How to Use This Site

The anatomy of a lesson

Sections appear in this order, and each is visually marked so you can navigate by sight.

1. Intuition

A plain-language explanation with no notation. One analogy, sometimes a diagram. If you read only this section you will still understand what the topic is for.

Marked with a green tint and a compass.

2. Notation table

Every symbol used later, defined before it appears, including how to say it out loud. Skipping notation is the main reason mathematical writing feels impossible — so nothing is assumed.

3. The formal treatment

Definitions, the actual statement of the result, and the algorithm where there is one. This is the body of the lesson.

4. Derivations — collapsed by default

5. Solved problems

Worked numerically, with every arithmetic step visible. The numbers are chosen to be small enough to verify with a pen, and answers are cross-checked a second way wherever possible.

6. Pitfalls

The mistakes that actually cost people marks and production incidents — stated directly, with what to do instead.

7. Code

Where code helps, it appears from scratch first — usually NumPy — so the mechanism is visible, then the library one-liner.

# From scratch: conditional probability from a contingency table.
import numpy as np

table = np.array([[35, 15],   # exercises:     sleeps well, badly
                  [15, 35]])  # does not:      sleeps well, badly

joint    = table / table.sum()          # P(E, W)
marginal = joint.sum(axis=1)            # P(E)  — sum out sleep
conditional = joint[0, 0] / marginal[0] # P(W | E)

print(conditional)  # 0.7

Deep-learning lessons give both PyTorch and TensorFlow/Keras versions.

8. Exercises

Two to four problems with full solutions behind a toggle. Attempt them before opening the solution — the gap between "I could follow that" and "I can do that" is where learning happens.

Three ways to read

Pick whichever matches you. Nothing is locked, and switching costs nothing.

See the three tracks for suggested module orders.

The curriculum is ordered, not a menu

The 522 lessons form one continuous path. Ordering is enforced mechanically: a build-time check fails if any lesson lists a prerequisite that appears later in the curriculum. When that check was first run it caught four genuine mistakes.

Practically, this means two things:

• You can start anywhere. Every lesson shows what it assumes as clickable chips at the top. Follow them back until you hit something familiar, then work forward.
• Reading in order works. Nothing will reference an idea you have not met.

What this site will not do

Worth being straight about the limits.

• No videos. Text is faster to skim, searchable, and possible to verify. If you prefer watching, this is the wrong resource.
• No hand-holding through setup. Environment configuration and tooling tutorials are covered only where they affect understanding.
• No claims without derivation. If something is asserted without proof or a citation, that is a defect — treat it as one.

Conventions

• Notation follows the notation guide. Vectors are lowercase bold in print, plain in prose; matrices are capitals.
• Logarithms are natural unless the base is written.
• Estimates carry a hat: $\hat{\theta}$ is an estimate of $\theta$.
• Code is Python 3, NumPy-first, with scikit-learn, PyTorch and TensorFlow/Keras where relevant.
• British spelling in prose; American spelling in code identifiers, since that is what the libraries use (normalize, color).

Cost

Every lesson on this site is free and stays free. No account, no paywall, no email capture. If interactive tooling gets built later — graded drills, timed mock papers, spaced repetition — that may be paid, but the written curriculum will not be.

Next: Choosing Your Track, or jump straight into Sample Spaces and the Axioms of Probability if you would rather begin with the material.