Graduate Courses
Graduate Mathematics Courses with descriptions
520. Solution of Nonlinear Systems.
II. 3 Hr. PR: MATH 420 or MATH 441. Solution of nonlinear systems of equations. Newton and Secant Methods. Unconstrained optimization. Nonlinear over relaxation techniques. Nonlinear least squares problems.
521. Numerical Analysis. I.
3 Hr. PR: MATH 261 and computer language. Number systems and errors,
interpolation by polynomials, linear systems, scalar algebraic equations and systems, optimization, approximation theory, integration initial, and boundary value problems.
522. Numerical Solution of PDE.
3 Hr. PR: MATH 261 and computer language. Finite difference and finite element methods for elliptic, parabolic, and hyperbolic problems. Study of properties such as consistency,
convergence, stability, conservation, and discrete maximum principles.
524. Middle School Number and Algebra 1.
2 cr hr. Co-requisite C&I 524. Designed only for in service middle school and elementary mathematics teachers. Sets of numbers as examples of algebraic systems, properties of groups, rings, and fields.
525. Middle School Number and Algebra 2.
2 cr hr. Co-requisite C&I 525. Continuation of Math 524. Designed only for in service middle school and elementary mathematics teachers. Properties of polynomials and polynomial rings. Mathematical modeling with finite differences and least squares.
528. Middle School Functions and Change 1.
2 cr hr. Co-requisite C&I 528. Designed only for in service middle school and elementary mathematics teachers. Function concept, operations on functions, limits, continuity, Intermediate Value Theorem, families of curves, optimization, area. Classroom applications, current research in learning. Applications in model curricula.
529. Middle School Functions and Change 2.
2 cr hr. Co-requisite C&I 529. Continuation of Math 528. Designed only for in service middle school and elementary mathematics teachers. Function concept, operations on functions, limits, continuity, Intermediate Value Theorem, families of curves, optimization, area. Classroom applications, current research in learning. Applications in model curricula.
530. Introduction to Applied Mathematics. S.
1-6 Hr. PR: MATH 251. (Designed especially for secondaryschool mathematics teachers; others admitted with departmental approval obtained before registration.) Problem solving and construction of mathematical models in the social, life, and physical sciences.
Examples illustrating the origins and use of secondary school mathematics in solving real world problems.
533. Modern Algebra for Teachers 1. I, S.
3 Hr. PR: MATH 251. (Designed especially for secondaryschool mathematics teachers. Others admitted with departmental approval obtained prior to registration.)
Introduction to algebraic structures; groups, rings, integral domains, and fields. Development and properties of the rational and real number systems.
534. Modern Algebra For Teachers 2. II, S.
3 Hr. PR: MATH 341 or MATH 533. Further investigation of algebraic structures begun in MATH 533. (Emphasis on topics helpful to secondary-school mathematics teachers.) Topics include Sylow theory, Jordan-Holder Theorem, rings and quotations, field extensions,
Galois theory, and solution by radicals.
535. Foundations of Geometry. S.
3 Hr. PR: MATH 251 (Designed especially for secondary mathematics teachers; others admitted with departmental approval obtained before registration.) Incidence geometrics
with models; order for lines and planes; separation by angles and by triangles; congruence; introduction to Euclidean geometry.
536. Transformation Geometry. S.
3 Hr. PR: MATH 341 or MATH 533. (Designed especially for
secondary-school mathematics teachers; others admitted with departmental approval obtained before registration.) A modern approach to geometry based on transformations in a vector space setting. The course unifies the development of geometry with the methods of modern algebra.
541. Modern Algebra. I, II.
3 Hr. PR: MATH 341 Concepts from set theory and the equivalence of the Axiom of Choice. Zorn‚s Lemma and the Well-Ordering Theorem; a study of the structure of groups, rings, fields, and vector spaces; elementary factorization theory; extensions of ring and fields; modules and ideals; and lattices.
543. Linear Algebra. II, S.
3 Hr. PR: MATH 441. Review of theory of groups and fields; linear vector spaces including the theory of duality; full linear group; bilinear and quadratic forms; and theory of isotropic and totally isotropic spaces.
