Graduate Courses at MSCS - MSCS supplemental public website

Computer Algorithms II (Gyorgy Turan)

PREREQUISITES:: MCS 401.
DESCRIPTION:: 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.

Combinatorial Optimization (Will Perkins)

PREREQUISITES:: MCS 423 and Stat 471.
DESCRIPTION:: Network flows, bipartite matching, Edmonds algorithm for non-bipartite matching, the matching polytope, matroids, greedy algorithm.

Analytic Symbolic Computation (Jan Verschelde)

PREREQUISITES:: Grade of C or better in MCS 460 or the equivalent, and MATH 480 or consent of the instructor.
DESCRIPTION:: Analytic computation, including integration algorithms, differential equations, perturbation theory, mixed symbolic-numeric algorithms, and other related topics.

Numerical Methods for Partial Differential Equations (Gerard Awanou)

PREREQUISITES:: Math 481 and MCS 471 or consent of instructor.
DESCRIPTION:: 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.

Topics in Numerical Analysis of Partial Differential Equations (David Nicholls)

PREREQUISITES:: Math 481 and MCS 471, or concurrent enrollment.
DESCRIPTION:: The Finite element Method: continuous and discontinuous Galerkin Formulations. A description of the Finite Element Method (FEM) for elliptic boundary value problems. Theoretical developments include weak formulations, the continuous Galerkin method, and convergence theory. Numerical details include relevant data structures, Lagrange triangles of linear and arbitrary degree, and techniques for accelerating the solution procedure.

Advanced Topics in Computer Science (Yu Cheng)

PREREQUISITES:: Background in algorithms and linear algebra recommended. Undergraduate,graduate students, and non-CS PhDs welcome.
DESCRIPTION:: Spectral graph theory: graph Laplacians, eigenvalues and eigenvectors of graphs, conductance and Cheeger's inequality, graph sparsification, effective resistance, faster algorithms for solving Laplacian linear systems and maximum flows, some applications to designing fast and robust learning algorithms.

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Graduate Courses at MSCS - MSCS@UIC