma$ used to signify summation. Limits written top and bottom show which terms are being summed
Recurrence relation of the form $U_{n+1}=f(U_n)$ defines each term as a function of the previous term
Sequence is increasing if $U_{n+1} > U_n$ for all $n \in \N$
A sequence is decreasing if $U_{n+1} < U_n$ for all $n \in \N$
A sequence is periodic if the terms repeat in a cycle. For a periodic sequence there is an integer $k$ such that $U_{n+k}=U_n$ for all $n \in \N$ . The values of $k$ is called the order of the sequence

4. Binomial expansion

This form of the binomial expansion can be applied to negative or fractional values of $n$ to obtain an infinite series

$(1+x)^n = 1+nx+\frac{n(n-1)x^2}{2!}+\frac{n(n-1)(n-2)x^3}{3!} + \ldots + \frac{n(n-1)\dots(n-r+1)x^r}{r!}+\ldots$ The expansion is valid when $|x<1|, n \in \R$

Expansion of $(1+bx)^n$ where $n$ is a negative or a fraction is valid for $|bx| < 1$ or $|x| < \frac{1}{|b|}$
Expansion of $(a+bx)^n$ where $n$ is negative or a fraction is valid for $|\frac{b}{a}x|<1$ or $|x| < |\frac{a}{b}|$

5. Radians

$2\pi \text{ radians} = 360 \degree$
$\pi \text{ radians} = 180 \degree$
$1 \text{ radians} = \frac{180 \degree}{\pi}$
$30 \degree = \frac{\pi}{6} \text{ radians}$
$45 \degree = \frac{\pi}{4} \text{ radians}$
$60 \degree = \frac{\pi}{3} \text{ radians}$
$90 \degree = \frac{\pi}{2} \text{ radians}$
Need to learn exact values of the trigonometric ratios of these angles measured in radians
$\sin \frac \pi 6 = \frac 1 2$
$\sin \frac \pi 3 = \frac{\sqrt 3}{2}$
$\sin \frac \pi 4 = \frac{1}{\sqrt 2}$
$\cos \frac \pi 6 = \frac{\sqrt 3}{2}$
$\cos \frac \pi 3 = \frac 1 2$
$\cos \frac \pi 4 = \frac{1}{\sqrt 2}$
$\tan \frac \pi 6 = \frac{1}{\sqrt 3}$
$\tan \frac \pi 3 = \sqrt 3$
$\tan \frac \pi 4 = 1$
To find arc length $1$ of a sector of a circle use $l=r\theta$ where $r$ radius of circle and $\theta$ the angle in radians contained by the sector
To find the area $A$ of a sector of a circle use $A=\frac 1 2 r^2 \theta$ where $r$ radius of circle and $\theta$ the angle in radians contained by the sector
The area of a segment in a circle of radius $r$ is $A=\frac 1 2 r^2(\theta - \sin \theta)$
When $\theta$ is small and measured in radians
- $\sin \theta \approx \theta$
- $\cos \theta \approx 1-\frac{\theta^2}{2}$
- $\tan \theta \approx \theta$

6. Trigonometric functions

$\sec x = \frac{1}{\cos x}$ (undefined for values of $x$ for which $\cos x = 0$ )
$\cosec x = \frac{1}{\sin x}$ (undefined for values of $x$ for which $\sin x = 0$ )
$\cot x = \frac{1}{\tan x} = \frac{\cos x}{\sin x}$ (undefined for values of $x$ for which $\tan x = 0$ )
The graph of $y = \sec x, x \in \R$ has symmetry in the y-axis and has a period $360 \degree$ or $2 \pi \text{ radians}$ . It has vertical asymptotes at all the values of $x$ for which $\cos x = 0$
- The domain of $y = \sec x$ is $x \in \R, x \ne 90 \degree, 270 \degree, 450 \degree \ldots$ or any odd multiple of $90 \degree$
- In radians the domain of is $x \in \R, x \ne \frac \pi 2, \frac 32 \pi, \frac 52 \pi \ldots$ or any odd multiple of $\frac \pi 2$
The graph of $y=\cosec x, x \in \R$ has period of $360 \degree$ or $2 \pi \text{ radians}$ . It has vertical asymptotes at all the values of $x$ for which $\sin x = 0$
- The domain of $y = \cosec x$ is $x \in \R, x \ne 0 \degree, 180 \degree, 360 \degree, \ldots$ or any multiple of $180 \degree$
- In radians the domain is $x \in \R, x \ne 0, \pi, 2\pi, \ldots$ or any multiple of $\pi$
- The range of $y = \cosec x$ is $y \le -1$ or $y \ge 1$
The graph of $y = \cot x, x \in \R$ has period $180 \degree$ or $\pi \text{ radians}$ . It has vertical asymptotes at all the values of $x$ for which $\tan x = 0$
- The domain of $y = \cot x$ is $x \in \R, x \ne 0 \degree, 180 \degree, 360 \degree, \ldots$ or any multiple of $180 \degree$
- In radians the domain is $x \in R, x \ne 0, \pi, 2 \pi, \ldots$ or any multiple of $\pi$
- The range of $y = \cot x$ is $y \in \R$
$\sec x = k$ and $\cosec x = k$ have no solutions for $-1 < k < 1$
You can use the identity $\sin^2 x + \cos^2 x \equiv 1$ to prove
- $1 + \tan^2 x \equiv \sec^2 x$
- $1 + \cot^2 x \equiv \cosec^2 x$
The inverse function of $\sin x$ is called $\arcsin x$
- The domain of $y=\arcsin x$ is $-1 \leq x \leq 1$
- The range of $y=\arcsin x$ is $-\frac \pi 2 \leq \arcsin x \leq \frac \pi 2$ or $-90 \degree \leq \arcsin x \leq 90 \degree$
The inverse function of $\cos x$ is called $\arccos x$
- The domain of $y = \arccos x$ is $-1 \leq x \leq 1$
- The range of $y = \arccos x$ is $0 \leq \arccos x \leq \pi$ or $0 \degree \leq \arccos x \leq 180 \degree$
The inverse fraction of $\tan x$ is called $\arctan x$
- The domain of $y = \arctan x$ os $x \in \R$
- The range of $y = \arctan x$ is $- \frac \pi 2 \leq \arctan \leq \frac \pi 2$ or $- 90 \degree \leq \arctan x \leq 90 \degree$

