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00_Start_Here

Level: 101 · for anyone

What this library is

One idea per page, and every claim backed by a program that runs. The pages are short, the programs are stdlib-only Python, and the output printed on any page came from an actual run that CI re-checks on every push.

It is not a textbook and does not try to be. A textbook covers a syllabus; this covers the handful of ideas that turned out to be worth writing down carefully, in the order that made them click.

What to read first

01_Precision/ — How much of this number is real? Four lessons, in order, on measurement, significant figures, uncertainty, and where digits go when a subtraction destroys them.

It begins with a question that sounds settled and is not: are significant figures just rounding? The answer is no, and unpacking why takes you from a blackboard example about a population estimate all the way to why the textbook quadratic formula returns an answer that is 25% wrong.

02_Measure_Zero/ — How can infinitely many points take up no room? Six lessons on sets so thin that they have no length, area or volume: the rationals, the Cantor set, the fat Cantor set (full of gaps, and still length 1/2), and the Cantor function, a staircase that climbs from 0 to 1 while standing still almost everywhere. It stands on its own; the one thing it assumes is the idea of a limit.

How to run anything here

Every lesson folder has an examples/ directory with a .py file and a .out answer key. Every command on these pages is written to be run from the root of a clone, so start there:

git clone https://github.com/masiarek/math-learning-library.git

cd math-learning-library

Then run any program directly:

python3 01_Precision/significant_figures/examples/significant_figures.py

Each program also runs from its own examples/ folder, as python3 significant_figures.py: the examples read no files, so they do not care where they are started.

No virtual environment, no install step, no dependencies. If you have python3, you are ready.

To verify the whole library the way CI does:

python3 tools/run_examples.py --check

Reading it as a website

https://masiarek.github.io/math-learning-library/ — same content, with search. Built by MkDocs Material straight from this repo's Markdown; there is no separate docs/ copy, so what GitHub renders and what the site serves are the same files.

To preview it locally:

uv run --group docs mkdocs serve

Sibling libraries