# 4000 Level

**MTH 4312 - Cryptology**

Prerequisite(s): MTH 2311, and either MTH 3312 or CSI 2350; or consent of instructor.

Introduction to cryptology, the study of select codes and ciphers. Included is a historical content, a survey of modern crypto systems, and an exposition of the rule of mathematical topics such as number theory and elliptic curves in the subject. Mathematical software will be available.

**MTH 4313 - Number Theory**

Pre-requisite(s): A grade of C or above in MTH 3300 or consent of instructor.

Algebraic number theory including linear Diophantine equations, distribution of primes, congruence, number theoretic functions, Euler's and Wilson's theorems, Pythagorean triples, Mersenne and Fermat primes, Fibonacci numbers, and sums of squares. Continued fractions, quadratic reciprocity, Mobius inversion, Bertrand's postulate, prime number theorem, and zeta function may also be included.

**MTH 4314 - Abstract Algebra**

Prerequisite(s): A grade of C or above in MTH 3312 and a grade of C or above in MTH 4316, or consent of the instructor.

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 4316 - Linear Algebra and Matrix Theory**

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

Matrix calculus, eigenvalues and eigenvectors, canonical forms, orthogonal and unitary transformation, and quadratic forms. Applications of these concepts.

**MTH 4322 - Numerical Analysi**s (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 4324 - Systems of Ordinary Differential Equations**

Prerequisite(s): A grade of C or above in MTH 2311 and MTH 3325.

A continuation of MTH 3325 with emphasis on systems of ordinary differential equations. Topics include matrix and first order linear systems of differential equations, eigenvalues and eigenvectors, two-dimensional autonomous systems, critical point analysis, phase plane analysis, Liapunov, stability theory, limit cycles and Poincare-Bendixson theorem, periodic solutions, perturbation methods, and some fixed point theory.

**MTH 4326 - Advanced Calculus I**

Prerequisite(s): A grade of C or above in MTH 2321 and MTH 3323 or consent of instructor.

The real and complex number systems, basic topology, numerical sequences and series, continuity, differentiation, integration, sequences and series of functions

**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.

**MTH 4343 - Topics in Mathematics for Prospective Teachers**

Prerequisite(s): A grade of C or above in MTH 3312, 3323, or 3350.

Prospective middle and secondary school mathematics teachers engage in an in-depth analysis of mathematical topics encountered in the middle and secondary curriculum. Does not apply toward the mathematics major.

**MTH 4375 - Linear Programming**

Prerequisite(s): A grade of C or above in MTH 2311 and 3370.

An introduction to the theory and applications of linear programming, including the simplex algorithm, duality, sensitivity analysis, parametric linear programming, and integer programming, with applications to transportation, allocation problems, and game theory.

**MTH 4V90 - Topics in Mathematics** 1 to 3 sem. hrs.

Prerequisite(s): Consent of instructor.

Topics in contemporary mathematics not covered in ordinary courses. May be repeated once for credit if content is different.