545. Number Theory 1. I, II.
3 Hr. PR: MATH 155 or MATH 156. Introduction to classical number theory covering such topics as divisibility, the Euclidean algorithm, Diophantine equations, congruences,
primitive roots, quadratic residues, number-theoretic functions, distribution of primes, irrationals, and combinatorial methods. Special numbers such as those of Bernoulli, Euler, and Stirling.
551. Real Variables 1. I, II.
3 Hr. PR: MATH 451. A development of Lebesgue integral, function spaces and Banach spaces, differentiation, complex measures, the Lebesgue-Radon-Nikodym theorem.
555. Complex Variables 1. I, II.
3 Hr. PR: MATH 451. Number systems, the complex plane and its geometry. Holomorphic functions, power series, elementary functions, complex integration, representation theorems, the calculus of residues, analytic continuation and analytic function, elliptic functions, Holomorphic functions of several complex variables.
557. Calculus of Variations. II.
3 Hr. PR: (MATH 261 and MATH 452) or MATH 568. Necessary conditions and sufficient conditions for weak and strong relative minimums of an integral, Euler-Lagrange equation.
Legendre condition, field construction, Weierstrass excess function, and the Jacobi equation.
561. Geometric Modeling-Curves/Surf.
3 Hr. PR: MATH 261 and linear algebra. Mathematical techniques used in CAD/CAM environments, including conics, cubic splines, Bezier splines, B-splines rational Bezier and B-splines, interpolation, geometric continuity, and data exchange.
563. Mathematics Modeling.
3 Hr. PR: MATH 261 and MATH 465. This course is concerned with construction, analysis, and interpretation of mathematical models that shed light on important problems in the sciences. Emphasis is on the simplification, dimensional analysis, and scaling of mathematical models.
564. Intermediate Differential Equations. II.
3 Hr. PR: MATH 261. A rigorous study of ordinary differential equations including linear and nonlinear systems, self-adjoint eigenvalue problems, non-self-adjoint boundary-value problems, pertutbation theory of autonomous systems, Poincare-theorem.
565. Wave Propagation.
3 Hr. PR: MATH 465 or MATH 567 or consent. Study of waves in applied mathematics. The wave equation and geometrical optics, water waves, exact solutions, and interacting
solitary waves. Basic concepts of hyperbolic and dispersive waves, conservation laws and scalar PDE‚s shock waves, Bateman Burgers equation, and hyperbolic systems.
567. Advanced Calculus. I.
3 Hr. per semester. PR: MATH 261. Primarily for engineers and scientists. Functions of several variables, partial differentiation, implicit functions, transformations; line surface and volume integrals; point set theory, continuity, integration, infinite series and convergence, power series, and improper integrals.
568. Advanced Calculus. II.
3 Hr. per semester. PR: MATH 567. Primarily for engineers and scientists. Functions of several variables, partial differentiation, implicit functions, transformations; line surface and volume integrals; point set theory, continuity, integration, infinite series and convergence, power series, and improper integrals.
569. Seminar in Applied Mathematics.
1-12 Hr. PR: Consent. Selected topics in applied mathematics. Topics previously offered include applied linear algebra, computational fluid dynamics, numerical partial differential equations, ordinary differential equations, perturbation methods, and stochastic processes.
571. Combinatorial Analysis 1. I, II.
3 Hr. PR: One year of calculus. Permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, compositions, trees, and networks.
573. Graph Theory.
3 Hr. PR: MATH 343 and MATH 283. Basic concepts of graphs and digraphs, trees, cycles and circuits, connectivity, traversibility, planarity, colorability, and chromatic polynomials. Further topics from among factorization, line graph, covering and independence, graph matrices and groups, Ramsey theory, and packing theory.
578. Applied Discrete Mathematics.
3 Hr. PR: MATH 375 or MATH 378 or MATH 341 or MATH 343 or MATH 283. Topics may include combinatorial optimization, applied coding theory, integer programming,linear programming, matching, and network flows.
581. Topology 1. I, II
3 Hr. PR: MATH 452. A detailed treatment of topological spaces covering the topics of continuity, convergence, compactness, and connectivity; product and identification space, function spaces, and the topology in Euclidean spaces.
