## Course Catalog - 2016-2017

### MATH 007 - VISITING RESEARCH

Long Title: VISITING RESEARCH
Department: Mathematics
Grade Mode: Satisfactory/Unsatisfactory
Course Type: Research
Credit Hours: 0
Description: Research conducted by visiting student scholars. Department Permission Required. Repeatable for Credit.

### MATH 101 - SINGLE VARIABLE CALCULUS I

Long Title: SINGLE VARIABLE CALCULUS I
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 102 - SINGLE VARIABLE CALCULUS II

Long Title: SINGLE VARIABLE CALCULUS II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 111 - FUND THEOREM OF CALCULUS

Long Title: FUNDAMENTAL THEOREM OF CALCULUS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 112 - CALCULUS AND ITS APPLICATIONS

Long Title: CALCULUS AND ITS APPLICATIONS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Continuation of the study of calculus from MATH 111.

### MATH 211 - ORD DIFFERENTIAL EQUATIONS

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
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 212 - MULTIVARIABLE CALCULUS

Long Title: MULTIVARIABLE CALCULUS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 212 and MATH 222.

### MATH 221 - HONORS CALCULUS III

Long Title: HONORS CALCULUS III
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 222 - HONORS CALCULUS IV

Long Title: HONORS CALCULUS IV
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: See MATH 221. A student may not receive credit for both MATH 222 and MATH 212. Mutually Exclusive: Credit cannot be earned for both MATH 222 and MATH 212.

### MATH 300 - TOPICS IN UNDERGRADUATE MATH

Long Title: TOPICS IN UNDERGRADUATE MATH
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 302 - ELEMENTS OF ANALYSIS

Long Title: ELEMENTS OF ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 304 - ELEMENTS OF KNOT THEORY

Long Title: ELEMENTS OF KNOT THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 306 - ELEMENTS OF ABSTRACT ALGEBRA

Long Title: ELEMENTS OF ABSTRACT ALGEBRA
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 306 and MATH 356.

### MATH 321 - INTRODUCTION TO ANALYSIS I

Long Title: INTRODUCTION TO ANALYSIS I
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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. Mutually Exclusive: Credit cannot be earned for both MATH 321 and MATH 331.

### MATH 322 - INTRODUCTION TO ANALYSIS II

Long Title: INTRODUCTION TO ANALYSIS II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 331 - HONORS ANALYSIS

Long Title: HONORS ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 221 OR MATH 302 or permission of department
Description: A careful treatment of basic topics in real analysis, including metric spaces and their topology, sequences and series, continuity, and differentiation. The content of this course is similar to that of MATH 321, but the intensity and conceptual level will be higher. Mutually Exclusive: Credit cannot be earned for both MATH 331 and MATH 321.

### MATH 354 - HONORS LINEAR ALGEBRA

Long Title: HONORS LINEAR ALGEBRA
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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. Recommended Prerequisite(s): A 200-level math class. Mutually Exclusive: Credit cannot be earned for both MATH 354 and MATH 355.

### MATH 355 - LINEAR ALGEBRA

Long Title: LINEAR ALGEBRA
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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. Mutually Exclusive: Credit cannot be earned for both MATH 355 and MATH 354.

### MATH 356 - ABSTRACT ALGEBRA I

Long Title: ABSTRACT ALGEBRA I
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 356 and MATH 306.

### MATH 365 - NUMBER THEORY

Long Title: NUMBER THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Properties of numbers depending mainly on the notion of divisibility. Continued fractions.

### MATH 366 - GEOMETRY

Long Title: GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 368 - TOPICS IN COMBINATORICS

Long Title: TOPICS IN COMBINATORICS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Study of combinatorics and discrete mathematics. Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games.

### MATH 370 - CALCULUS ON MANIFOLDS

Long Title: CALCULUS ON MANIFOLDS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 371 - LIE THEORY

Long Title: LIE THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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).

