Choosing Your Track

Intuition first

A track is a reading order, not a separate course. Every lesson is open to everyone, and nothing is hidden behind a choice made here. What a track changes is what you see first and how much of the heavy machinery you are expected to work through.

The reason tracks exist is that a beginner and someone preparing for graduate study genuinely need different routes through the same material. A beginner who starts with measure-theoretic framing will quit. A researcher who is given only intuition will be bored and under-prepared.

Rather than writing two courses, each lesson is layered — and the track tells you which layers to read.

The three tracks

Novice

For: first exposure to the field, or returning after a long gap.

Read: intuition, notation tables, the formal statement, solved problems, exercises.

Skip: the collapsible Advanced derivation blocks. They are closed by default for exactly this reason.

Route: foundations before applications, and probability before statistics. Deliberately omits reinforcement learning, formal logic and the heavier theory on a first pass — you can return to them once the core is solid.

The trap to avoid on this track is skipping the solved problems because the explanation felt clear. Following a worked example and producing one are different skills, and the gap only shows up under exam conditions or in a code review.

Practitioner

For: building models or LLM applications in industry.

Read: everything except the heaviest proofs. All code, all pitfalls, all metrics and deployment material.

Emphasis: what breaks in production. Leakage, imbalance, calibration, drift, the difference between a metric that fits your cost structure and one that does not.

Route: weighted towards the applied modules — databases, feature engineering, fine-tuning, RAG, MLOps — with just enough theory to debug a model rather than to prove a theorem about it.

The trap here is treating derivations as optional forever. You do not need to prove the bias–variance decomposition, but if you cannot say which term a given intervention reduces, you will reach for the wrong fix.

Researcher

For: graduate entrance exams, postgraduate study, or research work.

Read: everything, derivations first.

Emphasis: why results are true, when they fail, and what assumptions each one smuggles in. Includes optimisation theory, game theory, formal logic, VC dimension and the full RL progression.

Route: mathematics in full — linear algebra, calculus, probability, statistics, optimisation, game theory, logic — before any applications.

The trap on this track is derivation without computation. Being able to derive the EM algorithm and never having watched it converge on real data leaves a gap that shows up the moment something diverges.

How the tracks differ in practice

See the tracks page for the exact module ordering each one recommends.

Choosing honestly

Answer these three:

Can you differentiate $x^2\ln x$ without looking it up? If not, start Novice regardless of your job title. The calculus is not optional later, and it is cheaper to fix now.

Have you shipped a model that other people depend on? If yes, Practitioner — you already have the intuition that the Novice track builds, and you need the failure modes.

Do you want to know why, or what to type? If a formula without a derivation feels unsatisfying rather than convenient, take Researcher.

A better guide than any track

Every lesson lists its prerequisites as clickable chips at the top. That dependency graph is more reliable than a recommended ordering, because it is checked mechanically — the build fails if a lesson depends on something taught later.

So the most robust way to use the site is:

1. Open whichever lesson you actually want.
2. Follow the prerequisite chips backwards until you hit something familiar.
3. Work forwards from there.

This handles the common case that tracks cannot: you already know statistics but not linear algebra, or you have used transformers without ever studying probability.

Exercise 1

Pick the lesson furthest from your current knowledge that you genuinely want to understand — say Variational Autoencoders or GraphRAG. Follow its prerequisite chips backwards and write down the chain.

Show solutionHide solution

There is no single right answer, but the exercise usually reveals one of two things.

A short chain (two or three steps back) to something you know. You are closer than you thought; read forwards along that chain.

A long chain (six or more steps). The topic sits on foundations you have not built. Attempting the lesson directly will feel like failure when the real issue is sequencing — which is precisely the pattern that makes people conclude they are "bad at maths".

For VAEs the chain runs roughly: variational autoencoders → regularised autoencoders → autoencoders → backpropagation → forward propagation → multivariable chain rule, and in parallel → expectation maximisation → Gaussian mixtures → multivariate normal → normal distribution. Two branches, and both have to be walked.

That is genuinely eight to ten lessons. Knowing it in advance turns an intimidating topic into a finite plan.

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Next: The Prerequisite Map, which shows the whole dependency graph at once.