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AI Mastery Path

Mathematics for AI

The exact mathematics you need to master AI — machine learning, deep learning, and large language models — and the computer science under them. It starts at counting and assumes nothing. Every lesson is here because something in AI demands it: nothing more, nothing less, each one resting on the last.

Curriculum · 13 areas, 100 lessons

Part I · Arithmetic & number sense

Start from zero — what numbers are and how they combine. The ground everything else stands on.

• 1Numbers and counting→
• 2Addition and subtraction→
• 3Multiplication and division→
• 4Negative numbers and the integers→
• 5Fractions, decimals, and percentages→
• 6Powers and roots→
• 7Order of operations and number sense→

Part II · Algebra — the language of patterns

Letters for numbers: the notation every later idea is written in, and the function — the object ML is built from.

• 8Variables and expressionssoon
• 9Solving linear equationssoon
• 10Inequalitiessoon
• 11The laws of exponentssoon
• 12Polynomials and factoringsoon
• 13The coordinate plane and graphssoon
• 14What a function is — the input–output machinesoon

Part III · Logic, sets & counting

The discrete foundation under both probability and computer science — how to reason, and how to count.

• 15Statements and logic — and, or, not, if–thensoon
• 16Sets and their operationssoon
• 17Relations and functions, formallysoon
• 18Counting — permutations and combinationssoon
• 19Proof and mathematical inductionsoon
• 20Sequences, recursion, and recurrencessoon

Part IV · Functions, exponentials & logarithms

The specific functions ML runs on — exponentials, logs, sigmoids — and the rate-of-change idea that opens calculus.

• 21Linear functions and slope — the seed of "rate of change"soon
• 22Quadratic and polynomial functionssoon
• 23Exponential functions — growth and decaysoon
• 24Logarithms→
• 25The number e and the natural logarithmsoon
• 26The logistic (sigmoid) function — your first activationsoon
• 27Sinusoids and periodicity — for positional encodingssoon

Part V · Single-variable calculus

The mathematics of change. The derivative and the chain rule are the literal machinery of how networks learn.

• 28Limits, intuitivelysoon
• 29Continuitysoon
• 30The derivative as a rate of change→
• 31Rules of differentiationsoon
• 32The chain rule — the engine of backpropagationsoon
• 33Maxima, minima, and optimizationsoon
• 34The integral as accumulationsoon
• 35The fundamental theorem of calculussoon

Part VI · Linear algebra — the engine of ML

Vectors, matrices, and the operations on them. This is the single most-used branch of math in all of AI.

• 36Vectors — points, arrows, and lists of numberssoon
• 37Vector addition, scaling, and linear combinationssoon
• 38The dot product, norms, and distance — similaritysoon
• 39Matrices and matrix multiplicationsoon
• 40Matrices as linear transformationssoon
• 41Systems of linear equations and Gaussian eliminationsoon
• 42Linear independence, span, basis, and ranksoon
• 43The four fundamental subspacessoon
• 44Determinants and invertibilitysoon
• 45Eigenvalues and eigenvectorssoon
• 46Diagonalization and the spectral theoremsoon
• 47The singular value decomposition (SVD)soon
• 48Orthogonality, projections, and least squaressoon
• 49Tensors and broadcasting — the data of deep learningsoon

Part VII · Multivariable & matrix calculus

Calculus and linear algebra meet. Gradients, Jacobians, and the chain rule on a computation graph: this is backprop.

• 50Functions of several variablessoon
• 51Partial derivativessoon
• 52The gradient and directional derivatives — steepest ascentsoon
• 53The multivariable chain rulesoon
• 54The Jacobian and the Hessiansoon
• 55Matrix calculus — gradients of vector and matrix expressionssoon
• 56Backpropagation as the chain rule on a computation graphsoon

Part VIII · Optimization — how models learn

Turning learning into minimizing a loss, and the algorithms — gradient descent and its kin — that actually do it.

• 57The optimization problem — minimizing a losssoon
• 58Convexity and why it matterssoon
• 59Gradient descentsoon
• 60Stochastic and mini-batch gradient descentsoon
• 61Momentum and adaptive methods (Adam)soon
• 62Constrained optimization and Lagrange multiplierssoon
• 63Regularization — L1, L2, and the bias toward simplicitysoon

Part IX · Probability — reasoning under uncertainty

AI is probabilistic to the core. Distributions, expectation, and Bayes' theorem are the language of every model's predictions.

• 64Sample spaces, events, and probabilitysoon
• 65Conditional probability and independencesoon
• 66Bayes' theoremsoon
• 67Random variables — discrete and continuoussoon
• 68Distributions you'll meet — Bernoulli, binomial, Gaussiansoon
• 69Expectation, variance, and covariancesoon
• 70Joint, marginal, and conditional distributionssoon
• 71The law of large numbers and the central limit theoremsoon
• 72Sampling and Monte Carlo methodssoon

Part X · Statistics & data analysis

Learning from data: estimation, maximum likelihood, the bias–variance tradeoff, and the first models that come straight out of statistics.

• 73Descriptive statistics and data summariessoon
• 74Populations, samples, and sampling distributionssoon
• 75Estimation and confidence intervalssoon
• 76Maximum likelihood estimation — the objective behind most MLsoon
• 77Hypothesis testing, p-values, and A/B testingsoon
• 78The bias–variance tradeoffsoon
• 79Correlation, causation, and confounderssoon
• 80Linear regression — your first modelsoon
• 81Logistic regression and classificationsoon

Part XI · Information theory — the math of LLMs

Entropy, cross-entropy, and KL divergence: the quantities that define how language models are trained and scored.

• 82Information and surprisesoon
• 83Entropy — measuring uncertaintysoon
• 84Cross-entropy — the loss function of language modelssoon
• 85KL divergence — the distance between distributionssoon
• 86Mutual informationsoon
• 87Perplexity — how language models are scoredsoon

Part XII · Algorithms & computation

The math under computer science and data structures — how to measure cost and reason about programs. Builds on Part III; take it any time after.

• 88Asymptotics and Big-O notationsoon
• 89Analyzing recursion and recurrence relationssoon
• 90Combinatorics for algorithmssoon
• 91Graphs and treessoon
• 92Graph algorithms and traversalsoon
• 93Computational complexity — P, NP, and intractabilitysoon
• 94Modular arithmetic and hashingsoon

Part XIII · Numerical & computational methods

Where the math meets the machine — floating point, numerical stability, and how autodiff actually computes every gradient.

• 95Floating-point numbers and precisionsoon
• 96Numerical stability — log-sum-exp and the softmax tricksoon
• 97The cost of linear algebra — vectorization and complexitysoon
• 98Iterative and approximate methodssoon
• 99Automatic differentiation — how backprop is really computedsoon
• 100Putting it together — the math inside a training loopsoon