Course Schedule and Catalog

Long Title: SINGLE VARIABLE CALCULUS I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Differentiation, extrema, Newton's method, integration, fundamental theorem of calculus, area, volume, natural logarithm, exponential, arc length, surface area, Simpson's rule, L'Hopital's rule. May substitute MATH 111-112 or take MATH 101 after completing MATH 111.

Long Title: SINGLE VARIABLE CALCULUS II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Continuation of MATH 101. Includes further techniques of integration, as well as infinite sequences and series, tests for convergence, power series, radius of convergence, polar coordinates, parametric equations, and arc length.

Long Title: FUNDAMENTAL THEOREM OF CALCULUS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of calculus, forming with MATH 112 a slower-paced version of MATH 101/102. Contains less detail in the coverage of infinite series. Students may take MATH 111/112 followed by MATH 102, or MATH 111 followed by MATH 101/102.

Long Title: CALCULUS AND ITS APPLICATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Continuation of the study of calculus from MATH 111.

Long Title: ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of ordinary differential equations (e.g., solutions to separable and linear first-order equations and to higher-order linear equations with constant coefficients, the properties of solutions to differential equations, and numerical solution methods) and linear algebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the application of linear algebra to first-order systems of differential equations and the qualitative theory of nonlinear systems and phase portraits.

Long Title: MULTIVARIABLE CALCULUS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of gradient, divergence, and curl, Lagrange multipliers, multiple integrals, as well as line integrals, conservative vector fields, Green's theorem, Stokes's theorem, and Gauss's theorem. May substitute Math 221 and 222. Mutually Exclusive: Cannot register for MATH 212 if student has credit for MATH 222.

Long Title: HONORS CALCULUS III

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: This course and MATH 222 include the material of MATH 212 and much more. Topology of Rn, calculus for functions of several variables, linear and multilinear algebra, theory of determinants, inner product spaces, integration on manifolds.

Long Title: HONORS CALCULUS IV

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: See MATH 221. A student may not receive credit for both MATH 222 and MATH 212. Mutually Exclusive: Cannot register for MATH 222 if student has credit for MATH 212.

Long Title: TOPICS IN UNDERGRADUATE MATH

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 102

Description: Treatment of topics in undergraduate mathematics with an emphasis on writing of clear, cogent complete mathematical proofs. Topics vary by year. May be repeated for credit with permission of department. Repeatable for Credit.

Long Title: ELEMENTS OF ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): MATH 102

Description: Introductory treatment of topics in analysis and topology, with the real line as a central example. Techniques include connected and compact sets, sequences and subsequences, continuity, and uniform approximation. Clear, cogent, and complete mathematical arguments are emphasized.

Long Title: ELEMENTS OF KNOT THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Introduction to the mathematical theory of knots. Techniques to distinguish knots from one another, Reidemeister moves, mod-p colorings, knot determinants, knot polynomials, Seifert surfaces, Euler characteristic, knot groups, and untying knots in four dimensions. We will also discuss open problems in knot theory. Recommended Prerequisite(s): MATH 221 OR MATH 354 OR MATH 355.

Long Title: ELEMENTS OF ABSTRACT ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Introduction treatment of the basic structures of abstract algebra: groups, rings, and fields. Clear, cogent, and complete mathematical arguments are emphasized. A student many not receive credit for both MATH 306 and MATH 356. Recommended Prerequisite(s): MATH 222 and MATH 354 and MATH 355. Mutually Exclusive: Cannot register for MATH 306 if student has credit for MATH 356.

Long Title: INTRODUCTION TO ANALYSIS I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): MATH 221 OR MATH 302 or permission of department

Description: A thorough treatment of basic methods of analysis such as metric spaces, compactness, sequences and series of functions. Also further topics in analysis, such as Hilbert spaces, Fourier series, Sturm- Liouville theory.

Long Title: INTRODUCTION TO ANALYSIS II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 321 or permission of instructor

Description: See MATH 321. Includes proofs of the basic results for multivariable calculus (MATH 321 provides proofs for single-variable calculus). Repeatable for Credit.

Long Title: HONORS LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Vector spaces, linear transformations and matrices, theory of systems of linear equations, determinants, eigenvalues and diagonalizability, inner product spaces; and optional material chosen from: dual vector spaces, spectral theorem for self-adjoint operators, Jordan canonical form. Content is similar to that of MATH 355, but with more emphasis on theory. The course will include instruction on how to construct mathematical proofs. This course is appropriate for potential Mathematics majors and others interested in learning how to construct rigorous mathematical arguments. Credit may not be received for both MATH 354 and MATH 355. Recommended Prerequisite(s): A 200-level math class. Mutually Exclusive: Cannot register for MATH 354 if student has credit for MATH 355.

