Math
Mathematics
Mathematics here is the working language for vectors, matrices, gradients, probability, optimization, information, and the models built from them.
Preface
The goal is understanding, not mathematical performance. Each chapter should help you read equations, compute small examples, check the same idea in code, and connect the result to machine learning.
The order matters. Mathematical language comes before vectors. Vectors come before matrices. Geometry gives those operations a picture. Linear systems and decompositions expose structure before calculus introduces gradients and backpropagation. Probability, numerical computation, optimization, statistics, and information theory support the later deep learning and language-model chapters.
How to study this path
Make the ideas usable.
Mathematics here is not a gatekeeping test. It is a language for reading machine learning ideas precisely. Read slowly. Translate notation into words. Work the small checks. Move on when the idea is usable, then return when later chapters make it sharper.
- Do not memorize every formula before moving forward.
- For each page, say the main idea in plain language.
- Use the checks to catch doubts while the idea is still small.
- If a definition feels abstract, read the example first and then return to the definition.
- Come back later. Mathematics compounds because ideas are reused.
- The chapters are in prerequisite order, but review pages are safe to revisit whenever a later topic exposes a gap.
Chapters
Move through the path in order.
All current Mathematics chapters are open for reading. Start at Chapter 1 unless the language of notation already feels comfortable, then keep the order because later chapters reuse earlier ideas.
Notation, variables, functions, sets, sums, and the habit of reading formulas aloud.
8 lessons + 5 review pagesChapter 2VectorsVectors as data, positions, directions, weighted sums, and the beginning of representation geometry.
10 lessons + 5 review pagesChapter 3MatricesMatrices as tables, shape rules, linear maps, and neural network layers.
9 lessons + 5 review pagesChapter 4GeometryLength, distance, angles, orthogonality, projection, subspaces, and embedding geometry.
11 lessons + 5 review pagesChapter 5Linear Systems and DecompositionsRank, span, basis, eigenvalues, SVD, low-rank approximation, and PCA.
11 lessons + 5 review pagesChapter 6CalculusDerivatives, gradients, Jacobians, chain rule, computation graphs, and backpropagation.
10 lessons + 5 review pagesChapter 7ProbabilityEvents, random variables, distributions, expectation, variance, conditional probability, and Bayes' rule.
11 lessons + 5 review pagesChapter 8Numerical ComputationFloating point, rounding, overflow, underflow, stable softmax, log-sum-exp, and gradient checks.
10 lessons + 5 review pagesChapter 9OptimizationLoss functions, gradient descent, learning rates, momentum, regularization, and training as search.
11 lessons + 5 review pagesChapter 10StatisticsSamples, splits, estimators, bias and variance, likelihood, uncertainty, and validation.
12 lessons + 5 review pagesChapter 11Information TheoryEntropy, cross-entropy, KL divergence, mutual information, perplexity, and compression as prediction.
10 lessons + 5 review pagesProgress
Progress is saved locally on this device. Use it as a private reading marker while moving through the path.