7. Trigonometry and modelling

The addition a.k.a. compound angle formulae are
- $\sin (A+B) \equiv \sin A \cos B + \cos A \sin B$
- $\sin (A-B) \equiv \sin A \cos B - \cos A \sin B$
- $\cos (A+B) \equiv \cos A \cos B - \sin A \sin B$
- $\cos (A-B) \equiv \cos A \cos B + \sin A \sin B$
- $\tan (A+B) \equiv \frac{\tan A + \tan B}{1 - \tan A \tan B}$
- $\tan (A-B) \equiv \frac{\tan A - \tan B}{1 + \tan A \tan B}$
The double-angle formulae are
- $\sin 2A \equiv 2 \sin A \cos A$
- $\cos 2A \equiv \cos^2 A - \sin^2 A \equiv 2 \cos^2 A - 1 \equiv 1 - 2 \sin^2 A$
- $\tan 2A \equiv \frac{2 \tan A}{1 - \tan^2 A}$
For positive $a,b$
- $a \sin x \pm b \cos x$ can be expressed in the form $R \sin (x \pm \alpha)$
- $a \cos x \mp b \sin x$ can be expressed in the form $R \cos (x \mp \alpha)$
- with $R > 0$ and $0 < \alpha < 90 \degree$ or $\frac \pi 2$
- where $R \cos \alpha = a$ and $R \sin \alpha = b$ and $R = \sqrt{a^2 + b^2}$

8. Parametric equations

A curve can be defined using parametric equations $x=p(t)$ and $y=q(t)$
You can convert between parametric equations and Cartesian equations by using substitution to eliminate the parameter
For parametric equations $x=p(t)$ and $y=q(t)$ with Cartesian $y=f(x)$
- the domain of $f(x)$ is the range of $p(t)$
- the range of $f(x)$ is the range of $q(t)$
Can use e.g. parametric equations with time as a parameter to model motion in two dimensions

9. Differentiation

$y = \sin kx \implies \frac{dy}{dx} = k \cos kx$
$y = \cos kx \implies \frac{dy}{dx} = - k \sin kx$
$y=e^{kx} \implies \frac{dy}{dx} = ke^{kx}$
$y=\ln x \implies \frac{dy}{dx} = \frac 1x$
$y=a^{kx} \implies \frac{dy}{dx} = a^{kx}k \ln a$ (where $k$ a real constant and $a > 0$ )
The chain rule: $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$
The chain rule enables you to differentiate a function of a function. In general
- if $y = (f(x))^n$ then $\frac{dy}{dx} = n(f(x))^{n-1} f'(x)$
- if $y = f(g(x))$ then $\frac{dy}{dx} = f'(g(x))g'(x)$
$\frac{dy}{dx} = 1 / \frac{dx}{dy}$
The product rule
- if $y=uv$ then $\frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}$ where $u$ and $v$ are functions of $x$
- if $f(x)=g(x)h(x)$ then $f'(x) = g(x)h'(x) + h(x)g'(x)$
The quotient rule
- if $y=\frac uv$ then $\frac{dy}{dx} = (v \frac{du}{dx} - u \frac{dv}{dx}) / v^2$ where $u$ and $v$ are functions of $x$
- if $f(x) = \frac{g(x)}{h(x)}$ then $f'(x) = (h(x)g'(x)-g(x)h'(x))/(h(x))^2$
$y=\tan kx \implies \frac{dy}{dx} = k \sec^2 kx$
$y=\cosec kx \implies \frac{dy}{dx} = -k \cosec kx \cot kx$
$y=\sec kx \implies \frac{dy}{dx} = k \sec kx \tan kx$
$y=\cot kx \implies \frac{dy}{dx} = -k \cosec^2 kx$
$y=\arcsin x \implies \frac{dy}{dx} = \frac{1}{\sqrt{1-x^2}}$
$y=\arccos x \implies \frac{dy}{dx} = - \frac{1}{\sqrt{1-x^2}}$
$y=\arctan x \implies \frac{dy}{dx} = \frac{1}{1+x^2}$
If $x$ and $y$ are given as functions of some parameter $t$ : $\frac{dy}{dx}=\frac{dy}{dt}/\frac{dx}{dt}$
$\frac{d}{dx} (f(y)) = f'(y) \frac{dy}{dx}$
$\frac{d}{dx} (y^n) = ny^{n-1} \frac{dy}{dx}$
$\frac{d}{dx} (xy) = x \frac{dy}{dx} +y$
The function $f(x)$ is concave on a given interval if and only if $f''(x) \le 0$ for every values of $x$ in that interval
The function $f(x)$ is convex on a given interval if and only if $f''(x) \ge 0$ for every value of $x$ in that interval
A point of inflection is a point at which $f''(x)$ changes sign
Can use the chain rule to connect rates of change involving more than two variables

10. Numerical methods

If the function $f(x)$ is continuous on the interval $[a,b]$ and $f(a)$ and $f(b)$ have opposite signs, then $f(x)$ has at least one root, $x$ , which satisfies $a < x < b$
To solve an equation of the form $f(x)=0$ by an iterative method , rearrange $f(x)=0$ into the form $x=g(x)$ and use the iterative formula $x_{n+1}=g(x_n)$
The Newton-Raphson formula for approximating the roots of a function $f(x)$ is $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