### MATH 373 - ELLIPTIC CURVES

Long Title: ELLIPTIC CURVES
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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

### MATH 374 - INTRO TO REPRESENTATION THEORY

Long Title: INTRODUCTION TO REPRESENTATION THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 381 - INTRO PARTIAL DIFF EQUATIONS

Long Title: INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 382 - COMPLEX ANALYSIS

Long Title: COMPLEX ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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. Equivalency: MATH 427. Recommended Prerequisite(s): MATH 212 OR 221. Mutually Exclusive: Credit cannot be earned for both MATH 382 and MATH 427/MATH 517.

### MATH 390 - UNDERGRADUATE COLLOQUIUM

Long Title: UNDERGRADUATE COLLOQUIUM
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 1
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 401 - DIFFERENTIAL GEOMETRY

Long Title: DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 402 - DIFFERENTIAL GEOMETRY

Long Title: DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 402 and MATH 500. Repeatable for Credit.

### MATH 410 - CALCULUS OF VARIATIONS

Long Title: CALCULUS OF VARIATIONS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 423 - PARTIAL DIFFERENTIAL EQNS I

Long Title: PARTIAL DIFFERENTIAL EQUATIONS I
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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 Mutually Exclusive: Credit cannot be earned for both MATH 423 and MATH 513.

### MATH 424 - PARTIAL DIFFERENTIAL EQUATIONS

Long Title: PARTIAL DIFFERENTIAL EQUATIONS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 423
Description: Continuation of MATH 423. Repeatable for Credit.

### MATH 425 - INTEGRATION THEORY

Long Title: INTEGRATION THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Lebesgue theory of measure and integration. Graduate/Undergraduate Equivalency: MATH 515. Mutually Exclusive: Credit cannot be earned for both MATH 425 and MATH 515.

### MATH 426 - TOPICS IN REAL ANALYSIS

Long Title: TOPICS IN REAL ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 426 and MATH 516. Repeatable for Credit.

### MATH 427 - COMPLEX ANALYSIS

Long Title: COMPLEX ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Distribution Group: Distribution Group III
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. Emphasis on the theory. Equivalency: MATH 382, Graduate/Undergraduate Equivalency: MATH 517. Mutually Exclusive: Credit cannot be earned for both MATH 427 and MATH 382/MATH 517.

### MATH 428 - TOPICS IN COMPLEX ANALYSIS

Long Title: TOPICS IN COMPLEX ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 428 and MATH 518. Repeatable for Credit.

### MATH 435 - DYNAMICAL SYSTEMS

Long Title: DYNAMICAL SYSTEMS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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).

### MATH 443 - GENERAL TOPOLOGY

Long Title: GENERAL TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 443 and MATH 538.

### MATH 444 - GEOMETRIC TOPOLOGY

Long Title: GEOMETRIC TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 444 and MATH 539.

### MATH 445 - ALGEBRAIC TOPOLOGY

Long Title: ALGEBRAIC TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 445 and MATH 540.

### MATH 463 - ABSTRACT ALGEBRA II

Long Title: ABSTRACT ALGEBRA II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 463 and MATH 563.

### MATH 464 - ABSTRACT ALGEBRA III

Long Title: ABSTRACT ALGEBRA III
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 464 and MATH 564.

### MATH 465 - TOPICS IN ALGEBRA

Long Title: TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 465 and MATH 565. Repeatable for Credit.

### MATH 466 - TOPICS IN ALGEBRA II

Long Title: TOPICS IN ALGEBRA II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: Content varies from year to year. Graduate/Undergraduate Equivalency: MATH 566. Mutually Exclusive: Credit cannot be earned for both MATH 466 and MATH 566.

### MATH 468 - POTPOURRI

Long Title: POTPOURRI
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: This course deals with miscellaneous special topics not covered in other courses. Repeatable for Credit.

### MATH 471 - MATHEMATICS OF APERIODIC ORDER

Long Title: MATHEMATICS OF APERIODIC ORDER
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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.

