Learning path / 7 published lessons
Mathematics for computing
Connect discrete reasoning, linear algebra, calculus and probability to computing. Work with small numbers first, then separate the general statement from the assumptions that make it true.
What you’ll work toward
- Pigeonhole guarantees some collisions, not infinitely many preimages in every bucket
- Cosine is undefined for a zero vector
- Small determinant magnitude is not a scale-invariant condition-number test: εI has tiny determinant and condition number one
- Chain rule applies local sensitivities; products of Jacobians are not guaranteed stable by residual connections
Completion is stored on this device only. Nothing is locked; start where it makes sense.
Start this pathBefore the first lesson
- Read the prerequisite section and complete its exercises
These are the starting lesson’s prerequisites, not requirements for every advanced topic below.
How to practise this subject
Derive a result by hand, check a finite example in code, and find a boundary case. Explain why the numerical check supports the calculation but is not a general proof.
- 01
Discrete Math — Sets, Logic, Combinatorics, Graphs
The vocabulary of computer science: sets, boolean logic, counting arguments, and graph theory — the four discrete-math tools you'll use in every subsequent session.
- 02
Linear Algebra I — Vectors, Dot Product, Geometry
The language ML speaks: vectors as arrows and lists of numbers, the dot product as similarity, norms as length, and cosine similarity as ‘how alike?’
- 03
Linear Algebra II — Matrices, Transforms, Eigenvalues
Matrices as linear transformations, matrix multiplication as function composition, and eigenvalues as the axes a transform respects — the shape of every neural net.
- 04
Calculus I — Derivatives & Chain Rule
Rate of change is the heart of learning: the derivative as slope, symbolic vs numeric differentiation, and the chain rule that powers every neural net.
- 05
Calculus II — Gradients & Gradient Descent from Scratch
The one algorithm behind all of ML: gradients as the ‘uphill direction’ in n dimensions, SGD as the workhorse, and the learning-rate/momentum knobs that decide whether you converge or explode.
- 06
Probability — Random Variables, Distributions, Expectation
Uncertainty, quantified: random variables, the distributions you'll actually meet (Bernoulli, binomial, normal, exponential, Poisson), expectation, variance, and Bayes' rule.
- 07
Statistics — CLT, Hypothesis Testing, Confidence Intervals
The three ideas that let you turn noisy data into defensible claims: the Central Limit Theorem, p-values, and confidence intervals — with the mistakes that get careers cancelled.