Mathematics framework for machine learning, mathematical foundations and computational principles of machine learning underlying modern learning algorithms, least squares methods, support vector machines, linear and nonlinear principal component analysis, neural networks, connections between deep learning and differential equations. Integration of theory with Python-based implementation to bridge mathematical models and practical algorithms.

Pre-requisites: (MATH 225 or MATH 208), STAT 201, and ISE 291

Development of mathematical models for engineering and applied sciences with emphasis on real-world systems, deterministic, discrete, and stochastic models, introductory data-driven modeling approaches models formulation from physical principles, analysis of system behavior, models’ validation considering data, assumptions, uncertainty, and errors, dimensional analysis and scaling laws, dynamical systems, conservation laws, partial differential equations, and probabilistic modeling with basic reliability concepts, use of computational tools (MATLAB/Python) for simulation, visualization, and model evaluation.

Pre-requisites: MATH 333, and STAT 201

Numerical linear algebra with emphasis on computational methods for solving matrix problems arising in scientific computing and data-driven applications, Matrix factorizations, least squares, singular value decomposition, conditioning, eigenvalue problems, iterative methods, efficient implementation and practical use in high-dimensional settings, including applications in data analysis and machine learning.

Pre-requisites: MATH 371 or CIE 301 or MATH 225 or MATH 208

Modern cryptography from a provable security perspective, formal security definitions (confidentiality, integrity, authentication), public-key encryption, signatures schemes, message authentication codes (MACs), zero-knowledge proofs, and foundational cryptographic protocols.

Pre-requisites: MATH 210, STAT 201, ICS 202

Foundations of error-correcting codes and their information-theoretic limits, code parameters, Hamming distance, linear codes, finite fields, fundamental bounds on codes, Reed–Solomon codes, channel capacity, Shannon’s theorem, list decoding, and polynomial-based codes including Reed–Muller codes.

Pre-requisites: MATH 210 and (MATH 225 or MATH 208)

Note: Not to be taken with EE 430

Advanced methods for high-dimensional, simulation-based engineering optimization; problem formulation, derivative computation including automatic differentiation, gradient-based optimization algorithms, derivative-free and heuristic methods, surrogate modeling and experimental design, and an introduction to optimization under uncertainty and robust design.

Pre-requisites: (MATH 104 or MATH 201), ICS 104, MATH 373