### MATH 479 - MATH UNDERGRADUATE RESEARCH

Long Title: MATHEMATICS UNDERGRADUATE RESEARCH
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Research
Credit Hours: 1 TO 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description: In depth investigation of a particular area of mathematics of mutual interest to the student and the faculty adviser. Instructor Permission Required. Repeatable for Credit.
Course URL: http://math.rice.edu

### MATH 490 - SUPERVISED READING

Long Title: SUPERVISED READING
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Independent Study
Credit Hours: 1 TO 6
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 498 - RESEARCH THEMES IN MATH. SCI.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1 TO 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 498 and MATH 698. Repeatable for Credit.

### MATH 499 - MATHEMATICAL SCIENCES

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1 TO 3
Restrictions:
May not be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 500 - DIFFERENTIAL GEOMETRY

Long Title: DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: . Graduate/Undergraduate Equivalency: MATH 402. Mutually Exclusive: Credit cannot be earned for both MATH 500 and MATH 402. Repeatable for Credit.

### MATH 501 - TOPICS DIFFERENTIAL GEOMETRY

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 502 - TOPIC DIFFERENTIAL GEOMETRY

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 513 - PARTIAL DIFFERENTIAL EQNS I

Long Title: PARTIAL DIFFERENTIAL EQUATIONS I
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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. Additional course work is required beyond the undergraduate course requirements. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Credit cannot be earned for both MATH 513 and MATH 423.

### MATH 515 - INTEGRATION THEORY

Long Title: INTEGRATION THEORY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: . Graduate/Undergraduate Equivalency: MATH 425. Mutually Exclusive: Credit cannot be earned for both MATH 515 and MATH 425.

### MATH 516 - TOPICS IN REAL ANALYSIS

Long Title: TOPICS IN REAL ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 425
Description: . Graduate/Undergraduate Equivalency: MATH 426. Mutually Exclusive: Credit cannot be earned for both MATH 516 and MATH 426. Repeatable for Credit.

### MATH 517 - COMPLEX ANALYSIS

Long Title: COMPLEX ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Credit cannot be earned for MATH 517 and MATH 382/MATH 427.

### MATH 518 - TOPICS IN COMPLEX ANALYSIS

Long Title: TOPICS IN COMPLEX ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 382 OR MATH 427
Description: . Graduate/Undergraduate Equivalency: MATH 428. Mutually Exclusive: Credit cannot be earned for both MATH 518 and MATH 428. Repeatable for Credit.

### MATH 521 - ADV TOPIC: REAL ANALYSIS

Long Title: ADVANCED TOPICS IN REAL ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 522 - TOPICS IN ANALYSIS

Long Title: TOPICS IN ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 523 - FUNCTIONAL ANALYSIS

Long Title: FUNCTIONAL ANALYSIS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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.

### MATH 524 - TOPICS IN PDE

Long Title: TOPICS IN PARTIAL DIFFERENTIAL EQUATIONS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 527 - ERGODIC THRY&TOP DYNAMICS

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 528 - ERGODIC THRY&TOPOLOGICAL DYN

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 538 - GENERAL TOPOLOGY

Long Title: GENERAL TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: . Graduate/Undergraduate Equivalency: MATH 443. Mutually Exclusive: Credit cannot be earned for both MATH 538 and MATH 443.

### MATH 539 - GEOMETRIC TOPOLOGY

Long Title: GEOMETRIC TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 356 AND MATH 443
Description: . Graduate/Undergraduate Equivalency: MATH 444. Mutually Exclusive: Credit cannot be earned for both MATH 539 and MATH 444.

### MATH 540 - ALGEBRAIC TOPOLOGY

Long Title: ALGEBRAIC TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 539
Description: . Graduate/Undergraduate Equivalency: MATH 445. Mutually Exclusive: Credit cannot be earned for both MATH 540 and MATH 445.

