# Mathematics (MATH)

**MATH 101 - SINGLE VARIABLE CALCULUS I**

**Short Title: **SINGLE VARIABLE CALCULUS I

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Limits, continuity, differentiation, integration, and the Fundamental Theorem of Calculus. Mutually Exclusive courses may only be taken with instructor permission. May substitute MATH 111-112 or take MATH 101 after completing MATH 111. Should not be taken if student already has credit for MATH 102, MATH 211, MATH 212, or MATH 221, without permission. Mutually Exclusive: Credit cannot be earned for MATH 101 and MATH 105/MATH 112.

**Course URL: **math.rice.edu

**MATH 102 - SINGLE VARIABLE CALCULUS II**

**Short Title: **SINGLE VARIABLE CALCULUS II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Continuation of MATH 101. Includes further techniques of integration, as well as infinite sequences and series, Taylor polynomials and Taylor series, parametric equations, arc length, polar coordinates, complex numbers, and Fourier polynomials. Should not be taken if student already has credit for MATH 211, MATH 212, or MATH 221, without permission. Mutually Exclusive: Credit cannot be earned for MATH 102 and MATH 106.

**Course URL: **math.rice.edu

**MATH 105 - AP/OTH CREDIT IN CALCULUS I**

**Short Title: **AP/OTH CREDIT IN CALCULUS I

**Department: **Mathematics

**Grade Mode: **Transfer Courses

**Course Type: **Transfer

**Credit Hours: **3

**Course Level: **Undergraduate Lower-Level

**Description: **Provides transfer credit based on student performance on approved examinations in calculus, such as the AB Calculus Advanced Placement exam or the International Baccalaureate higher-level calculus exams. This credit counts toward the total credit hours required for graduation, and satisfies major requirements in lieu of MATH 101, but does not count for distribution. Mutually Exclusive: Credit cannot be earned for MATH 105 and MATH 101/MATH 111/MATH 112.

**MATH 106 - AP/OTH CREDIT IN CALCULUS II**

**Short Title: **AP/OTH CREDIT IN CALCULUS II

**Department: **Mathematics

**Grade Mode: **Transfer Courses

**Course Type: **Transfer

**Credit Hours: **3

**Course Level: **Undergraduate Lower-Level

**Description: **Provides transfer credit based on student performance on approved examinations in calculus, such as the BC Calculus Advanced Placement exam or the International Baccalaureate higher-level calculus exams. This credit counts toward the total credit hours required for graduation, and satisfies major requirements in lieu of MATH 102, but does not count for distribution. Mutually Exclusive: Credit cannot be earned for MATH 106 and MATH 102.

**MATH 111 - CALCULUS: DIFFERENTIATION AND ITS APPLICATIONS**

**Short Title: **CALCULUS: DIFFERENTIATION

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Study of calculus, forming with MATH 112 a version of MATH 101/102 that does not cover infinite series. MATH 111 covers functions, limits, continuity, and derivatives and their applications. Mutually Exclusive courses may only be taken with instructor permission. Should not be taken if student aleady has credit for MATH 101, MATH 102, MATH 112, MATH 211, MATH 212, or MATH 221 without permission. Mutually Exclusive: Credit cannot be earned for MATH 111 and MATH 105.

**Course URL: **math.rice.edu

**MATH 112 - CALCULUS: INTEGRATION AND ITS APPLICATIONS**

**Short Title: **CALCULUS: INTEGRATION + APPS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Continuation of the study of calculus from MATH 111. Integration, the Fundamental Theorem of Calculus, techniques of integration and applications. Should not be taken if student already has credit for MATH 102, MATH 211, MATH 212, MATH 221, without permission. Mutually Exclusive: Credit cannot be earned for MATH 112 and MATH 101/MATH 105.

**Course URL: **math.rice.edu

**MATH 211 - ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA**

**Short Title: **ORD DIFFERENTIAL EQUATIONS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**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. Mutually Exclusive: Credit cannot be earned for MATH 211 and MATH 220.

**MATH 212 - MULTIVARIABLE CALCULUS**

**Short Title: **MULTIVARIABLE CALCULUS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Calculus of multiple variables. Vectors, partial derivatives and gradients, double and triple integrals, vector fields, line and surface integrals, Green's theorem, Stokes's theorem, and Gauss's theorem. May substitute Math 221 and 222. Mutually Exclusive: Credit cannot be earned for MATH 212 and MATH 222.