11. Integration

$\int x^n \, dx = \frac{1}{n+1} x^{n+1} + c$
$\int e^x \, dx = e^x + c$
$\int \frac 1x \, dx = \ln |x| + c$
$\int \cos x \, dx = \sin x + c$
$\int \sin x \, dx = - \cos x + c$
$\int \sec ^2 x \, dx = \tan x + c$
$\int \cosec x \cot x \, dx = - \cosec x + c$
$\int \cosec^2 x \, dx = - \cot x + c$
$\int \sec x \tan x \, dx = \sec x + c$
$\int f'(ax+b) \, dx = \frac 1a f (ax+b) + c$
Trigonometric identities can be used to integrate expressions. This allows an expression that cannon be integrated to be replaced by an identical expression can be integrated
To integrate expressions of the form $\int k \frac{f'(x)}{f(x)} \, dx$ try $\ln |f(x)|$ , differentiate, and then adjust any constant
Sometimes can simplify an integral by changing the variable. This process is similar to using the chain rule in differentiation and is called integration by substitution
The integration by parts formula is
- $\int u \, \frac{dv}{dx} \, dx = uv - \int v \frac{du}{dx} \, dx$
Partial fractions can be used to integrate algebraic fractions
The area bounded by two curves can be found using integration
- Area of $R = \int_a^b (f(x)-g(x)) \, dx = \int_a^b f(x) \, dx - \int_a^b g(x) \, dx$
The trapezium rule is
- $\int_a^b y \, dx \approx \frac 12 h (y_0 + 2(y_1 + y_2 + \ldots + y_{n-1}) + y_n)$ where $h = \frac{b-a}{n}$ and $y_i = f(a+ih)$
When $\frac{dy}{dx} = f(x) g(x)$ you can write
- $\int \frac{1}{g(y)} \, dy = \int f(x) \, dx$

12. Vectors

Distance from origin to point $(x, y, z)$ is $\sqrt{x^2+y^2+z^2}$
Distance from origin to points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$
The unit vectors along x-, y-, z-axis are denoted by $\mathbf{i,j,k}$ respectively $i=\begin{pmatrix} 1\\0\\0 \end{pmatrix} j=\begin{pmatrix} 0\\1\\0 \end{pmatrix} k=\begin{pmatrix} 0\\0\\1 \end{pmatrix}$ . Any three-dimensional vector can be written in column form as $p\mathbf i + q \mathbf j + r \mathbf k = \begin{pmatrix} p\\q\\r \end{pmatrix}$
If the vector $\mathbf a = x \mathbf i + y \mathbf j + z \mathbf k$ makes an angle $\theta_x$ with the positive x-axis then $\cos \theta_x = \frac{x}{|\mathbf a|}$ and similarly for the angles $\theta_y, \theta_z$
If $\mathbf{a,b,c}$ are vectors in three dimensions which do not all lie in the same plane then you can compare their coefficients on both sides of an equation

Core Pure Mathematics Book 1/AS

1. Complex numbers

$i=\sqrt{-1}$ and $i^2=-1$
An imaginary number is a number written in the form $bi$ where $b \in \R$
A complex number is written in the form $a+bi$ where $a,b \in \R$
Complex numbers can be added or subtracted by adding or subtracting their real and imaginary parts
Can multiply a real by complex number by multiplying out the brackets in the usual way
If $b^2-4ac < 0$ then the quadratic equation $ax^2+bx+c=0$ has two distinct complex roots, neither of which is real
For any complex number $z=a+bi$ the complex conjugate of the number is defined at $z^*=a-bi$
For real numbers $a,b,c \in \R$ if the roots of the quadratic equation $az^2+bz+c=0$ are non-real complex numbers, they occur as a conjugate pair
If the roots of a quadratic are $\alpha$ and $\beta$ , can write as

$(z-\alpha)(z-\beta)=0$ or $z^2-(\alpha+\beta)z+\alpha\beta=0$

If $f(z)$ is a polynomial with real coefficients and $z_1$ is a root of $f(z)=0$ then $z_1^*$ is also a root of $f(z)=0$
Equation of the form $az^3+bz^2+cz+d$ is a cubic and has three roots. For a cubic with real coefficients either:
- all three roots are real, or
- one root is real and the other two roots form a complex conjugate pair
A quartic $az^4+bz^3+cz^2+dz+e=0$ has four roots. For a quartic with real coefficients either
- all four roots are real, or
- two roots a real and the other two roots form a complex conjugate pair, or
- two roots form a complex conjugate pair and the other two roots also form a complex conjugate pair

2. Argand diagrams

Can represent complex numbers on an Argand diagram
- x-axis is the real, the y-axis is the imaginary
- The complex number $z=x+iy$ is represented on the diagram by the point $P(x,y)$ where $x$ and $y$ are Cartesian coordinates
The complex number $z=x+iy$ can be represented as vector $\begin{pmatrix} x \\ y\end{pmatrix}$ on an Argand diagram
The modulus of a complex number $z$ , $|z|$ , is the distance form the origin to that point on an Argand diagram. For a complex number $z=x+iy$ , the modulus $|z|=\sqrt{x^2+y^2}$
The argument of a complex number $z$ , $\arg z$ , is the angle between the positive real axis and the line joining that number to the origin on an Argand diagram. For a complex number $z=x+iy$ , the argument $\theta$ satisfies $\tan \theta = \frac{y}{x}$
For two complex numbers $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ the distance between the points $z_1$ and $z_2$ on an Argand diagram is represented by $|z_2-z_1|$
Given $z=x+iy$ the locus of points $z$ on an Argand diagram such that $|z-z_1|=r_1$ is a circle with centre $(x_1,y_1)$ and radius $r$
Given $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ the locus of points $z$ on an Argand diagram such that $|z-z_1|=|z-z_2|$ is the perpendicular bisector of the line segment joining $z_1$ and $z_2$
Given $z_1=x_1+iy_1$ the locus of points on an Argand digram such that $\arg(z-z_1)=\theta$ is a half-line from but not including the fixed point $z$ making an angle $\theta$ with a line from the fixed point $z_1$ parallel to the real axis

3. Series

To find the sum of a series of constant terms can use $\sum_{r=1}^{n} 1 = n$
The formula for the sum of the first $n$ natural numbers is $\sum_{r=1}^{n} r = \frac{1}{2} n(n+1)$
To find the sum of a series that does not start at $r=1$ use $\sum_{r=k}^{n} f(r) = \sum_{r=1}^{n} f(r) - \sum_{r=1}^{k-1} f(r)$
Can re-arrange expressions involving sigma notation
- $\sum_{r=1}^{n} kf(r) = k\sum_{r=1}^{n} f(r)$
- $\sum_{r=1}^{n} (f(r)+g(r)) = \sum_{r=1}^{n} f(r) + \sum_{r=1}^{n} g(r)$
The formula for the sum of the squares of the first $n$ natural numbers is $\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1)$
The formula for the sum of the cubes of the first $n$ natural numbers is $\sum_{r=1}^{n} r^3 = \frac{1}{4}n^2(n+1)^2$

