500
An introduction to the theory, practical applications, and algorithms of linear programming and nonlinear programming. Prerequisites:
MTH 233 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233 or graduate standing
Corequisites
None.
Properties of integers, divisibility, the Euclidean algorithm, distribution of primes, congruences, arithmetic functions, quadratic reciprocity. MTH 321 and MTH 521 cannot be taken in the same semester. Prerequisite: MTH 523 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 523 or graduate standing.
Corequisites
None.
Groups, rings, integral domains, fields, and fundamental homomorphism theorems. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate status
Corequisites
None.
Vector spaces, subspaces, bases and dimensions; linear transformations, their algebra, their representation by matrices, and linear functionals; eigenvalues, triangularizable and diagonalizable transformations; inner product spaces. Prerequisite:
MTH 523 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 523 or graduate status
Corequisites
None.
Representation theory of finite groups, Specht modules, combinatorics of Young tableaux, and symmetric functions. Prerequisite:
MTH 525.
Credits
3(3-0)
Prerequisites
MTH 525
Corequisites
None.
Rigorous development of calculus for functions of one variable. The real number system, sequences, limits, continuity, differentiation, integration, exponential and logarithmic functions, series, uniform convergence. Credits will not count towards MA or Ph.D. degree requirements in mathematics. Prerequisites:
MTH 233, 332; or graduate status.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 332; or graduate status
Corequisites
None.
Continuation of
MTH 532. Rigorous development of calculus of several variables. Limits, continuity, differentiation, integration, implicit and inverse function theorems, differential forms. Prerequisite:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 532
Corequisites
None.
High order equations, series solutions, Bessel functions, nonlinear differential equations, stability, introduction to partial differential equations, boundary value problems, SturmLiouville theory, applications to physical/engineering sciences. Prerequisites:
MTH 233, 334; or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 334; or graduate standing
Corequisites
None.
Differential geometry of curves and surfaces. Curvature, maps between surfaces, vector fields and differential forms, Stokes' theorem, Euler characteristic, Gauss-Bonnet theorem. Prerequisites:
MTH 233, 332; or admission to graduate program in Mathematics. Recommended:
MTH 532.
Credits
3(3-0)
Prerequisites
MTH 233, MTH 332; or admission to graduate program in Mathematics
Corequisites
None.
Sets, functions, metric spaces, topological spaces, homeomorphisms, compactness and connectedness, quotient spaces. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate status
Corequisites
None.
This course explores how popular culture (such as television, comics, movies, music and books) portrays mathematicians and mathematics as a discipline. Prerequisite: 45 credit hours completed or graduate status.
Credits
3(3-0)
Prerequisites
45 credit hours completed or graduate status.
Corequisites
None.
Survey of the history of mathematics, focusing on topics taught in secondary schools and undergraduate courses. Emphasis on representing diverse mathematics traditions and legacies. Prerequisite:
MTH 332 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 332 or graduate standing
Corequisites
None.
Introduction to enumerative combinatorics and graph theory. Topics include the graphs, networks and flows, partially ordered sets, principle of inclusion-exclusion, generating functions, and partitions. Prerequisites:
MTH 523.
Credits
3(3-0)
Prerequisites
MTH 523
Corequisites
None.
Theory and application of linear programming and mathematical programming. Simplex method, duality theory and sensitivity analysis, interior point algorithm, and mathematical programming problems. Prerequisite:
MTH 233 or graduate standing.
Credits
3(3-0)
Prerequisites
MTH 233 or graduate standing
Corequisites
None.
Subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed 6 hours. Prerequisite: Permission of instructor.
Credits
1-6(Spec)
Prerequisites
Permission of instuctor.
Corequisites
None.
The in-depth study of a topic in mathematics under the direction of a faculty member. Prerequisite: Permission of instructor.
Credits
1-6(Spec)
Prerequisites
Permission of instructor
Corequisites
None.