**Course URL: **math.rice.edu

**MATH 220 - HONORS ORDINARY DIFFERENTIAL EQUATIONS**

**Short Title: **HONORS ORD DIFFERENTIAL EQNS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **A rigorous introduction to the study of ordinary differential equations, including results about the existence, uniqueness and stability of solutions. Some concepts from multi-variable calculus and linear algebra will be introduced along the way. This course will introduce students to the understanding and writing of proofs. Mutually Exclusive: Credit cannot be earned for MATH 220 and MATH 211.

**MATH 221 - HONORS CALCULUS III**

**Short Title: **HONORS CALCULUS III

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**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**

**Short Title: **HONORS CALCULUS IV

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **See MATH 221. A student may not receive credit for both MATH 222 and MATH 212. Mutually Exclusive: Credit cannot be earned for MATH 222 and MATH 212.

**MATH 238 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Internship/Practicum, Lecture, Laboratory, Seminar

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Lower-Level

**Description: **Topics and credit hours may vary each semester. Contact Department for current semester's topic(s). Repeatable for Credit.

**MATH 300 - TOPICS IN UNDERGRADUATE MATH**

**Short Title: **TOPICS IN UNDERGRADUATE MATH

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 102

**Description: **Treatment of topics in undergraduate mathematics. Topics vary by year. May be repeated for credit with permission of department.

**Course URL: **math.rice.edu

**MATH 302 - ELEMENTS OF ANALYSIS**

**Short Title: **ELEMENTS OF ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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**

**Short Title: **ELEMENTS OF KNOT THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 221 or MATH 354 or MATH 355

**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.

**Course URL: **math.rice.edu

**MATH 306 - ELEMENTS OF ABSTRACT ALGEBRA**

**Short Title: **ELEMENTS OF ABSTRACT ALGEBRA

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(MATH 354 or MATH 355) and (MATH 302 or MATH 354 or MATH 221)

**Description: **Introductory 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. Mutually Exclusive: Credit cannot be earned for MATH 306 and MATH 356.

**Course URL: **math.rice.edu

**MATH 321 - INTRODUCTION TO ANALYSIS I**

**Short Title: **INTRODUCTION TO ANALYSIS I

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 221 or MATH 354 or MATH 302

**Description: **A thorough treatment of the foundations of real analysis such as metric spaces, compactness, sequences and series of functions, differentiation, Riemann integration. Mutually Exclusive: Credit cannot be earned for MATH 321 and MATH 331.

**Course URL: **math.rice.edu

**MATH 322 - INTRODUCTION TO ANALYSIS II**

**Short Title: **INTRODUCTION TO ANALYSIS II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 321 or MATH 331

**Description: **Further study in real analysis. Possible topics include analysis in higher dimensions, Hilbert spaces, Fourier series, Sturm-Liouville theory. Repeatable for Credit.

**Course URL: **math.rice.edu

**MATH 331 - HONORS ANALYSIS**

**Short Title: **HONORS ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 221 or MATH 302 or MATH 354

**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 MATH 331 and MATH 321.

**Course URL: **math.rice.edu

**MATH 354 - HONORS LINEAR ALGEBRA**

**Short Title: **HONORS LINEAR ALGEBRA

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 354 and MATH 355.

**MATH 355 - LINEAR ALGEBRA**

**Short Title: **LINEAR ALGEBRA

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 355 and MATH 354.

**MATH 356 - ABSTRACT ALGEBRA I**

**Short Title: **ABSTRACT ALGEBRA I

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(MATH 354 or MATH 355) and (MATH 302 or MATH 354 or MATH 221)

**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 MATH 356 and MATH 306.

**Course URL: **math.rice.edu

**MATH 365 - NUMBER THEORY**

**Short Title: **NUMBER THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 221 or MATH 302 or MATH 354

**Description: **Prime numbers and factorization, modular arithmetic, Diophantine equations, quadratic reciprocity, and other topics such as cryptography or continued fractions.