4. Roots of polynomials

If $\alpha$ and $\beta$ are roots of the equation $ax^2+bx+c=0$ then:
- $\alpha + \beta = - \frac{b}{a}$
- $\alpha \beta = \frac{c}{a}$
If $\alpha$ , $\beta$ , $\gamma$ are roots of the equation $ax^3+bx^2+cx+d=0$ then:
- $\alpha + \beta + \gamma = \Sigma \alpha = - \frac{b}{a}$
- $\alpha \beta + \beta \gamma + \gamma \alpha = \Sigma \alpha \beta = \frac{c}{a}$
- $\alpha \beta \gamma = - \frac{d}{a}$
If $\alpha$ , $\beta$ , $\gamma$ , $\sigma$ are roots of the equation $ax^4+bx^3+cx^2+dx+e=0$ then:
- $\alpha + \beta + \gamma + \sigma = \Sigma \alpha = - \frac{b}{a}$
- $\alpha\beta + \alpha\gamma + \alpha\sigma + \beta\gamma + \beta\sigma + \gamma\sigma = \Sigma \alpha \beta = \frac{c}{a}$
- $\alpha \beta \gamma + \alpha \beta \sigma + \alpha \gamma \sigma + \beta \gamma \sigma = \Sigma \alpha \beta \gamma= - \frac{d}{a}$
- $\alpha\beta\gamma\sigma = \frac{e}{a}$
The rules for reciprocals:
- Quadratic: $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha+\beta}{\alpha\beta}$
- Cubic: $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \frac{\alpha\beta+\beta\gamma+\gamma\alpha}{\alpha\beta\gamma}$
- Quartic: $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\sigma} = \frac{\alpha\beta\gamma+\beta\gamma\sigma+\gamma\sigma\alpha+\sigma\alpha\beta}{\alpha\beta\gamma\sigma}$
The rules for products of powers:
- Quadratic: $\alpha^n \times \beta^n = (\alpha \beta)^n$
- Cubic: $\alpha^n \times \beta^n \times \gamma^n= (\alpha \beta \gamma)^n$
- Quartic: $\alpha^n \times \beta^n \times \gamma^n \times \sigma^n = (\alpha \beta \gamma \sigma)^n$
The rules for sum of squares:
- Quadratic: $\alpha^2 + \beta^2 = (\alpha+\beta)^2-2\alpha\beta$
- Cubic: $\alpha^2 + \beta^2 + \gamma^2= (\alpha+\beta+\gamma)^2-2(\alpha\beta + \beta\gamma + \gamma\alpha)$
- Quartic: $\alpha^2 + \beta^2 + \gamma^2 + \sigma^2= (\alpha+\beta+\gamma+\sigma)^2-2(\alpha\beta + \alpha\gamma + \alpha\sigma + \beta\gamma + \beta\sigma + \gamma\sigma)$
The rules for sum of cubes:
- Quadratic: $\alpha^3 + \beta^3 = (\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)$
- Cubic: $\alpha^3 + \beta^3 + \gamma^3= (\alpha+\beta+\gamma)^3-3(\alpha+\beta+\gamma)(\alpha\beta + \beta\gamma + \gamma\alpha)+3\alpha\beta\gamma$

5. Volumes of a revolution

The volume of a revolution formed when $y=f(x)$ is rotated about the x-axis between $x=a$ and $x=b$ is given by Volume = $\pi \int_a^b y^2 \,dx$
The volume of a revolution formed when $x=f(y)$ is rotated about the y-axis between $y=a$ and $y=b$ is given by Volume = $\pi \int_a^b x^2 \,dy$
A cylinder of height $h$ and radius $r$ has volume $\pi r^2h$
A cone of height $h$ and base radius $r$ has volume $\frac{1}{3}\pi r^2h$

6. Matrices

A square matrix is one with the same numbers of rows and columns
A zero matrix is one in which all of the numbers are nought. The zero matrix is denoted by $\mathbf0$
An identity matrix is a square matrix in which the numbers in the leading diagonal (starting top left and ending bottom right) are 1 and all the rest are 0. Identity matrices are denoted by $\mathbf I_k$ where $k$ denotes the size
- The 3x3 identity matrix is $\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{pmatrix}$
To add or subtract matrices the corresponding elements in each matrix are added or subtracted. Can only add or subtract matrices that are the same size
To multiply a matrix by a scalar, multiply every element by that scalar
Matrix multiplication:
- Matrices can be multiplied together if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case the first is said to be multiplicatively conformable with the second
- To find the product of two multiplicatively conformable matrices you multiply the elements in each row in the left-hand matrix with the corresponding elements in each column in the right-hand matrix, then add the results together
For a 2x2 matrix $\mathbf M = \begin{pmatrix} a&b \\ c&d \end{pmatrix}$ the determinant of $\mathbf M$ is $ad-bc$
- If $\det \mathbf M = 0$ then $\mathbf M$ is a singular matrix
- If $\det \mathbf M \ne 0$ then $\mathbf M$ is a non-singular matrix
Can find the determinant of a 3x3 matrix by reducing the 3x3 determinant to 2x2 determinants using

$\begin{pmatrix} a&b&c \\ d&e&f \\ g&h&i \end{pmatrix} = a \begin{pmatrix} e&f \\ h&i \end{pmatrix} - b \begin{pmatrix} d&f \\ g&i \end{pmatrix} + c \begin{pmatrix} d&e \\ g&h \end{pmatrix}$ (note that the $a,b,c$ terms are the minors of each respectively)