Long Title: LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Linear transformations and matrices, solution of linear equations, inner products eigenvalues and eigenvectors, the spectral theorem for real symmetric matrices, applications of Jordan canonical form. Credit may not be received for both MATH 354 and MATH 355. Mutually Exclusive: Cannot register for MATH 355 if student has credit for MATH 354.

Long Title: ABSTRACT ALGEBRA I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Group theory: normal subgroups, factor groups, Abelian groups, permutations, matrix groups, and group action. Recommended Prerequisite(s): MATH 354 or MATH 355; and some proof-based course such as MATH 302, MATH 354, or MATH 365. Mutually Exclusive: Cannot register for MATH 356 if student has credit for MATH 306.

Long Title: NUMBER THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Properties of numbers depending mainly on the notion of divisibility. Continued fractions.

Long Title: GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Topics chosen from Euclidean, spherical, hyperbolic, and projective geometry, with emphasis on the similarities and differences found in various geometries. Isometries and other transformations are studied and used throughout. The history of the development of geometric ideas is discussed. This course is strongly recommended for prospective high school teachers.

Long Title: TOPICS IN COMBINATORICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of combinatorics and discrete mathematics. Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games.

Long Title: CALCULUS ON MANIFOLDS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): (MATH 212 OR MATH 222) AND (MATH 211 OR MATH 355 OR MATH 354)

Description: Differentiation and integration on manifolds: calculus on Rn, exterior differentiation, differentiation forms, vector fields, Stokes' theorem.

Long Title: LIE THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): (MATH 211 AND MATH 212) OR MATH 221

Description: Study of classical groups as symmentries of Euclidean spaces. Geometry of complex numbers and quaternions, rotations and reflections of Rn, the orthogonal, unitary and sympletic groups. Tangent spaces to matrix groups, Lie algebras and the exponential map. If time permits: the structure of Lie algebras and the matrix logarithm. Recommended Prerequisite(s): MATH 354 or MATH 355 (may be taken the same semester).

Long Title: ELLIPTIC CURVES

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Elliptic curves are central to modern number theory and instrumental in the proof of Fermat's Last Theorem. Topics will include: The addition law, solutions over the rational numbers, explicit computations, applications to factorization and cryptography; if time permits, infinite series attached to elliptic curves and the Birch-Swinnerton-Dyer conjecture. Recommended Prerequisite(s): 200 Level Math Course

Long Title: INTRODUCTION TO REPRESENTATION THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: First course in representation theory, with an emphasis on concrete examples, especially the symmetric group. Topics include representations of finite groups, characters, classification, symmetric functions, Young symmetrizers, and Schur-Weyl duality. Prior experience with proofs is necessary; some familiarity with linear or abstract algebra would be helpful, but can be acquired along the way. Recommended Prerequisite(s): Linear Algebra (MATH 221, MATH 354, or MATH 355) and MATH 356.

Long Title: INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Laplace transform: inverse transform, applications to constant coefficient differential equations. Boundary value problems: Fourier series, Bessel functions, Legendre polynomials. Recommended Prerequisite(s): MATH 211.

Long Title: COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of the Cauchy integral theorem, Taylor series, residues, as well as the evaluation of integrals by means of residues, conformal mapping, and application to two-dimensional fluid flow. Recommended Prerequisite(s): MATH 212 OR 221. Mutually Exclusive: Cannot register for MATH 382 if student has credit for MATH 427/MATH 517.

Long Title: UNDERGRADUATE COLLOQUIUM

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 1

Description: Lectures by undergraduate students on mathematical topics not usually covered in other courses. Presentation of one lecture and attendance at all sessions required. Repeatable for Credit.

Long Title: DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): MATH 212 OR MATH 222

Description: Study of the differential geometry of curves and surfaces in R3. Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem.

Long Title: DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Introduction to Riemannian geometry. Content varies from year to year. Graduate/Undergraduate Equivalency: MATH 500. Recommended Prerequisite(s): MATH 401 and MATH 321 or MATH 443. Mutually Exclusive: Cannot register for MATH 402 if student has credit for MATH 500. Repeatable for Credit.

Long Title: CALCULUS OF VARIATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 101 AND MATH 102 AND (MATH 211 OR MATH 212 OR MATH 221 OR MATH 222)

Description: Study of classical and modern theories about functions having some integral expression which is maximal, minimal, or critical. Geodesics, brachistochrone problem, minimal surfaces, and numerous applications to physics. Euler-Lagrange equations, 1st and 2nd variations, Hamilton's Principle.