**Course URL: **math.rice.edu

**MATH 366 - GEOMETRY**

**Short Title: **GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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**

**Short Title: **TOPICS IN COMBINATORICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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**

**Short Title: **CALCULUS ON MANIFOLDS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(MATH 302 or MATH 321 or MATH 331) and (MATH 354 or MATH 355)

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

**Course URL: **math.rice.edu

**MATH 371 - LIE THEORY**

**Short Title: **LIE THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 306 or MATH 356

**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).

**Course URL: **math.rice.edu

**MATH 373 - ELLIPTIC CURVES**

**Short Title: **ELLIPTIC CURVES

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 306 or MATH 356

**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

**Course URL: **math.rice.edu

**MATH 374 - INTRODUCTION TO REPRESENTATION THEORY**

**Short Title: **INTRO TO REPRESENTATION THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 306 or MATH 356

**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.

**Course URL: **math.rice.edu

**MATH 376 - ALGEBRAIC GEOMETRY**

**Short Title: **ALGEBRAIC GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **(MATH 354 or MATH 355) and (MATH 306 or MATH 356)

**Description: **An introduction to algebraic geometry, with an emphasis on algorithms. Topics include: polynomial rings and ideals, Groebner bases and elimination theory, affine varieties, Hilbert's Nullstellensatz, and the Algebra-Geometry correspondence. Projective varieties; Bezout's Theorem.

**MATH 381 - INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **INTRO PARTIAL DIFF EQUATIONS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 - COMPUTATIONAL COMPLEX ANALYSIS**

**Short Title: **COMPUTATIONAL COMPLEX ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

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

**Course URL: **math.rice.edu

**MATH 390 - UNDERGRADUATE COLLOQUIUM**

**Short Title: **UNDERGRADUATE COLLOQUIUM

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 OF CURVES AND SURFACES**

**Short Title: **DIFF GEOM OF CURVES/SURFACES

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 222 or MATH 354 or MATH 302

**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.

**Course URL: **math.rice.edu

**MATH 402 - DIFFERENTIAL GEOMETRY**

**Short Title: **DIFFERENTIAL GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 321 or MATH 331

**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 MATH 402 and MATH 500.

**Course URL: **math.rice.edu

**MATH 410 - CALCULUS OF VARIATIONS**

**Short Title: **CALCULUS OF VARIATIONS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 EQUATIONS I**

**Short Title: **PARTIAL DIFFERENTIAL EQNS I

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: MATH 513. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Credit cannot be earned for MATH 423 and MATH 513.

**MATH 424 - TOPICS IN PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **TOPICS IN PARTIAL DIFF EQNS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 423

**Description: **Continuation of MATH 423. Analysis of the solutions of second order differential equations. 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. Euler and Navier-Stokes equations. Graduate/Undergraduate Equivalency: MATH 514. Mutually Exclusive: Credit cannot be earned for MATH 424 and MATH 514. Repeatable for Credit.

**Course URL: **math.rice.edu

**MATH 425 - INTEGRATION THEORY**

**Short Title: **INTEGRATION THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 321 or MATH 331

**Description: **Lebesgue theory of measure and integration. Graduate/Undergraduate Equivalency: MATH 515. Mutually Exclusive: Credit cannot be earned for MATH 425 and MATH 515.

**Course URL: **math.rice.edu

**MATH 426 - TOPICS IN REAL ANALYSIS**

**Short Title: **TOPICS IN REAL ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 426 and MATH 516. Repeatable for Credit.

**MATH 427 - COMPLEX ANALYSIS**

**Short Title: **COMPLEX ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Distribution Group: **Distribution Group III

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 354 or MATH 222 or MATH 302

**Description: **Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. Emphasis on the theory. Recommended Prerequisite(s): MATH 321 or MATH 331. Mutually Exclusive: Credit cannot be earned for MATH 427 and MATH 382/MATH 517.

**Course URL: **math.rice.edu

**MATH 428 - TOPICS IN COMPLEX ANALYSIS**

**Short Title: **TOPICS IN COMPLEX ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 428 and MATH 518. Repeatable for Credit.

**MATH 435 - DYNAMICAL SYSTEMS**

**Short Title: **DYNAMICAL SYSTEMS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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): (MATH 212 or MATH 221) and (CAAM 335 or MATH 355 or MATH 354) and (MATH 302 or MATH 321 or MATH 331)

**Course URL: **math.rice.edu

**MATH 443 - GENERAL TOPOLOGY**

**Short Title: **GENERAL TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 321 or MATH 331

**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 MATH 443 and MATH 538.

**Course URL: **math.rice.edu

**MATH 444 - GEOMETRIC TOPOLOGY**

**Short Title: **GEOMETRIC TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 444 and MATH 539.

**Course URL: **math.rice.edu

**MATH 445 - ALGEBRAIC TOPOLOGY**

**Short Title: **ALGEBRAIC TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 445 and MATH 540.

**MATH 448 - CONCRETE MATHEMATICS**

**Short Title: **CONCRETE MATHEMATICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **COMP 182

**Description: **Concrete mathematics is a blend of continuous and discrete mathematics. Major topics include sums, recurrences, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability and asymptotic methods. Cross-list: COMP 448.

