Mathematical Foundations

Mathematics is the language of machine learning and deep learning. This section covers the mathematical tools and theories commonly used in AI research.

Contents:

• Calculus — Derivatives, integrals, multivariable optimization
• Linear Algebra — Matrix operations, eigendecomposition, SVD
• Probability Theory — Probability distributions, Bayes' theorem, stochastic processes
• Information Theory — Entropy, KL divergence, mutual information
• Statistics — Hypothesis testing, estimation theory, regression analysis
• Automatic Differentiation — Forward mode, reverse mode, computational graphs
• Discrete Mathematics — Set theory, graph theory, combinatorics, Boolean algebra
• Numerical Methods — Interpolation, numerical integration, ODE solvers, numerical stability
• Optimization Theory — Convex optimization, gradient descent, KKT conditions, duality
• Graph Theory Fundamentals — Directed/undirected graphs, Euler paths, graph coloring, network flows

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