590. Teaching Practicum. I, II, S.
1-3 Hr. PR: Consent. Supervised practice in college teaching of mathematics. Note: this course is intended to insure that graduate assistants are adequately prepared
and supervised when they are given college teaching responsibility. It will also present a mechanism for students not on assistantships to gain teaching experience. (Grading will be S/U.)
591 A-Z. Advanced Topics. I, II. S.
1-6 Hr. PR: Consent. Investigation of advanced topics not covered in regularly scheduled courses.
592. Directed Study. I, II, S.
1-6 Hr. Directed study, reading, and/or research.
593 A-Z. Special Topics. I, II, S.
1-6 Hr. A study of contemporary topics selected from recent developments in the field.
595. Independent Study. I, II, S.
1-6 Hr. Faculty supervised study of topics not available through regular course offerings.
641. Modern Algebra 2. II.
3 Hr. PR: MATH 545. Concepts from set theory and the equivalence of the Axiom of Choice. Zorn‚s Lemma and the Well-Ordering Theorem; a study of the structure of groups, rings,
fields, and vector spaces; elementary factorization theory; extensions of ring and fields; modules and ideals; and lattices.
645. Number Theory 2. II.
3 Hr. PR: MATH 305. Introduction to classical number theory covering such topics as divisibility, the Euclidean algorithm, Diophantine equations, congruences, primitive roots,
quadratic residues, number-theoretic functions distribution of primes, irrationals, and combinatorial methods. Special numbers such as those of Bernoulli, Euler, and Stirling.
651. Real Variables 2. I, II.
3 Hr. PR: MATH 551. A development of the Lebesgue integral, function spaces and differentiation, complex measures, the Lebesgue-Radon-Nikodym theorem.
655. Complex Variables 2. I, II.
3 Hr. PR: MATH 555. Number systems, the complex plane and its geometry. Holomorphic functions, power series, elementary functions, complex integration, representation
theorems, the calculus of residues, analytic continuation and analytic function, elliptic functions, Holomorphic functions of several complex variables.
661. Geometric Modeling-Solids.
3 Hr. PR: MATH 561. Mathematical techniques used in CAD/CAM environments, including basic primitives, manifold and non-manifold solids, Euler characteristic, halfspace models, constructive solid geometry (CSG), boundary representation (B-rep), Euler operators,
Boolean operations, and data exchange.
671. Combinatorial Analysis 2. I, II.
3 Hr. PR: MATH 571. Permutations, combinations, generating functions, principle of inclusion and exclusion, distributions, partitions, compositions, trees, and networks.
677 A-Z. Topics in Discrete Mathematics.
3 Hr. PR: MATH 571 or MATH 543 or MATH 573. Topics may include algorithmic graph theory, combinatiorial designs, matroid theory, (0,1)-matrics, and permanents.
681. Topology 2. II.
3 Hr. PR: MATH 581. A detailed treatment of topological spaces covering the topics of continuity, convergence, compactness, and connectivity; product and identification space, function spaces, and the topology in Euclidean spaces.
683. Set Theory and Applications.
3 Hr. PR: MATH 541 or MATH 551 or MATH 581. The course concentrates on the typical methods of set theory, transfinite induction, and Zorn‚s Lemma with emphasis on their applications outside set theory. The fundamentals of logic and basic set theory are included.
690. Teaching Practicum. I, II, S.
1-3 Hr. PR: Consent. Supervised practice in college teaching of mathematics. Note: this course is intended to insure that graduate assistants are adequately prepared and supervised when they are given college teaching responsibility. It will also present a mechanism for students not on assistantships to gain teaching experience. (Grading will be S/U.)
691 A-Z. Advanced Topics. I, II. S.
1-6 Hr. PR: Consent. Investigation of advanced topics not covered in
regularly scheduled courses.
692. Directed Study. I, II, S.
1-6 Hr. Directed study, reading, and/or research. 693 A-Z. Special Topics. I, II, S. 1-6 Hr. A study of contemporary topics selected from recent developments in the field.