Long Title: PARTIAL DIFFERENTIAL EQUATIONS I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: First order of partial differential equations. The method of characteristics. Analysis of the solutions of the wave equation, heat equation and Laplace's equation. Integral relations and Green's functions. Potential theory, Dirichlet and Neumann problems. Asymptotic methods: the method of stationary phase, geometrical optics, regular and singular perturbation methods. Cross-list: CAAM 423. Recommended Prerequisite(s): MATH 321 AND MATH 322

Long Title: PARTIAL DIFFERENTIAL EQUATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 423

Description: Continuation of MATH 423. Repeatable for Credit.

Long Title: INTEGRATION THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Lebesgue theory of measure and integration. Graduate/Undergraduate Equivalency: MATH 515. Mutually Exclusive: Cannot register for MATH 425 if student has credit for MATH 515.

Long Title: TOPICS IN REAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 425

Description: Content varies from year to year. May include Fourier series, harmonic analysis, probability theory, advanced topics in measure theory, ergodic theory, and elliptic integrals. Graduate/Undergraduate Equivalency: MATH 516. Mutually Exclusive: Cannot register for MATH 426 if student has credit for MATH 516. Repeatable for Credit.

Long Title: COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. Emphasis on the theory. Graduate/Undergraduate Equivalency: MATH 517. Mutually Exclusive: Cannot register for MATH 427 if student has credit for MATH 382/MATH 517.

Long Title: TOPICS IN COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 382 OR MATH 427

Description: Special topics include Riemann mapping theorem, Runge's Theorem, elliptic function theory, prime number theorem, Riemann surfaces, et al. Graduate/Undergraduate Equivalency: MATH 518. Mutually Exclusive: Cannot register for MATH 428 if student has credit for MATH 518. Repeatable for Credit.

Long Title: DYNAMICAL SYSTEMS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Theory and theoretical examples are complemented by computational, model driven examples from biological and physical sciences. Cross-list: CAAM 435. Recommended Prerequisite(s): CAAM 210 AND MATH 212 AND (CAAM 335 OR MATH 355) AND (MATH 302 OR MATH 321).

Long Title: GENERAL TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Study of basic point set topology. Includes a treatment of cardinality and well ordering, as well as metrization. Graduate/Undergraduate Equivalency: MATH 538. Mutually Exclusive: Cannot register for MATH 443 if student has credit for MATH 538.

Long Title: GEOMETRIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 356 AND MATH 443

Description: Introduction to algebraic methods in topology and differential topology. Elementary homotopy theory. Covering spaces. Graduate/Undergraduate Equivalency: MATH 539. Mutually Exclusive: Cannot register for MATH 444 if student has credit for MATH 539.

Long Title: ALGEBRAIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 444

Description: Introduction to the theory of homology. Includes simplicial complexes, cell complexes and cellular homology and cohomology, as well as manifolds, and Poincare duality. Graduate/Undergraduate Equivalency: MATH 540. Mutually Exclusive: Cannot register for MATH 445 if student has credit for MATH 540.

Long Title: ABSTRACT ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 356 or permission of instructor

Description: Ring theory: ideals, polynomials, factorization. Advanced linear algebra: quadratic forms, canonical forms. Field theory: extensions, Galois theory, soluability in radicals. Continuation of MATH 356. Graduate/Undergraduate Equivalency: MATH 563. Mutually Exclusive: Cannot register for MATH 463 if student has credit for MATH 563.

Long Title: ABSTRACT ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 463 or permission of instructor

Description: Continuation of MATH 463. Tensor and exterior algebra, introductory commutative algebra, structure of modules, and elements of homological algebra. Additional advanced topics may include representations of finite groups and affine algebraic geometry. Graduate/Undergraduate Equivalency: MATH 564. Mutually Exclusive: Cannot register for MATH 464 if student has credit for MATH 564.

Long Title: TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Varieties as solution sets of systems of polynomial equations, varieties in projective space, rational and regular functions, maps of varieties, local properties and singularities. Graduate/Undergraduate Equivalency: MATH 565. Mutually Exclusive: Cannot register for MATH 465 if student has credit for MATH 565. Repeatable for Credit.

Long Title: TOPICS IN ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Content varies from year to year. Graduate/Undergraduate Equivalency: MATH 566. Mutually Exclusive: Cannot register for MATH 466 if student has credit for MATH 566.

Long Title: POTPOURRI

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course deals with miscellaneous special topics not covered in other courses. Repeatable for Credit.

Long Title: MATHEMATICS OF APERIODIC ORDER

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 321 OR MATH 354 OR MATH 355

Description: Mathematical models of quasicrystals, whose discovery in the early 1980's led to a paradigm shift in materials science. Topics include: classical theory of ordered structures (i.e., lattices modeling crystals), Delone subsets and tilings of Euclidean space, aperiodically ordered structures generated by inflation or cut-and-project schemes. Recommended Prerequisite(s): MATH 356.

