General theory of measure and integration and its specialization to Euclidean spaces and Lebesgue measure; modes of convergence, Lp spaces, product spaces, differentiation of measures and functions, signed measures, Radon-Nikodym theorem.

Introduction to groups, rings, and fields. Direct sums and products of groups, cosets, Lagrange's theorem, normal subgroups, quotient groups. Polynomial rings, UFDs and PIDs, division rings. Fields of fractions, GCD and LCM, irreducibility criteria for polynomials. Prime field, characteristic, field extension, finite fields. Some topics from Math 612 included.

Not available at this time

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.

The Commonwealth Honors College thesis or project is intended to provide students with the opportunity to work closely with faculty members to define and carry out in-depth research or creative endeavors. It provides excellent preparation for students who intend to continue their education through graduate study or begin their professional careers. The student works closely with their 499Y Honors Research sponsor to pursue research on a topic or question of special interest to them in preparation for writing a 499T Honors Thesis or completing a 499P Honors Project.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses:

- are 6 credits or more of sustained research on a single topic, typically conducted over two semesters.

- begin with creative inquiry and systematic research.

- include documentation of substantive scholarly endeavor.

- culminate in an oral defense or other form of public presentation.

Honors Project expectations are high. The intended end-product is a traditional project manuscript with accompanying artifact(s), all projects:

- are 6 credits or more of sustained research on a single topic, typically conducted over two semesters.

- begin with creative inquiry and systematic research.

- include documentation of substantive scholarly endeavor.

- culminate in an oral defense or other form of public presentation.

Not available at this time

Not available at this time

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Theory applied to develop algorithms and computational techniques of computer science and to cryptography. To help learn these materials, students will be assigned computational projects using computer algebra software. Prerequisite: MATH 233 and 235. Math 300 or COMPSCI 250 as a co-requisite is not absolutely necessary but highly recommended.