Characterizations of optimal solutions and efficient algorithms for optimization problems over discrete structures. Topics include network flows,...
Formulation of problems as integer linear programs. Solution by branch-and-bound and cutting plane algorithms. Introduction to the theory of valid...
Network design under constraints on cost, capacity, distance and reliability. Approximation algorithms. The set covering problem. Tree solutions:...
An overview of practical optimization problems that can be posed as scheduling problems. Characterizations of optimal schedules. Simple and efficient...
A broad introduction to game theory and its applications to the modeling of competition and cooperation in business, economics and society. Two-person...
An undergraduate seminar in optimization. The primary objective is to study recent work in specific areas of optimization. Course content may vary...
An introduction to the modern theory of convex programming, its extensions and applications. Structure of convex sets, separation and support,...
Theory and practical algorithms for nonlinear continuous optimization. Fundamentals of unconstrained optimization: conjugate gradient methods and...
Optimization over convex sets described as the intersection of the set of symmetric, positive semidefinite matrices with affine spaces. Formulations...
An in-depth examination of the origins of mathematics, beginning with examples of Babylonian mathematics. Topics may include Pythagorean triples,...
Basics of computational complexity; basics of quantum information; quantum phenomena; quantum circuits and universality; relationship between quantum...
An in-depth study of public-key cryptography. Number-theoretic problems: prime generation, integer factorization, discrete logarithms. Public-key...
A broad introduction to cryptography, highlighting the major developments of the past twenty years. Symmetric ciphers, hash functions and data...
Department Consent Required Prereq: Not open to General Mathematics students