Long Title: SUPERVISED READING

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 6

Description:  Repeatable for Credit.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The course may be repeated multiple times for credit. Cross-list: CAAM 498, STAT 498, Graduate/Undergraduate Equivalency: MATH 698. Mutually Exclusive: Cannot register for MATH 498 if student has credit for MATH 698. Repeatable for Credit.

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description:  Repeatable for Credit.

Long Title: DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Credit cannot be earned for MATH 500 and MATH 402.  Repeatable for Credit.

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: INTEGRATION THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Credit cannot be earned for MATH 515 and MATH 425.

Long Title: TOPICS IN REAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 425

Description: Credit cannot be earned for MATH 516 and MATH 426.  Repeatable for Credit.

Long Title: COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Credit cannot be earned for MATH 517 and MATH 382/MATH 427.

Long Title: TOPICS IN COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 382 OR MATH 427

Description: Credit cannot be earned for MATH 518 and MATH 428.  Repeatable for Credit.

Long Title: ADVANCED TOPICS IN REAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: FUNCTIONAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Banach spaces: review of L^p spaces, linear operators, dual space, Hahn-Banach theorem, weak topologies, Banach-Alaoglu theorem, compact and bounded operators, closed graph theorem; Hilbert spaces: self-adjoint and unitary operators (including spectral theorem), symmetric operators and self-adjoint extensions; if time allows, distributions and Sobolev spaces. Repeatable for Credit.

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description:  Repeatable for Credit.

Long Title: GENERAL TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Credit cannot be earned for MATH 538 and MATH 443.

Long Title: GEOMETRIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 356 AND MATH 443

Description: Credit cannot be earned for MATH 539 and MATH 444.

Long Title: ALGEBRAIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 539

Description: Credit cannot be earned for MATH 540 and MATH 445.

Long Title: TOPICS IN TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN ADVANCED TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN LOW-DIMENSIONAL TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 1 TO 3

Description:  Repeatable for Credit.

Long Title: ABSTRACT ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 357

Description: Credit cannot be earned for MATH 563 and MATH 463.

Long Title: ABSTRACT ALGEBRA III

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 563

Description: Credit cannot be earned for MATH 564 and MATH 464.

Long Title: TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Varieties as solution sets of systems of polynomial equations, varieties in projective space, rational and regular functions, maps of varieties, local properties and singularities. Graduate/Undergraduate Equivalency: MATH 465. Mutually Exclusive: Cannot register for MATH 565 if student has credit for MATH 465. Repeatable for Credit.

Long Title: TOPICS IN ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Credit cannot be earned for MATH 566 and MATH 466.  Repeatable for Credit.

Long Title: TOPICS IN ALGEBRAIC GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Possible topics include rational points on algebraic varieties, moduli spaces, deformation theory, and Hodge structures. Recommended Prerequisite(s): MATH 463 and MATH 464. Repeatable for Credit.

Long Title: CURRENT MATHEMATICS SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1

Description: Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Repeatable for Credit.

Long Title: GRADUATE TEACHING SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1

Description: Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Repeatable for Credit.

Long Title: MATHEMATICS COLLOQUIUM

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Lecture

Credit Hours: 1

Description: Presentations of research topics in mathematics and related fields. Repeatable for Credit.

Long Title: TOPOLOGY SEMINAR

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Seminar

Credit Hours: 1

Description: Presentations of research in topology and related areas. Repeatable for Credit.

Long Title: ALGEBRAIC GEOMETRY SEMINAR

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Seminar

Credit Hours: 1

Description: Presentations of research in algebraic geometry and related areas. Repeatable for Credit.

Long Title: GEOMETRY AND ANALYSIS SEMINAR

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Seminar

Credit Hours: 1

Description: Presentations of research in geometric analysis, mathematical physics, dynamics and related areas. Repeatable for Credit.

Long Title: SUPERVISED READING

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 6

Description:  Repeatable for Credit.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The course may be repeated multiple times for credit. Cross-list: CAAM 698, STAT 698, Graduate/Undergraduate Equivalency: MATH 498. Mutually Exclusive: Cannot register for MATH 698 if student has credit for MATH 498. Repeatable for Credit.

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 9

Description:  Repeatable for Credit.

Long Title: VISITING RESEARCH TRAINEE

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Research

Credit Hours: 0

Long Title: GRADUATE THESIS AND RESEARCH

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Research

Credit Hours: 1 TO 15

Description:  Repeatable for Credit.