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MTH 402 Linear Algebra with Applications
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 141
or permission of instructor.
Vector spaces, matrices, systems of linear equations, determinants, inner products, linear transformations, similar matrices, eigenvalues and eigenvectors of a matrix. | 3 | 0 | 0 | | |
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MTH 405 Introduction to Modern Algebra I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
Sets and mappings, an axiomatic approach to the number system, groups, rings, ideals, fields, isomorphism theorems, induction, permutations. | 3 | 0 | 0 | | |
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MTH 406 Introduction to Modern Algebra II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
Euclidean domains, polynomial rings, field extension, finite fields, finite groups, p-groups, the Sylow theorems, introduction to Galois theory. | 3 | 0 | 0 | | |
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MTH 410 Foundations of Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
(Prerequisite: MTH 402 or permission of instructor.)
Logic, set theory, axiomatic structure of the number system, infinite sets, cardinal numbers, ordinal numbers, axiom of choice. | 3 | 0 | 0 | | |
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MTH 415 Theory of Numbers
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 142
Divisibility, congruences, quadratic reciprocity, number theoretic functions, Diophantine equations, prime number theorems, recent developments in number theory. | 3 | 0 | 0 | | |
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MTH 423 Probability
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 241
Probability theory based on the Kolmogorov axioms, combinatorics, independence, random variables, expectation, probability distributions, Chebyshev's inequality, central limit theorem. | 3 | 0 | 0 | | |
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MTH 435 Modern Analysis I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
Techniques of mathematical proofs chosen from real numbers, sets, functions, point set theory, theory of limits, continuity, differentiation, Riemann integral, and infinite series. | 3 | 0 | 0 | | |
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MTH 436 Modern Analysis II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 435
Infinite series, sequences of functions, differentiation of functions of several variables, maxima and minima, function spaces, norms, operator theory. | 3 | 0 | 0 | | |
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MTH 451 Techniques of Advanced Calculus
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 214
Mth 372
Real vector spaces, Laplace transforms, Fourier series, boundary value theorems, series solution about singular points, Bessel functions, Legendre polynomials. | 3 | 0 | 0 | | |
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MTH 452 Nonlinear Differential Equations
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 451
Boundary value problems, asymtotic solutions, autonomous systems, systems of equations, applications. | 3 | 0 | 0 | | |
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MTH 453 Linear Partial Differential Equations
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 451
First- and second-order equations, initial and boundary value problems, integral transforms, Green's function, perturbations, variational and asymtotic methods. | 3 | 0 | 0 | | |
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MTH 455 Operations Research
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
Linear programming, project scheduling, dynamic programming, integer programming, queuing theory. | 3 | 0 | 0 | | |
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MTH 459 Principles of Model Building
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Introduction to the ideas of a mathematical model and model building, linear programming models, game-theoretic models, regression analysis models. Applications in business, ecology, psychology, sociology, and political science. | 3 | 0 | 0 | | |
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MTH 461 Transformational Geometry
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 142
Transformations of the Euclidean, affine and projective planes. Classification of these transformations by groups and their invariant properties. | 3 | 0 | 0 | | |
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MTH 462 The Projective Plane
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 142
An axiomatic development of the projective plane, models of the projective plane, analytic plane geometry. | 3 | 0 | 0 | | |
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MTH 466 Introduction to Topology
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 435
Topics to be chosen from metric spaces, topological spaces, compactness, product spaces, the Tychonoff theorem, rubber sheet geometry, Euler's formula, the Four-Color Problem, the Jordan curve theorem, topological properties of figures. | 3 | 0 | 0 | | |
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MTH 477 Concepts of Modern Elementary School Mathematics I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
(Credit applies only in undergraduate or graduate programs in mathematics education.) Sets, logic, mathematical systems, systems of numeration, natural numbers, whole numbers, integers, rational numbers, real numbers. | 3 | 0 | 0 | | |
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MTH 478 Concepts of Modern Elementary School Mathematics II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
(Credit applies only in undergraduate or graduate programs in mathematics education.) Foundations of algebra, metric and nonmetric geometry, probability and statistics. | 3 | 0 | 0 | | |
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MTH 480 Analysis for Teachers
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
(Credit applies only in undergraduate or graduate programs in mathematics education.) Topics chosen from algebra and trigonometry, including roots of polynomial equations, root approximation techniques, the factor theorem, the remainder theorem, Descartes' rule of signs, trigonometric functions, law of sines, law of cosines, complex numbers. | 3 | 0 | 0 | | |
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MTH 490 Topics in Advanced Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
(Prerequisite: Permission of the chairperson.)
Course may be repeated for additional credit. Content of the course varies according to the needs or desires of the students. | 1 | 0 | 0 | | |
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MTH 502 Advanced Linear Algebra
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
Vector spaces, linear transformations, canonical matrices, metric spaces, linear programming optimization, applications to business and engineering. | 3 | 0 | 0 | | |
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MTH 505 Introduction to Modern Algebra I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 402
or permission of chair.
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 506 Introduction to Modern Algebra II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
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 507 Theory of Groups
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
Groups, normal subgroups, homomorphism, Abelian groups, Sylow theorems, permutation groups, composition series, solvable groups. | 3 | 0 | 0 | | |
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MTH 508 Theory of Rings and Fields
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
Rings, ideals, fields, extensions, Galois theory of fields, Noetherian rings. | 3 | 0 | 0 | | |
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MTH 515 Advanced Theory of Numbers
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 415
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 523 Advanced Probability
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
MTH 423
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 524 Theory of Statistical Estimation and Testing Hypotheses
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 427
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 527 Applied Probability and Statistics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 241
Elements of sampling and descriptive statistics, sampling distributions, estimation and hypothesis testing, regression and correlation analysis. | 3 | 0 | 0 | | |
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MTH 528 Analysis of Variance
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 427
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 533 Measure Theory
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 436
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 534 Functional Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 435
Normed linear spaces, Banach spaces, Hilbert spaces. | 3 | 0 | 0 | | |
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MTH 537 Complex Variables
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 241
Analytic functions, complex integration, application of Cauchy's theorem, power series, conformal mapping, applications. | 3 | 0 | 0 | | |
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MTH 549 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 550 Vector and Tensor Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 372
or equivalent.
Vector differential calculus, vector interval calculus, functions of a complex variable, conformal mappings. | 3 | 0 | 0 | | |
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MTH 552 Non-Linear Partial Differential Equations I
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 550
or equivalent.
Formal and computational aspects of solutions and related equations. Focus on engineering applications. | 3 | 0 | 0 | | |
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MTH 553 Non-Linear Partial Differential Equations II
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Formal and computational aspects of Navier-Stokes and related equations. Focus on engineering applications. | 3 | 0 | 0 | | |
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MTH 557 Graduate Applied Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 241
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 558 Graduate Applied Analysis
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 372
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 560 Graph Theory
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
(Prerequisite: Permission of instructor.)
Trees, connectivity, coverings, planarity, colorability, networks, digraphs. | 3 | 0 | 0 | | |
|
MTH 563 Algebraic Geometry
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 405
MTH 461
Plane algebraic curves, singularities, formal power series, transformations. | 3 | 0 | 0 | | |
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MTH 565 Differential Geometry
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 436
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 566 General Topology
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
MTH 466
Abstract topological spaces, classification and properties, Moore-Smith convergence, compact and uniform spaces. | 3 | 0 | 0 | | |
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MTH 590 Topics in Graduate Mathematics
| Credit Hours | Recitation/Lecture Hours | Studio Hours | Clinical Hours | Lab Hours |
Prerequisites:
(Prerequisite: Permission of the chairperson.)
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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