694. Seminar. I, II, S.
1-6 Hr. Seminars arranged for advanced graduate students.
695. Independent Study. I, II, S.
1-6 Hr. Faculty supervised study of topics not available through regular course offerings.
696. Graduate Seminar. I, II, S.
1 Hr. PR: Consent. It is anticipated that each graduate student will present at least one seminar to the assembled faculty and graduate student body of his/her program.
697. Research.
1-15 Hr. PR: Consent. Research activities leading to thesis, problem report, research
paper or equivalent scholarly project or a dissertation. (Grading may be S/U.)
698. Thesis or Dissertation. I, II, S.
2-4 Hr. PR: Consent. Note: this is an optional course for programs that believe that this level of control and supervision is needed during the writing of their students reports,
thesis, or dissertations. (Grading may be S/U.)
699. Graduate Colloquium. I, II, S.
1-6 Hr. PR: Consent. For graduate students not seeking coursework credit but who wish to meet residence requirements, use the University‚s facilities, and participate in its academic and cultural programs. Note: graduate students not actively involved in coursework or research are entitled, through enrollment in his/her department‚s 799 or 899 graduate colloquium, to consult with graduate faculty, participate in both formal and informal academic activities sponsored by his/her program, and retain all of the rights and privileges of duly enrolled students. (Grading is S/U; colloquium credit may not be counted against requirements for masters programs.)
740. Seminar in Number Theory. I, II.
............................................................1-12 Hr.
741. Group Theory 1.
.............................................................................................. 3 Hr.
742. Group Theory 2.
....................................................................... 3 Hr. PR: MATH 741.
743. Algebraic Theory Semi-Groups 1.
......................................... 3 Hr. PR: Math 641.
744. Algebraic Theory Semi-Groups 2.
........................................3 Hr. PR: MATH 743.
745. Analytic Number Theory 1. I, II.
3 Hr. PR: MATH 555 and MATH 645. Selected topics in analytic number theory such as the prime number theorem, primes in an arithmetical progression, the Zeta function, the Goldbach conjecture.
746. Analytic Number Theory 2. II.
3 Hr. PR: MATH 745. Selected topics in analytic number theory such as the prime number theorem, primes in an arithmetical progression, the Zeta function, the Goldbach conjecture.
750. Seminar in Analysis.
..................................................................................1-12 Hr.
751. Functional Analysis 1. I, II.
3 Hr. PR: MATH 551. A study of Banach and Hilbert spaces; the Hahn-Banach theorem, uniform boundedness principle, and the open mapping theorem; dual spaces and the
Riesz representation theorem; Banach algebras; and spectral theory.
752. Functional Analysis 2. I.
3 Hr. PR: MATH 751. A study of Banach and Hilbert spaces; the Hahn-Banach theorem, uniform boundedness principle, and the open mapping theorem; dual spaces and the
Riesz representation theorem; Banach algebras; c+algebras; spectral theory.
753. Special Functions. I, II,
3 Hr. PR: MATH 261 and MATH 452. Operational techniques, generalized hypergeometric functions, classical polynomials of Bell, Hermite, Legendre, Noerlund, etc. Introduction
to recent polynomial systems. Current research topics.
757. Theory of Partial Differential Equations 1. I, II.
3 Hr. PR: MATH 452. Cauchy-Kowaleski theorem, Cauchy‚s problem, the Dirichlet and Neumann problems, Dirichlet‚s principle, potential theory, integral equations, eigenvalue problems, numerical methods.
758. Theory of Partial Differential Equations 2. II.
3 Hr. PR: MATH 757. Cauchy-Kowaleski theorem, Cauchy‚s problem, the Dirichlet and Neumann problems, Dirichlet‚s principle, potential theory, integral equations, eigenvalue problems, numerical methods.
764. Asymptotic Methods.
3 hr. PR: MATH 564. Study of asymptotic methods for differential equations. Basic concepts˜asymptotic expansions, asymptotic approximation; asymptotic evaluations of integrals˜ Laplace‚s methods, Kelvin‚s methods, the steepest descent; asymptotic solutions of equations; perturbation of eigenvectors; the difference between singular and regular perturbations; multiple scale analysis; the method of matched asymptotic expansions; perturbations of periodic systems.
