Mathematical Theory of Artificial Intelligence
- MCS 541.
- Valiant's learning model, positive and negative results in learnability, automation inference, perceptrons, Rosenblatt's theorem, convergence theorem, threshold circuits, inductive inference of programs, grammars and automata.
Analytic Symbolic Computation
- Grade of C or better in MCS 460 or the equivalent, and MATH 480 or consent of the instructor.
- Analytic computation, including integration algorithms, differential equations, perturbation theory, mixed symbolic-numeric algorithms, and other related topics.
Advanced Topics in Combinatorial Theory: Extremal Combinatorics
- An undergraduate course in combinatorics/graph theory or probability, and the mathematical maturity of a (relatively advanced) graduate student.
- Extremal combinatorics studies the extreme value of a parameter over a class of discrete objects. The subject has been growing for the past century and by now it encompasses some of the most important contributions to combinatorics and has applications to many other disciplines including discrete geometry, number theory, coding theory, computer science. This course will study the modern developments in the subject focusing on graph and hypergraph theory. Throughout the course open problems will be presented that are suitable for thesis research
Computer Algorithms II
- MCS 401.
- Continuation of MCS 401. Advanced topics in algorithms, lower bounds, union-find problems, fast Fourier transform, complexity of arithmetic, polynomial and matrix calculations, approximation algorithms, parallel algorithms.
Numerical Methods for Partial Differential Equations
- Math 481 and MCS 471 or consent of instructor.
- Finite difference methods for parabolic, elliptic and hyperbolic differential equations: explicit, Crank-Nicolson implicit, alternating directions implicit, Jacobi, Gauss-Seidel, successive over-relaxation, conjugate gradient, Lax-Wendroff, Fourier stability.
Introduction to Supercomputing
- MCS 471 or 571 or consent of instructor.
- Introduction to supercomputing on vector and parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines.
Advanced Topics in Computer Science: Turan