# 4000 Level - Electives

**MTH 4314 - Abstract Algebra **

Prerequisite(s): A grade of C or above in MTH 3312.

Fundamentals of group, ring, and field theory. Topics include permutation groups, group and ring homomorphisms, direct products of groups and rings, quotient objects, integral domains, field of quotients, polynomial rings, unique factorization domains, extension fields, and finite fields.

**MTH 4322 - Numerical Analysis (Cross-listed as CSI 4322) **

Prerequisite(s): A grade of C or above in MTH 2321.

Numerical evaluation of derivatives and integrals, solution of algebraic and differential equations, and approximation theory.

**MTH 4326 - Advanced Calculus I **

Prerequisite(s): A grade of C or above in MTH 3323.

Sequences and series of functions, multiple integrals, improper multiple integrals, functions of several variables, extreme value problems, and implicit function theorems.

**MTH 4327 - Advanced Calculus II **

Prerequisite(s): A grade of C or above in MTH 4326.

Line and surface integrals, Green, Gauss, Stokes theorems with applications, Fourier series and integrals, functions defined by integrals, introduction to complex functions.

**MTH 4328 - Numerical Linear Algebra (Cross-listed as CSI 4328) **

Prerequisite(s): A grade of C or above in MTH 2311 and 3324.

Numerical methods for solution of linear equations, eigenvalue problems, and least squares problems, including sparse matrix techniques with applications to partial differential equations.

**MTH 4329 - Theory of Functions of a Complex Variable **

Prerequisite(s): A grade of C or above in MTH 2321.

Number systems: the complex plane; fractions, powers, and roots; analytic functions; elementary functions; complex integration; power series; mapping by elementary functions; calculus of residues.