771. Matroid Theory 1. I.
3 Hr. PR: MATH 541 or MATH 543 and MATH 571 or MATH 573. Independent sets, circuits, bases, rank functions, closure operators and close sets, other axiom systems, geometric representations, duality and minors, linear and algebraic representability, connectivity, basics of partial ordered sets, flats and lattices, relationship between lattices and matroids.
772. Matroid Theory 2. II.
3 Hr. PR: MATH 771. Matroid representability, representability over finite fields, algebraic matroids,matroid constructions, higher connectivity of matroids, binary and ternary matroids, the splitter theorem and its applications, submodular functions, matroid intersection theorem, matroids in combinatorial optimizations.
773. Advanced Topics in Graph Theory.
3 Hr. PR: MATH 573. Topics may include: algebraic graph theory, random graph theory, extremal graph theory, topological graph theory, and structural graph theory. (May
be repeated for credit with consent.)
777. Advanced Topics in Combinatorics.
3 Hr. PR: MATH 571 or MATH 677. Topics may include:Combinatorics on finite sets, probabilistic methods in combinatorics, enumerations, Polya Theory, combinatorial matroid theory, coding theory, combinatorial identities, infinite combinatorics, transversal theory, and matriod theory. (May be repeated for credit with consent.)
780. Seminar in Topology.
................................................................................ 1-12 Hr.
781. Continuum Theory 1. I, II.
3 Hr. PR: MATH 581. The fundamental properties of continua (compact, connected, metric spaces), including boundary bumping, space filling curves, structure of special continua, and inverse limits.
782. Continuum Theory 2.
3 Hr. PR: MATH 781. The fundamental properties of continua (compact,
connected, metric spaces), including boundary bumping, space filling curves, structure of specialcontinua, and inverse limits.
783. Set Theory and Applications.
3 Hr. PR: MATH 683. The course elaborates on the applications of the transfinite induction, and combines recursion methods with other elements of modern set theory, including the use of additional axioms of set theory, introduction to the forcing method.
790. Teaching Practicum. I, II, S.
1-3 Hr. PR: Consent. Supervised practice in college teaching of mathematics. Note: this course is intended to insure that graduate assistants are adequately prepared and supervised when they are given college teaching responsibility. It will also present a mechanism for students not on assistantships to gain teaching experience. (Grading will be S/U.)
791 A-Z. Advanced Topics. I, II. S.
1-6 Hr. PR: Consent. Investigation of advanced topics not covered in regularly scheduled courses.
792. Directed Study. I, II, S.
1-6 Hr. Directed study, reading, and/or research.793 A-Z. Special Topics. I, II, S. 1-6 Hr. A study of contemporary topics selected from recent developments in the field.
794. Seminar. I, II, S.
1-6 Hr. Seminars arranged for advanced graduate students.
795. Independent Study. I, II, S.
1-6 Hr. Faculty supervised study of topics not available through regular course offerings.
796. Graduate Seminar. I, II, S.
1 Hr. PR: Consent. It is anticipated that each graduate student will present at least one seminar to the assembled faculty and graduate student body of his/her program.
797. Research. I, II, S.
1-15 Hr. PR: Consent. Research activities leading to thesis, problem report, research paper or equivalent scholarly project, or dissertation. (Grading may be S/U.)
798. Thesis or Dissertation. I, II, S.
2-4 Hr. PR: Consent. Note: this is an optional course for programs that believe that this level of control and supervision is needed during the writing of their students reports,
thesis, or dissertations. (Grading may be S/U.)
799. Graduate Colloquium. I, II, S.
1-6 Hr. PR: Consent. For graduate students not seeking coursework credit but who wish to meet residence requirements, use the University's facilities, and participate in its academic and cultural programs. Note: graduate students not actively involved in coursework or research are entitled, through enrollment in his/her department‚s 799 or 899 graduate colloquium, to consult with graduate faculty, participate in both formal and informal academic activities sponsored by his/her program, and retain all of the rights and privileges of duly enrolled students. (Grading is S/U; colloquium credit may not be counted against requirements for masters programs.