400

MATH 407 Introduction to Graph Theory

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.

Credits

3.0

Cross Listed Courses

Double-numbered course; offered with graduate-level MATH 507

Offered

Spring Semester (Odd Years)

MATH 409 Elementary Number Theory

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.

Credits

3.0

Cross Listed Courses

Double-numbered course; offered with graduate-level MATH 509

Offered

Fall Semester (Odd Years)

MATH 440 Introduction to Abstract Algebra

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.

Credits

3.0

Offered

Spring Semester (Even Years)

MATH 453 Introduction to Real Analysis

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.

Credits

3.0

Offered

Spring Semester (Odd Years)

MATH 454 The Real Number System

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.

Credits

1.0

Offered

Fall Semester (Even Years)

MATH 456 Numerical Analysis

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.

Credits

3.0

Offered

Fall Semester (Even Years)

MATH 470 Seminar: The History of Mathematics

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.

Credits

2.0

Offered

Fall Semester

MATH 471 Research Project in the History of Mathematics

Prerequisite: MATH 470. Each student will complete a conference poster and a substantial research paper on a topic in the history of mathematics. Students will present the results of their research at an appropriate venue.

Credits

1.0

Core

Global Perspectives

Offered

Spring Semester

MATH 499 Departmental Honors

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.

Credits

6.0

Offered

Year Long