### MATH 541 - TOPICS IN TOPOLOGY

Long Title: TOPICS IN TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 542 - TOPICS IN ADVANCED TOPOLOGY

Long Title: TOPICS IN ADVANCED TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Topic to be announced. Repeatable for Credit.

### MATH 543 - TOPICS IN L-D TOPOLOGY

Long Title: TOPICS IN LOW-DIMENSIONAL TOPOLOGY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 1 TO 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 563 - ABSTRACT ALGEBRA II

Long Title: ABSTRACT ALGEBRA II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 356
Description: . Graduate/Undergraduate Equivalency: MATH 463. Mutually Exclusive: Credit cannot be earned for both MATH 563 and MATH 463.

### MATH 564 - ABSTRACT ALGEBRA III

Long Title: ABSTRACT ALGEBRA III
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 563
Description: . Graduate/Undergraduate Equivalency: MATH 464. Mutually Exclusive: Credit cannot be earned for both MATH 564 and MATH 464.

### MATH 565 - TOPICS IN ALGEBRA

Long Title: TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 565 and MATH 465. Repeatable for Credit.

### MATH 566 - TOPICS IN ALGEBRA II

Long Title: TOPICS IN ALGEBRA II
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: . Graduate/Undergraduate Equivalency: MATH 466. Mutually Exclusive: Credit cannot be earned for both MATH 566 and MATH 466. Repeatable for Credit.

### MATH 567 - TOPICS IN ALGEBRAIC GEOMETRY

Long Title: TOPICS IN ALGEBRAIC GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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.

### MATH 590 - CURRENT MATHEMATICS SEMINAR

Long Title: CURRENT MATHEMATICS SEMINAR
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Repeatable for Credit.

### MATH 591 - GRADUATE TEACHING SEMINAR

Long Title: GRADUATE TEACHING SEMINAR
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Repeatable for Credit.

### MATH 680 - MATHEMATICS COLLOQUIUM

Long Title: MATHEMATICS COLLOQUIUM
Department: Mathematics
Grade Mode: Satisfactory/Unsatisfactory
Course Type: Lecture
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Presentations of research topics in mathematics and related fields. Repeatable for Credit.

### MATH 681 - TOPOLOGY SEMINAR

Long Title: TOPOLOGY SEMINAR
Department: Mathematics
Grade Mode: Satisfactory/Unsatisfactory
Course Type: Seminar
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Presentations of research in topology and related areas. Repeatable for Credit.

### MATH 682 - ALGEBRAIC GEOMETRY SEMINAR

Long Title: ALGEBRAIC GEOMETRY SEMINAR
Department: Mathematics
Grade Mode: Satisfactory/Unsatisfactory
Course Type: Seminar
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Presentations of research in algebraic geometry and related areas. Repeatable for Credit.

### MATH 683 - GEOMETRY AND ANALYSIS SEMINAR

Long Title: GEOMETRY AND ANALYSIS SEMINAR
Department: Mathematics
Grade Mode: Satisfactory/Unsatisfactory
Course Type: Seminar
Credit Hours: 1
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description: Presentations of research in geometric analysis, mathematical physics, dynamics and related areas. Repeatable for Credit.

### MATH 690 - SUPERVISED READING

Long Title: SUPERVISED READING
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Independent Study
Credit Hours: 1 TO 6
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 698 - RESEARCH THEMES IN MATH. SCI.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1 TO 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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: Credit cannot be earned for both MATH 698 and MATH 498. Repeatable for Credit.

### MATH 699 - MATHEMATICAL SCIENCES

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Seminar
Credit Hours: 1 TO 9
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.

### MATH 800 - GRADUATE THESIS AND RESEARCH

Long Title: GRADUATE THESIS AND RESEARCH
Department: Mathematics
Grade Mode: Standard Letter
Course Type: Research
Credit Hours: 1 TO 15
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Description:  Repeatable for Credit.