The minor of an element is a 3x3 matrix is the 2x2 matrix that remains after the row and column containing that element have been crossed out
The inverse of a matrix $\mathbf M$ is the matrix $\mathbf M^{-1}$ such that $\mathbf{ MM^{-1} = M^{-1}M = I}$
If $\mathbf M = \begin{pmatrix} a&b \\ c&d \end{pmatrix}$ then $\mathbf M^{-1} = \frac{1}{\det \mathbf M} \begin{pmatrix} d&-b \\ -c&a \end{pmatrix}$
If $\mathbf A$ and $\mathbf B$ are non-singular matrices then $\mathbf{ (AB)^{-1} = B^{-1}A^{-1}}$
The transpose of a matrix is found by interchanging the rows and the columns
Finding the inverse of a 3x3 matrix $\mathbf A$ usually consists of the following 5 steps
1. Find $\det \mathbf A$
2. Form the matrix $\mathbf M$ of the minors of $\mathbf A$ . In forming the matrix $\mathbf M$ each of the nine elements of the matrix $\mathbf A$ is replaced by its minor
3. From the matrix of minors, form the matrix of cofactors, $\mathbf C$ by changing the signs of some elements of the matrix of minors according to the rule of alternating signs illustrated by the pattern $\begin{pmatrix} +&-&+ \\ -&+&- \\ +&-&+ \end{pmatrix}$ . Elements of the matrix of minors corresponding to the + signs in the pattern remain unchanged, with the sings of the elements corresponding to the - signs changing
4. Write down the transpose of the matrix of cofactors $\mathbf C^T$
5. The inverse of the matrix $\mathbf A$ is given by $\mathbf{ A^{-1} = \frac{1}{\det A} C^T}$
If $\mathbf A \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \mathbf v$ then $\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \mathbf{A^{-1}v}$ , where $\mathbf A$ a matrix, $\mathbf v$ a vector
A system of linear equations is consistent if there is at least one set of values that satisfies all the equations simultaneously otherwise it is inconsistent

7. Linear transformations

Linear transformations always map the origin onto itself
Any linear transformation can be represented as a matrix
The linear transformation $T: \begin{pmatrix} x\\y\end{pmatrix} \mapsto \begin{pmatrix} ax+by\\cx+dy\end{pmatrix}$ can be represented by the matrix $\mathbf M = \begin{pmatrix} a&b\\c&d\end{pmatrix}$ since $\begin{pmatrix} a&b\\c&d\end{pmatrix} \begin{pmatrix} x\\y\end{pmatrix} = \begin{pmatrix} ax+by\\cx+dy\end{pmatrix}$
A reflection in the y-axis is represented by the matrix $\begin{pmatrix} -1&0\\0&1\end{pmatrix}$ . Points on the y-axis are invariant points, and the lines $x=0$ and $y=k$ for any value of $k$ are invariant lines
A reflection in the x-axis is represented by the matrix $\begin{pmatrix} 1&0\\0&-1\end{pmatrix}$ . Points on the x-axis are invariant points, and the lines $y=0$ and $x=k$ for any value of $k$ are invariant lines
A reflection in the line $y=x$ is represented by the matrix $\begin{pmatrix} 0&1\\1&0\end{pmatrix}$ . Points on the line $y=x$ are invariant points, and the lines $y=x$ and $y=-x+k$ for any value of $k$ are invariant lines
A reflection in the line $y=-x$ is represented by the matrix $\begin{pmatrix} 0&-1\\-1&0\end{pmatrix}$ . Points on the line $y=-x$ are invariant points, and the lines $y=-x$ and $y=x+k$ for any value of $k$ are invariant lines
The matrix representing a rotation through the angle $\theta$ anticlockwise about the origin is $\begin{pmatrix} \cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{pmatrix}$ . The only invariant point is the origin $(0,0)$ . For $\theta \ne 180 ^\circ$ there are no invariant lines. For $\theta = 180 ^\circ$ any line passing through the origin is an invariant line
A transformation represented by the matrix $\begin{pmatrix} a&0\\0&b\end{pmatrix}$ is a stretch of scale factor a parallel to the x-axis and a stretch of scale factor b parallel to the y-axis. In the case where $a=b$ the transformation in an enlargement with scale factor $a$
For any stretch of the above form, the x- and y-axis are invariant lines and the origin is an invariant point
For a stretch parallel to the x-axis only points on the y-axis are invariant points, and any line parallel to the x-axis is an invariant line
For a stretch parallel to the y-axis only points on the x-axis are invariant points and any line parallel to the y-axis is an invariant line
For a linear transformation represented by a matrix $\mathbf M$ , $\det \mathbf M$ represents the scale factor of the change in area, also known as the area scale factor
The matrix $PQ$ represents the transformation Q, with matrix $\mathbf Q$ followed by the transformation P with matrix $\mathbf P$
A reflection in the plane $x=0$ is represented by the matrix $\begin{pmatrix} -1&0&0\\0&1&0\\0&0&1\end{pmatrix}$
A reflection in the plane $y=0$ is represented by the matrix $\begin{pmatrix} 1&0&0\\0&-1&0\\0&0&1\end{pmatrix}$
A reflection in the plane $z=0$ is represented by the matrix $\begin{pmatrix} 1&0&0\\0&1&0\\0&0&-1\end{pmatrix}$
A rotation of angle $\theta$ anticlockwise about the x-axis is represented by the matrix $\begin{pmatrix} 1&0&0\\0&\cos\theta&-\sin\theta\\0&\sin\theta&\cos\theta\end{pmatrix}$
A rotation of angle $\theta$ anticlockwise about the y-axis is represented by the matrix $\begin{pmatrix} \cos\theta&0&\sin\theta\\0&1&0\\-\sin\theta&0&\cos\theta\end{pmatrix}$
A rotation of angle $\theta$ anticlockwise about the z-axis is represented by the matrix $\begin{pmatrix} \cos\theta&-\sin\theta&0

\\sin\theta&\cos\theta&0\0&0&1\end{pmatrix}$

The transformation described by the matrix $\mathbf A^{-1}$ has the effect of reversing the transformation described by the matrix $\mathbf A$

8. Proof by induction

Can use proof by induction to prove that a general statement is true for all positive integers
Proof by mathematical induction usually consists of the following four steps
- Basis: show the general statement is true for $n=1$
- Assumption: assume that the general statement is true for $n=k$
- Inductive: show the general statement is true for $n=k+1$
- Conclusion: state the general statement is then true for all positive integers i.e. $n \in \Z^+$

9. Vectors

A vector equation of a straight line passing through the point A with position vector $\mathbf a$ and parallel to the vector $\mathbf b$ is

$\mathbf r = \mathbf a + \lambda \mathbf b$ where $\lambda$ a scalar

A vector equation of a straight line passing through points C and D with position vectors $\mathbf c$ and $\mathbf d$ respectively is

