01Module 08 - Numerical Methods for ML EngineeringOverview of numerical methods for AI - floating-point precision, linear solvers, automatic differentiation, sparse matrices, and why numerical stability determines whether your model trains or diverges.02Floating-Point Arithmetic - Precision, Overflow, and Mixed Precision TrainingDeep engineering guide to IEEE 754 floating-point, machine epsilon, catastrophic cancellation, float16/bfloat16/float32 in deep learning, and numerical stability techniques for production ML systems.03Numerical Linear Algebra - Condition Numbers, Solvers, and Backprop StabilityEngineering guide to condition numbers, ill-conditioned matrices, LU/QR/Cholesky factorizations, why you should never invert a matrix, and the numerical stability of neural network backpropagation.04Iterative Solvers - Conjugate Gradient, Krylov Methods, and Large-Scale MLEngineering guide to iterative methods for linear systems - conjugate gradient, GMRES, preconditioning, and when iterative solvers beat direct methods in large-scale ML workloads.05Numerical Differentiation - Finite Differences, Gradient Checking, and AutodiffEngineering guide to finite difference methods, central difference formulas, step size selection, truncation vs rounding error, and gradient checking to validate automatic differentiation implementations.06Numerical Integration - Quadrature, Monte Carlo, and Bayesian InferenceEngineering guide to numerical integration methods - quadrature rules, Monte Carlo integration, importance sampling, and applications in Bayesian inference, variational methods, and normalizing constants.07Root-Finding Algorithms - Bisection, Newton-Raphson, and ML ApplicationsEngineering guide to root-finding algorithms - bisection method, Newton-Raphson, secant method, convergence rates, and ML connections including learning rate scheduling and fixed-point iterations.08Sparse Matrix Methods - CSR/CSC Formats, Efficient Operations, and ML SparsityEngineering guide to sparse matrix storage formats (CSR, CSC, COO, LIL), sparse operations in SciPy, and why sparsity is fundamental to attention masks, graph adjacency matrices, and embedding tables in production ML.
