400

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

A foundations course in elementary geometry discussing the following: incidence geometries; finite, metric, and synthetic geometries; Euclidean, hyperbolic, and elliptical geometries; and some axiomatic theory.

An introduction to fundamental concepts in point-set topology. Topics are taken from the following: open and closed sets, continuity, connectedness, compactness, separability, metric spaces.

The study of algebraic structures that are like the integers, polynomials, and the rational numbers. The integers and their properties. Groups: examples, properties, and counting theorems. Rings: examples and properties. Fields: roots of polynomials and field extensions.

Unique factorization in special rings. Field theory and the use of groups to understand field extensions: finite fields, Galois theory. Classical construction problems, solution of n-th degree polynomials.

Cryptography is the science of encoding and decoding information for the purpose of secure communication. With an emphasis on utilization of both modern and classical cryptosystems, this course introduces students to the mathematical underpinnings of cryptography.

Numerical techniques for computer-aided solution and analysis of systems using MATLAB. Emphasis on applications from engineering and the physical sciences. Topics covered may include non-linear equations, systems of equations, interpolation, integration and differentiation, and ordinary and partial differential equations.

Probability, discrete and continuous random variables, expectation, important probability distributions, introduction to sampling, estimation, and hypothesis testing.

Credit arranged.

Carries a title reflecting the subject or subjects studied and/or the nature of the class structure. May be repeated for credit.

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.

Math 497 is a course for students with strong mathematical preparation.  Students will work in teams on a project from an industrial or governmental firm.  Student success will depend on realistic industry evaluations such as teamwork, communication, individual initiative, and final products.

Research, study, or original work under the direction of a faculty mentor, leading to a scholarly thesis document with a public presentation of results. Requires approval of thesis director, department chair, dean, and the director of the honors program, when appropriate.