Mathematics for AI — Roadmap

The math you actually need before the rest of this site makes sense. Work top to bottom; each module unlocks the next.

1. Linear Algebra

• Vectors, dot product, norms, cosine similarity
• Matrices, matrix multiplication, transpose, inverse
• Rank, linear independence, span, basis
• Eigenvalues & eigenvectors
• Singular Value Decomposition (SVD)
• Positive semi-definite matrices, quadratic forms
• Matrix calculus: gradients w.r.t. vectors and matrices
• Why it matters: embeddings, PCA, attention (Q·Kᵀ), weight matrices

2. Calculus & Optimization

• Derivatives, partial derivatives, gradients
• Chain rule → backpropagation
• Jacobians and Hessians (intuition, not just formulas)
• Convex vs non-convex functions
• Gradient descent, SGD, momentum
• Adaptive optimizers: AdaGrad, RMSProp, Adam
• Learning rate schedules & warmup
• Lagrange multipliers (used in SVM, constrained optimization)

3. Probability & Statistics

• Random variables, distributions (Bernoulli, Binomial, Gaussian, Poisson)
• Expectation, variance, covariance, correlation
• Bayes' theorem and conditional probability
• Maximum Likelihood Estimation (MLE) vs Maximum A Posteriori (MAP)
• Central Limit Theorem
• Hypothesis testing, p-values, confidence intervals, statistical power
• A/B testing and statistical significance
• Bootstrap and permutation tests (distribution-free uncertainty estimation)
• Causal inference basics: confounders, RCTs, sampling bias
• Entropy, cross-entropy, KL divergence — the loss-function math

4. Algorithms & Data Structures (for ML engineering)

• Big-O complexity analysis
• Arrays, hash maps, trees, graphs, heaps
• Sorting & searching
• Time/space complexity of common ML algorithms (e.g. k-NN, k-means, matrix ops)
• Why this belongs here: ML interviews test general coding fluency alongside ML theory