A free, interactive, semester-wise mathematics roadmap for B.Tech AI/ML students. Learn the math behind artificial intelligence and machine learning — from Class 12 foundations to research-grade theory. Built by Debojyoti Pal.
Every machine learning algorithm is built on mathematics. Linear algebra powers neural networks and data transformations. Calculus enables gradient descent and backpropagation. Probability theory underpins Bayesian inference and generative models. Optimization theory explains how models are trained. This roadmap gives you a structured, semester-wise path through all of it.
Sets, relations, functions, polynomials, exponentials, logarithms, trigonometry, sequences and series, complex numbers. Fills Class 12 gaps before rigorous calculus.
Limits and continuity, differentiation rules, chain rule, Mean Value Theorem, integration, Riemann sums, Fundamental Theorem of Calculus, Taylor and Maclaurin series. Essential for gradient descent and loss functions.
Propositional logic, predicate logic, proof by induction, contradiction, sets and functions, countability. Foundation of formal mathematical reasoning.
Vectors, dot product, cross product, matrices, transpose, inverse, Gaussian elimination, vector spaces, subspaces, span, basis, linear transformations, determinants. Everything in ML is linear algebra.
Combinatorics, permutations, combinations, graph theory, recurrence relations, Boolean algebra. Foundation for algorithm analysis and probabilistic models.
Eigenvalues and eigenvectors, diagonalization, Singular Value Decomposition (SVD), Principal Component Analysis (PCA) from SVD, positive definite matrices, L1 L2 Frobenius norms, Jacobian matrix, Hessian matrix, matrix calculus. SVD powers recommender systems and compression. Hessian used in second-order optimizers.
Sample space, events, Bayes theorem, random variables, PMF, PDF, CDF, expectation, variance, moments, Bernoulli, Binomial, Poisson, Normal, Exponential distributions. Every ML model makes probabilistic assumptions.
Partial derivatives, gradient vector, directional derivatives, chain rule for multiple variables, Jacobian, Hessian, Lagrange multipliers, constrained optimization. Backpropagation is multivariable chain rule applied recursively.
Joint distributions, marginal distributions, covariance, correlation, Multivariate Normal distribution, Central Limit Theorem, Law of Large Numbers, Markov chains. Required for Bayesian models, GANs, and VAEs.
Convex sets, convex functions, convex optimization, gradient descent derivation, stochastic gradient descent, mini-batch SGD, momentum, Adam optimizer mathematics, KKT conditions, duality theory. Training any neural network is solving an optimization problem.
Maximum Likelihood Estimation (MLE), Maximum A Posteriori (MAP), bias-variance tradeoff, confidence intervals, hypothesis testing, Bayesian inference, conjugate priors, Ordinary Least Squares (OLS), Ridge regression, Lasso regression. MLE and MAP are the theoretical basis of model training.
Entropy, joint entropy, conditional entropy, KL Divergence, cross-entropy loss, mutual information, Fisher information. Cross-entropy loss, VAE ELBO, and attention mechanisms all come from information theory.
Floating point arithmetic, numerical stability, Newton-Raphson root finding, numerical integration, LU decomposition, QR decomposition, conjugate gradient, condition numbers. GPU computation and stable training depend on numerical methods.
Markov chains, stationary distributions, Hidden Markov Models, Gaussian processes, Brownian motion, MCMC, Metropolis-Hastings, Gibbs sampling. Used in reinforcement learning and diffusion models.
Metric spaces, normed spaces, Hilbert spaces, inner product spaces, Reproducing Kernel Hilbert Spaces (RKHS), sigma-algebras, Lebesgue integral, convergence types. Required for kernel methods, SVMs, and PAC learning theory.
Directed and undirected graphical models, belief propagation, variational inference, ELBO derivation, Expectation-Maximization (EM) algorithm, Variational Autoencoders (VAE) mathematics. Backbone of generative models.
Manifolds, tangent spaces, Riemannian geometry, geodesics, Lie groups, Lie algebras, latent space geometry, natural gradient. Used in geometric deep learning and graph neural networks.
PAC learning, VC dimension, Rademacher complexity, generalization bounds, minimax risk, online learning regret bounds. Rigorously answers why machine learning generalizes.
Natural gradient descent, Newton method, L-BFGS, optimal transport, Wasserstein distance, mirror descent, non-convex optimization landscape. Powers state-of-the-art model training.
Built by Debojyoti Pal — indie developer and AI/ML builder. GitHub: github.com/Debojyoti-hub-tech. Instagram: @_coral_soul_