$\mathbf r = \mathbf c + \lambda (\mathbf d - \mathbf c)$

If $\mathbf a = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}$ and $\mathbf b = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}$ the equation of the line with vector equation $\mathbf r = \mathbf a + \lambda \mathbf b$ can be given in Cartesian form as:

$\displaystyle \frac{x-a_1}{b_1} = \frac{x-a_2}{b_2} = \frac{x-a_3}{b_3}$ where each of these expressions is equal to $\lambda$

The vector equation of a plane is

$\mathbf{r = a} + \lambda \mathbf b + \mu \mathbf c$ where $\mathbf{r}$ is the position vector of a general point in the plane $\mathbf{a}$ is the position vector of a point in the plane $\mathbf{b, c}$ are non-parallel, non-zero vectors in the plane $\lambda , \mu$ are scalars

A Cartesian equation of the plane in three dimensions can be written in the form $ax+by+cz=d$ where $a,b,c,d$ are constants and $(a,b,c)$ the normal vector to the plane
The scalar product of the two vectors $\mathbf a$ and $\mathbf b$ is written $\mathbf{a \cdot b}$ and defined as

$\mathbf{a \cdot b = |a| |b|} \cos \theta$ where $\theta$ is the angle between $\mathbf a$ and $\mathbf b$

Non-zero vectors $\mathbf{a}$ and $\mathbf{b}$ perpendicular if $\mathbf{a \cdot b}=0$
If $\mathbf{a}$ and $\mathbf{b}$ are parallel $\mathbf{a \cdot b = |a| |b|}$ and $\mathbf{a \cdot a=|a|}^2$
Acute angle $\theta$ between two intersecting lines given by

$\displaystyle \cos \theta = | \frac{\mathbf {a \cdot b}}{\mathbf {|a| |b|}} |$ where $\mathbf{a}$ and $\mathbf{b}$ are direction vectors of the lines

The scalar product form of the equation of a plane is $\mathbf{r \cdot n} = k$ where $k = \mathbf{a \cdot n}$ for any pin tin the plane with position vector $\mathbf a$
The acute angle $\theta$ between the line with equation $\mathbf r = \mathbf a + \lambda \mathbf b$ and the plane with equation $\mathbf{r \cdot n} = k$ is given by the formula

$\displaystyle \sin \theta = | \frac{\mathbf {b \cdot n}}{\mathbf {|b| |n|}} |$

The acute angle $\theta$ between the plane with equation $\mathbf{r \cdot n_1} = k_1$ and the plane with equation $\mathbf{r \cdot n_2} = k_2$ is given by the formula

$\displaystyle \sin \theta = | \frac{\mathbf {n_1 \cdot n_2}}{\mathbf {|n_1| |n_2|}} |$

Two lines are skew if they are not parallel and do not intersect
For any two non-intersecting lines $l_1$ and $l_2$ there is a unique line segment AB such that A lies on $l_1$ , B lies on $l_2$ and AB is perpendicular to both lines
The perpendicular from a point P to a line $l$ is a line drawn from P at right angles to $l$
The perpendicular form a point P to a plane $\it\Pi$ is a line drawn from P parallel to the normal vector $\mathbf n$
$k$ is the length of the perpendicular from the origin to a plane $\it\Pi$ where the equation of a plane $\it\Pi$ is written in the form $\mathbf{r \cdot \hat n} = k$ where $\mathbf{\hat n}$ is a unit vector perpendicular to $\it\Pi$

Brownies

Sun, 22 Oct 2023 00:00:00 GMT

Tried-and-tested brownie recipe for brownie in a loaf tin which remains a bit gooey in at the centre

Ingredients

100g dark chocolate
225g butter
275g flour
3 eggs
300g sugar

Method

In a saucepan, gently heat chocolate and butter, being careful not to burn the chocolate
- Use the lowest possible heat setting if you are not sure
- Stir until both molten and mixed
Whisk/blend eggs
- I just use the blender but a whisk and bowl is fine too
Pour whisked/blended eggs into a bowl/saucepan
- Bowl/saucepan needs to be large enough to hold all ingredients
Add sugar to eggs stir until mixed
Add butter and chocolate mixture, stir until mixed
Add flour, stir until mixed
Pour into greased loaf-tin
Bake in oven for 40 mins at 160 degrees centigrade
- The middle will not be firm and so the loaf-tin needs to be left to cool
- It should then be refrigerated before being cut into slices

Do not start Spotify automatically

Sat, 21 Oct 2023 00:00:00 GMT

Spotify now wants to start automatically by default. If you would rather it did not:

Spotify → Settings → Start-up and window behaviour → Open Spotify automatically after you log in to your computer → No

Nerdy nutrition tips

Sun, 10 Sep 2023 00:00:00 GMT

A staple of science fiction, along with hover-boards and iPads, is the pill that somehow contains the nutrition of a single meal. That’s still a bit of a long way off, despite what others (e.g. 1, e.g. 2) may tell you.

In order to attend conveniently and reasonably cheaply to my nutritional needs at breakfast and lunch, I use overnight oats and a protein-based smoothie respectively, such that I only need to consider one ‘proper’ meal per day—supper—which changes daily and where more effort goes into sourcing ingredients and preparation.

Overnight oats

This will do two small-ish servings:

50 grams oats
300 grams oat milk (Oatley Barista Edition gets my vote)
10 grams chia seeds
cocoa powder (optional)
honey or other (optional)
berries e.g. blueberries, raspberries, cherries (optional)

Put the oats, oat milk, and chia seeds in a large jar (or other sealable container) and leave in the refrigerator over night
In the morning, heat (in pan on the stove or in the microwave) and serve

Lunchtime smoothie

For one:

two scoops flavoured impact whey protein powder (I use myprotein impact whey protein usually in strawberry flavour)
nuts (whatever types I have to hand e.g. red peanuts, almonds, cashews, sunflower seeds, pumpkin seeds, flax seed), 1x tablespoon of each type
goji berry, teaspoon

The nuts and goji berries go in the blender with enough water to completely cover—this is then blended into a reasonably viscous liquid akin to a paste
Water is added up to the normal volume of 500 millilitres or so, with the protein powder then being added on top, blending again

(I buy raw nuts mail order in bulk and then roast them at home in the oven such that I always have plenty of nuts to hand. The only exception to this is flax seed which I buy in pre-ground.)

