MATH-650 Abstract Algebra

Elementary number theory, polynomial and abstract rings, ideals and quotient rings, PID's and Eclidean rings, groups, cyclic and Abelian groups, direct products, algebraic field extensions, splitting fields, field automorphisms, finite fields.
Further topics may include Noetherian rings and finitely generated Abelian Groups.
Prerequisite: Undergraduate abstract algebra

MATH-688 Combinatorics and Graph Theory I

Combinatorial enumeration, designs and geometries, graphs, set systems, partially ordered sets, existence and construction of various combinatorial objects, Ramsey theory.
Prerequisite: MATH-650 or consent from instructor

MATH-689 Combinatorics and Graph Theory II

Methods of linear algebra in combinatorics and graph theory, basics of coding theory and associated designs, number theory and cryptography, communication complexity.
Prerequisite: Knowledge of linear algebra

MATH-845 Groups and Their Applications

Review of elementary group theory, permutation groups, group actions, Sylow theorems, semi-direct and wreath products, classical matrix groups, automorphism groups of combinatorial structures, Polya enumeration.
Further topics may include representation theory, free groups, finite groups of isometries of Euclidean spaces.
Prerequisite: MATH-650 or consent of instructor

MATH-850 Theory of Probability

Mathematical rigorous treatment of probability theory with emphasis on methods and tools for applications. Axioms of probability and independence. The weak and strong laws of large numbers, the central limit theorems and Poisson convergence. An introduction to large deviation theory and martingale theory. Probabilistic methods in combinatorics and analysis.
Prerequisite: MATH-602 or consent of instructor

MATH-884 Finite Geometries and Designs

Classical projective and affine spaces, nondesarguesian planes, coordinate systems, spreads and packings, conics and unitals, collineation groups and Singer cycles.
Further topics chosen from related geometrical designs, associated codes, and algebraic surfaces/varieties.
Prerequisite: MATH-688, MATH-845

MATH-885 Extremal Combinatorics

Topics from extremal graph theory, extremal set theory, and combinatorial geometry. Methods used will be algebraic, geometric, and probabilistic.
Prerequisite: MATH-688, MATH-689

MATH-826 Topics in Pure Mathematics

Topics vary from year to year and will be chosen from a variety of areas in pure mathematics (not necessarily discrete mathematics).
Prerequisite: Requires permission of instructor

Last modified by Renate Scheidler