How to read this site

Two depths on every page

Each unit opens in Dense mode: definitions, statements of results, short intuitions and examples. That is the version for reviewing, or for when you already half-know the topic.

Everything longer sits in a collapsible block. Open one block to read it, or press Full under the page title to open every explanation, derivation and proof on the page at once. The site remembers your choice.

Blocks in both courses

Definition X.1Definitions, conventions#

Green rule. The precise meaning of a term. Everything else rests on these.

Theorem X.2Theorems, propositions, lemmas#

Blue rule. A statement that follows from the definitions. Each one has a proof.

Proofof X.2

Proofs and derivations are closed in Dense mode. They end with ∎.

Example X.3Examples#

Grey rule. Concrete instances, worked through.

Non-example X.4Non-examples#

Rust rule. Things that look like they qualify but fail one specific condition. They show what each condition is for.

Full explanationFull explanations

The long form: the intuition behind a definition, how to read it, why it is set up this way, edge cases, history, and where it leads.

Check What is a Check?

A question to answer before revealing. Retrieval, actually recalling the answer, is what makes knowledge stick; re-reading mostly makes it feel familiar. The Full switch never opens these.

Blocks in the AI course

Model X.5Models and tools#

Green rule, like a definition. The dense card for what you build: what it computes, its objective or rule, its assumptions and its cost.

Failure mode X.6Failure modes#

Rust rule, like a non-example. Where the method breaks, which assumption it violates, and what the symptom looks like.

Build Build boxes

• mlkit/example.py
• tests/test_example.py

What you implement in the repo, and the command that tells you it works. The tests are the specification.

In production

How the idea behaves in real systems: scale, cost, monitoring, and how it fails in the wild.

Blocks in the Math course

Where this shows up in AI

Connections to machine learning practice. Always visible.

Numbering and links

Results are numbered by unit. In the Math course, LA2.5 is item 5 of unit LA2 (linear algebra, unit 2); F1 is foundations. In the AI course, units are numbered by week: W0.3 is item 3 of week 0. Every numbered block has a stable link (the # on its right). A link to a result inside a closed block opens that block. The AI course links into the Math course this way, straight to the result a build needs.

Notation

$\mathbb{N} = \{0, 1, 2, \dots\}$. $\mathbb{F}$ is $\mathbb{R}$ or $\mathbb{C}$ unless stated. "$:=$" means “is defined as”. Vectors are plain letters ($u, v, w$), scalars usually $a, b, c$. Each unit introduces any new notation where it is first used.

Sources

Results are cross-checked against standard texts and, for models, the original papers. They are cited at the end of each unit and next to the result as “Compare:”. Numbering and presentation here are our own.