Things to not use

Thu, 03 Aug 2023 00:00:00 GMT

TP-LINK AV500 2-port power-line adapter with AC pass through (model: TL-PA4020P)

Pop!_OS 22.04 on Mac Pro 5,1

Wed, 02 Aug 2023 00:00:00 GMT

Brief coverage below of installing Pop!_OS 22.04 LTS on a Mac Pro 5,1 from early 2009; or, more correctly, a Mac Pro 4,1 which has had a firmware upgrade applied such that it now reports as a 5,1.

Installation

Installation was a breeze with the usual steps:

Add in a fresh SSD¹
Download image from PopOS website
Write to USB with balenaEtcher
Power off and remove original drive with MacOS on it
Boot from USB by pressing and holding alt on boot until you get the option (UEFI boot or similar)
Install Pop!_OS onto new drive
Power off, remove USB stick, put original drive with MacOS on it back in
Boot from new drive by pressing and holding alt on boot until you get the option

Small issues to sort out

Sleep/suspend

Sleep/suspend does not seem to work, as a result I turned this off
- Settings -> Power -> Automatic suspend: Off

Drivers for older Nvidia graphics cards

For old Nvidia cards², you are likely to get a cheeky message like the below in the kernel ring buffer …

[   50.017989] nvidia-nvlink: Nvlink Core is being initialized, major device number 235
[   50.018002] NVRM: The NVIDIA GeForce 9500 GT GPU installed in this system is
               NVRM:  supported through the NVIDIA 340.xx Legacy drivers. Please
               NVRM:  visit http://www.nvidia.com/object/unix.html for more
               NVRM:  information.  The 535.86.05 NVIDIA driver will ignore
               NVRM:  this GPU.  Continuing probe...
[   50.020267] NVRM: No NVIDIA GPU found.

… the upshot of which being desktop rendering with no hardware acceleration.

Thankfully there is a PPA we can use to easily get hold of the 340 drivers:

sudo add-apt-repository ppa:kelebek333/nvidia-legacy
sudo apt update
sudo apt-get purge '*nvidia*'
sudo apt install nvidia-340-updates nvidia-340-updates-dev xorg-modulepath-fix

A quick reboot later and a run of nvidia-settings should then confirm everything is in order, and the display is commensurately snappier.

Shorter password

If you want short password
- https://askubuntu.com/questions/113682/how-to-change-disable-password-complexity-test-when-changing-password

References

OWC Mount Pro brackets are nice for this but not necessary because 2.5” SSD drives are so light that you can just push them into the SATA connector and they will stay put.↩
In this case a GeForce 9500 GT which admittedly was released around 15 years ago. sudo dmesg | less will print the kernel ring buffer.↩

Adventures with the Elgato Streamdeck

Thu, 29 Jun 2023 00:00:00 GMT

The Elgato Streamdeck is a programmable console with illuminated buttons which supports both Windows and MacOS, with third-party open source software is also available for linux support. It has taken the internet by storm and has been particularly well received by streamers/video content producers, as a quick search on youtube for ‘Elgato Streamdeck’ will confirm.

This is what the Elgato Streamdeck Mk. II looks like:

On MacOS, the buttons can be made to e.g. open websites. To run arbitrary commands, shell scripts can be executed. Alternatively, it can issue a HTTP(S) GET request when a button is pressed. For more involved automation, a simple locally-running server can be used to do whatever we want when a given HTTP endpoint/route is hit. Go and the Gin HTTP server framework are ideal for this task.

Using the Streamdeck on linux

The software you want here is streamdeck-ui.

The instructions at https://timothycrosley.github.io/streamdeck-ui/docs/installation/ubuntu/ worked well for me on Ubuntu/Pop!_OS 22.04 LTS, though I did run into an error with the QT library when launching:

Could not load the Qt platform plugin "xcb" in "" even though it was found.

which was solved with:

sudo apt-get install '^libxcb.*-dev' libx11-xcb-dev libglu1-mesa-dev libxrender-dev libxi-dev libxkbcommon-dev libxkbcommon-x11-dev

Using the Streamdeck to control Squeezebox Touch and Squeezebox Radio

As a specific example, I wanted to be able to control my Squeezebox Touch and Squeezebox Radio from my Streamdeck. To do this, a locally running server is used to send JSON commands to the Logitech Media Server when a HTTP endpoint is hit as a result of a button being pressed on the Streamdeck.

In the below, Gin is used to set up the following routes:

/lms/play
/lms/pause
/touch/volup
/touch/voldown
/radio/volup
/radio/voldown

which are then hit with a GET request by the Streamdeck when button is pressed, and send JSON to the Logitech Media Service with a POST to effect the action.

go mod init github.com/algrt-hm/steamdeck-intermediary
go get github.com/gin-gonic/gin

// server.go

package main

import (
	"github.com/algrt-hm/steamdeck-intermediary/service"
	"github.com/gin-gonic/gin"
)

func main() {
	// playerMacAddressConst is the MAC address of the Squeezebox player we want to control
	const touchMacAddress = "00:04:20:23:a1:b5"
	const radioMacAddress = "00:04:20:2b:76:f6"

	gin.SetMode(gin.ReleaseMode)
	// instantiate server, includes logger and recovery middleware
	server := gin.Default()

	// Test / status endpoint
	server.GET("/", func(c *gin.Context) {
		c.JSON(200, gin.H{
			"message": "Hello World!",
		})
	})

