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MTH 5020 Advanced Linear Algebra
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Vector spaces, linear transformations, canonical matrices, metric spaces, linear programming optimization, applications to business and engineering. | 3 | 0 | 0 | | |
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MTH 5050 Introduction to Modern Algebra I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4020 (Minimum Grade of C, May not be taken concurrently)
Sets and mapping, an axiomatic approach to the number system, general algebraic systems, groups, rings and ideals, fields, isomorphism theorems. | 3 | 0 | 0 | | |
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MTH 5060 Introduction to Modern Algebra II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 5050 (Minimum Grade of C, May not be taken concurrently)
Euclidean domains, polynomial rings, field extensions, finite fields, finite groups, p-groups, the Sylow theorems, introduction to Galois theory. | 3 | 0 | 0 | | |
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MTH 5070 Theory of Groups
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Groups, normal subgroups, homomorphism, Abelian groups, Sylow theorems, permutation groups, composition series, solvable groups. | 3 | 0 | 0 | | |
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MTH 5080 Theory of Rings and Fields
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4050 (Minimum Grade of C, May not be taken concurrently)
Rings, ideals, fields, extensions, Galois theory of fields, Noetherian rings. | 3 | 0 | 0 | | |
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MTH 5150 Advanced Theory of Numbers
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4150 (Minimum Grade of C, May not be taken concurrently)
Farey fractions, distribution of primes, quadratic forms, representation of integers as sums of k-th powers, quadratic fields, introduction to algebraic number theory and foundations of analytic number theory. | 3 | 0 | 0 | | |
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MTH 5230 Advanced Probability
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4350 (Minimum Grade of C, May not be taken concurrently)
MTH 5230 (Minimum Grade of C, May not be taken concurrently)
Probability spaces, extension of probability, Boolean semi-algebras, compact classes, integration of random variables, Laplace spaces, product of measurable spaces, conditional expectations and Martingales, ergodic theory and Markov processes. | 3 | 0 | 0 | | |
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MTH 5240 Theory of Statistical Estimation and Testing Hypotheses
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4270 (Minimum Grade of C, May not be taken concurrently)
Testing of hypotheses in one-parameter cases, power of a test, most powerful critical regions, asymptotically best tests, estimation of a single parameter, some properties of efficient statistics, the multi parameter theory. | 3 | 0 | 0 | | |
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MTH 5270 Applied Probability and Statistics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)
Elements of sampling and descriptive statistics, sampling distributions, estimation and hypothesis testing, regression and correlation analysis. | 3 | 0 | 0 | | |
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MTH 5280 Analysis of Variance
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4270 (Minimum Grade of C, May not be taken concurrently)
Completely randomized design, randomized complete block design, Latin square design, complete factorial designs, split-plot designs, analysis of covariance, multivariate regression, covariance and correlation, introduction to distribution-free methods. | 3 | 0 | 0 | | |
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MTH 5330 Measure Theory
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4360 (Minimum Grade of C, May not be taken concurrently)
Lesbegue outer measure and Lesbegue measure of sets, measurable functions, Lesbegue integrable functions and square integrable functions. | 3 | 0 | 0 | | |
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MTH 5340 Functional Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4350 (Minimum Grade of C, May not be taken concurrently)
Normed linear spaces, Banach spaces, Hilbert spaces. | 3 | 0 | 0 | | |
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MTH 5370 Complex Variables
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)
Analytic functions, complex integration, application of Cauchy's theorem, power series, conformal mapping, applications. | 3 | 0 | 0 | | |
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MTH 5490 Graduate Seminar
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Students undertake a significant mathematical project in area of interest to them, prepare a scholarly paper, and make an oral presentation in class. This should ordinarily be taken in the last semester of graduate studies. | 3 | 0 | 0 | | |
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MTH 5500 Vector and Tensor Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 3720 (Minimum Grade of C, May not be taken concurrently)
Vector differential calculus, vector interval calculus, functions of a complex variable, conformal mappings. | 3 | 0 | 0 | | |
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MTH 5520 Non-Linear PDE's I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 5500 (Minimum Grade of C, May not be taken concurrently)
Formal and computational aspects of solutions and related equations. Focus on engineering applications. | 3 | 0 | 0 | | |
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MTH 5530 Non-Linear PDE's II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 5500 (Minimum Grade of C, May not be taken concurrently)
Formal and computational aspects of Navier-Stokes and related equations. Focus on engineering applications. | 3 | 0 | 0 | | |
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MTH 5570 Graduate Applied Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)
Mathematical modeling concepts utilizing qualitative and quantitative variables and applied regression analysis. Practical interaction of mathematics, basic statistics and regression analysis. | 3 | 0 | 0 | | |
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MTH 5580 Graduate Applied Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 3720 (Minimum Grade of C, May not be taken concurrently)
Optimization concepts, maxima and minima for functions of one and several variables, calculus of variations using direct and indirect methods. | 3 | 0 | 0 | | |
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MTH 5600 Graph Theory
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Trees, connectivity, coverings, planarity, colorability, networks, digraphs. | 3 | 0 | 0 | | |
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MTH 5630 Algebraic Geometry
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4050 (Minimum Grade of C, May not be taken concurrently)
MTH 4610 (Minimum Grade of C, May not be taken concurrently)
Plane algebraic curves, singularities, formal power series, transformations. | 3 | 0 | 0 | | |
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MTH 5650 Differential Geometry
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4360 (Minimum Grade of C, May not be taken concurrently)
Theory of curves and surfaces in ordinary space, Frenet formulas, curves in a surface, developable surfaces, intrinsic geometry on a surface, geodesics, quadric surfaces, ruled surfaces. | 3 | 0 | 0 | | |
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MTH 5660 General Topology
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 4660 (Minimum Grade of C, May not be taken concurrently)
Abstract topological spaces, classification and properties, Moore-Smith convergence, compact and uniform spaces. | 3 | 0 | 0 | | |
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MTH 5900 Topics in Graduate Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Course may be repeated for additional credit. Content of the course varies according to the needs and desires of the student. | 1 | 0 | 0 | | |
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