400

Prerequisite: MATH 333 or equivalent A rigorous study of the theory of graphs, including simple and directed graphs, circuits, graph algorithms, connectedness, planarity and coloring problems.

Prerequisite: MATH 333 An introduction to the theory of numbers: divisibility, prime numbers, unique factorization, congruences, Euler’s phi-function, Fermat’s and Wilson’s theorems, multiplicative functions, quadratic reciprocity, perfect numbers and applications to Diophantine equations. Applications include public-key cryptography and integer arithmetic.

Prerequisites: MATH 333 and MATH 339, or permission of the instructor. The study of the basic structures of modern abstract algebra: groups, rings and fields. Topics include cosets, direct products, homomorphisms, quotient structures and factorization. Applications may include symmetry groups, coding theory and connections with graph theory.

Prerequisites: MATH 253 and MATH 333, or permission of the instructor. An introduction to real analysis and its development: infinite series, differentiability, continuity, the Riemann and Cauchy integrals, uniform convergence. Computer exploration and visualization are an essential part of the course.

Prerequisites: MATH 253 and MATH 333. A theoretical development of the real number system. Properties of real numbers. Binary operations. Associative, commutative, and distributive laws. Rational and irrational numbers. Laws of exponents. Radicals. Decimal representation. This course is intended only for students enrolled in the secondary mathematics education program. A student may not receive credit for both MATH 454 and MATH 453.

Prerequisites: MATH 339 or permission of the instructor. The theory and applications of numerical computing: interpolation and curve-fitting, solutions of algebraic and functional equations, numerical integration, numerical solutions of differential equations.

Prerequisites: Senior standing and either MATH 440 OR MATH 453 or permission of the department. A seminar in the history of mathematics. Students will use primary and secondary resources, both print and non-print, to explore the history of mathematics from pre-history to the present.

Prerequisite: By invitation of the department. The departmental honors paper is a two-semester senior-year program designed for students who wish to pursue intensive research or special projects in close coordination with faculty advisers. Departmental honors students are known as the Christine P. Tischer Scholars and receive 6 credits for this work.