	// Simple group: lms
	lms := server.Group("/lms")
	{
		lms.GET("/play", func(c *gin.Context) {
			code, body := service.LmsPost(touchMacAddress, service.LmsPlay)
			c.String(code, body)
		})
		lms.GET("/pause", func(c *gin.Context) {
			code, body := service.LmsPost(touchMacAddress, service.LmsPause)
			c.String(code, body)
		})

		touch := lms.Group("/touch")
		{
			touch.GET("/voldown", func(c *gin.Context) {
				code, body := service.LmsPost(touchMacAddress, service.LmsVolumeDown)
				c.String(code, body)
			})
			touch.GET("/volup", func(c *gin.Context) {
				code, body := service.LmsPost(touchMacAddress, service.LmsVolumeUp)
				c.String(code, body)
			})
		}

		radio := lms.Group("/radio")
		{
			radio.GET("/voldown", func(c *gin.Context) {
				code, body := service.LmsPost(radioMacAddress, service.LmsVolumeDown)
				c.String(code, body)
			})
			radio.GET("/volup", func(c *gin.Context) {
				code, body := service.LmsPost(radioMacAddress, service.LmsVolumeUp)
				c.String(code, body)
			})
		}
	}

	server.Run(":8080")
}

// service/lms-service.go

package service

import (
	"bytes"
	"encoding/json"
	"io"
	"log"
	"net/http"
)

/*
Example of what we're doing here:
We send a post request to e.g: http://lms-host:9000/jsonrpc.js

The body looks like e.g. (for pause):
   {"id":1,"method":"slim.request","params":["00:04:20:2b:76:f6",["pause"]]}
e.g. (for play):
   {"id":1,"method":"slim.request","params":["00:04:20:2b:76:f6",["play"]]}
*/

// lmsHostnameConst is the hostname of the LMS server; here I am using a local DNS entry
// that is in my /etc/hosts file
const lmsHostnameConst = "lms-host"

// form of the JSON we send to the LMS server
type LmsService struct {
	Id     string `json:"id"`
	Method string `json:"method"`
	Params []any  `json:"params"`
}

// checkErr will call log.Fatal if the error is not nil i.e. there is an error
func checkErr(err error) {
	if err != nil {
		log.Fatal(err)
	}
}

// LmsSimple is a helper function to create a LmsService struct for a simple operation
// with a given player MAC address and verb (e.g. "play" or "pause")
func LmsSimple(playerMacAddress string, verb string) LmsService {
	/*
		Looks like e.g:

		{
			"id": "1",
			"method": "slim.request",
			"params": [
				"00:04:20:2b:76:f6",
				[
					"pause"
				]
			]
		}
	*/

	return LmsService{
		Id:     "1",
		Method: "slim.request",
		Params: []any{playerMacAddress, []string{verb}},
	}
}

// LmsPlay is a helper function to create a LmsService struct for a "play" operation
func LmsPlay(playerMacAddress string) LmsService {
	return LmsSimple(playerMacAddress, "play")
}

// LmsPause is a helper function to create a LmsService struct for a "pause" operation
func LmsPause(playerMacAddress string) LmsService {
	return LmsSimple(playerMacAddress, "pause")
}

// LmsVolumeDown is a helper function to create a LmsService struct for a "volume down" operation
func LmsVolumeDown(playerMacAddress string) LmsService {
	return LmsService{
		Id:     "1",
		Method: "slim.request",
		Params: []any{playerMacAddress, []string{"mixer", "volume", "-10"}},
	}
}

// LmsVolumeUp is a helper function to create a LmsService struct for a "volume up" operation
func LmsVolumeUp(playerMacAddress string) LmsService {
	return LmsService{
		Id:     "1",
		Method: "slim.request",
		Params: []any{playerMacAddress, []string{"mixer", "volume", "+10"}},
	}
}

// LmsPost is a helper function to send a POST request to the LMS server
// with the given LmsService struct
// returning the HTTP status code and body text
func LmsPost(playerMacAddress string, fn func(string) LmsService) (int, string) {
	postUrl := "http://" + lmsHostnameConst + ":9000/jsonrpc.js"
	jsondata, err := json.Marshal(fn(playerMacAddress))
	checkErr(err)

	r, err := http.NewRequest("POST", postUrl, bytes.NewBuffer(jsondata))
	checkErr(err)
	r.Header.Set("Content-Type", "application/json")

	client := &http.Client{}
	res, err := client.Do(r)
	checkErr(err)
	defer res.Body.Close()

	bodyText, err := io.ReadAll(res.Body)
	checkErr(err)
	return res.StatusCode, string(bodyText)
}

go build
./steamdeck-intermediary

We can then hit those endpoints from the streamdeck (example below):

These screenshots show MacOS. Using streamdeck-ui on linux, the HTTP GET option is not baked-in, so e.g. curl -X GET http://hansolo:8080/lms/pause is the command to have run on the button press.

That takes care of volume control: for a re-scan we can hit http://lms-host:9000/settings/index.html?p0=rescan in the browser:

Reference

Adventures with tmux

Thu, 29 Jun 2023 00:00:00 GMT

algrt.hm RSS Feed

Technology consulting

Who does what on the project

Project management

Various consulting tips

Teams status

OoO

Appendices

Appendix: job grades

Developing with agents

AGENTS.md/CLAUDE.md

Which is best?

Using in combination

Usage

MCP servers

Favourite prompts

CC

makefile

AGENTS.md

Windows 11 PIN change

Which version?

How to change PIN

Auto log-out

Developer setup speedrun for Pop!_OS

Nodejs

uv

Claude Code

OpenCode

ungoogled-chromium

zed

Go

gollm

Cursor

Beeper

claude-monitor

How do I set the default browser?

A plan for contacts

A table

A handy shell function

A sample note

Some Python to extract bods from our notes

Updating the database

Data taxonomy

Working with me guide

Keeping credentials out of the repo

Data preparation

Meeting quality

uv to manage packages

Consultancy B

New project considerations

Overall objectives

Pre-engagement: alignment & readiness

Start of engagement

Ongoing processes & governance

Proposal context

UBS dresscode from 2010

UBS Dress Code

For the attention of PKB employees

Contents

Introduction

The UBS Dress Code

The UBS Dress Code for Women

The UBS Dress Code for Men

Check Your Look!

Don’ts

Leaked 2018 Tesla email

Advice for IBD interns from 2010

Stop AirPods from switching connection from iPhone to Mac

Python on Windows

Comparisons which may not make sense

RocksDB versus Redis

Team check-in

Step 1: vote and feedback

Step 2: brainstorm

A very efficient turmeric latte

Cursor in WSL2 on Windows

Innovation

Presentation pointers

Titles

Underlining

`AGENTS.md`/`CLAUDE.md`

`makefile`

`AGENTS.md`