Neural-PathPart II
Mathematics
The mathematical backbone of modern machine learning — from vector spaces and calculus through probability, information theory, convex optimization, and the functional analysis underlying deep learning. Treated rigorously, with ML motivation throughout.
Linear Algebra & Matrix Analysis
Vector spaces, spectral theory, matrix decompositions, and the geometric machinery behind every ML model — developed from first principles.
Multivariate Calculus & Differential Geometry
Gradients, Hessians, manifolds, and Riemannian geometry — the geometric foundation of learning.
Convex Analysis & Optimization Theory
Duality, KKT conditions, proximal methods, and the geometry of non-convex loss landscapes.
Probability Theory
Measure-theoretic probability, distributions, convergence modes, limit theorems, and concentration inequalities.
Statistical Inference & Learning Theory
MLE, Bayesian inference, PAC learning, VC dimension, and the theory behind why models generalize.
Information Theory
Entropy, mutual information, KL divergence, channel capacity, and the deep connection between compression and intelligence.
Stochastic Processes
Markov chains, martingales, Brownian motion, Itô calculus, and stochastic differential equations.
Numerical Methods & Scientific Computing
Floating point, direct and iterative solvers, automatic differentiation, and numerical stability in practice.
Operations Research
Linear programming, integer programming, network flows, combinatorial optimization, and dynamic programming.
Game Theory & Mechanism Design
Nash equilibria, minimax, mechanism design, and the multi-agent foundations of GANs and RLHF.
Functional Analysis & Operator Theory
Hilbert and Banach spaces, bounded operators, RKHS, and the operator-theoretic view of attention and kernels.
Graph Theory & Combinatorics
Spectral graph theory, random graphs, the probabilistic method, and the combinatorial foundations of GNNs.