**MATH 463 - ABSTRACT ALGEBRA II**

**Short Title: **ABSTRACT ALGEBRA II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 356

**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 MATH 463 and MATH 563.

**MATH 464 - ABSTRACT ALGEBRA III**

**Short Title: **ABSTRACT ALGEBRA III

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Prerequisite(s): **MATH 463

**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 MATH 464 and MATH 564.

**MATH 465 - TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY**

**Short Title: **TOPICS IN ALGEBRA

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 465 and MATH 565. Repeatable for Credit.

**MATH 466 - TOPICS IN ALGEBRA II**

**Short Title: **TOPICS IN ALGEBRA II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Content varies from year to year. Graduate/Undergraduate Equivalency: MATH 566. Mutually Exclusive: Credit cannot be earned for MATH 466 and MATH 566.

**MATH 468 - POTPOURRI**

**Short Title: **POTPOURRI

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

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

**MATH 471 - MATHEMATICS OF APERIODIC ORDER**

**Short Title: **MATHEMATICS OF APERIODIC ORDER

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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. Graduate/Undergraduate Equivalency: MATH 571. Recommended Prerequisite(s): MATH 356. Mutually Exclusive: Credit cannot be earned for MATH 471 and MATH 571.

**MATH 477 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Internship/Practicum, Seminar, Lecture, Laboratory

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Topics and credit hours may vary each semester. Contact department for current semester's topic(s). Repeatable for Credit.

**MATH 479 - MATHEMATICS UNDERGRADUATE RESEARCH**

**Short Title: **MATH UNDERGRADUATE RESEARCH

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Research

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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: **math.rice.edu

**MATH 490 - SUPERVISED READING**

**Short Title: **SUPERVISED READING

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Independent Study

**Credit Hours: **1-6

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Repeatable for Credit.

**MATH 498 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCES**

**Short Title: **RESEARCH THEMES IN MATH. SCI.

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**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 MATH 498 and MATH 698. Repeatable for Credit.

**MATH 499 - MATHEMATICAL SCIENCES VIGRE SEMINAR**

**Short Title: **MATHEMATICAL SCIENCES

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Undergraduate, Undergraduate Professional or Visiting Undergraduate level students.

**Course Level: **Undergraduate Upper-Level

**Description: **Repeatable for Credit.

**MATH 500 - DIFFERENTIAL GEOMETRY**

**Short Title: **DIFFERENTIAL GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **. Graduate/Undergraduate Equivalency: MATH 402. Mutually Exclusive: Credit cannot be earned for MATH 500 and MATH 402. Repeatable for Credit.

**MATH 501 - TOPICS IN DIFFERENTIAL GEOMETRY**

**Short Title: **TOPICS DIFFERENTIAL GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 502 - TOPICS IN DIFFERENTIAL GEOMETRY**

**Short Title: **TOPIC DIFFERENTIAL GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 513 - PARTIAL DIFFERENTIAL EQUATIONS I**

**Short Title: **PARTIAL DIFFERENTIAL EQNS I

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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. Cross-list: CAAM 523. Graduate/Undergraduate Equivalency: MATH 423. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Credit cannot be earned for MATH 513 and MATH 423.

**MATH 514 - TOPICS IN PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **TOPICS IN PARTIAL DIFF EQNS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 513 or MATH 423

**Description: **Continuation of MATH 513. Analysis of the solutions of second order differential equations. 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. Euler and Navier-Stokes equations. Graduate/Undergraduate Equivalency: MATH 424. Mutually Exclusive: Credit cannot be earned for MATH 514 and MATH 424.

**Course URL: **math.rice.edu

**MATH 515 - INTEGRATION THEORY**

**Short Title: **INTEGRATION THEORY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **. Graduate/Undergraduate Equivalency: MATH 425. Mutually Exclusive: Credit cannot be earned for MATH 515 and MATH 425.

**MATH 516 - TOPICS IN REAL ANALYSIS**

**Short Title: **TOPICS IN REAL ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 425

**Description: **. Graduate/Undergraduate Equivalency: MATH 426. Mutually Exclusive: Credit cannot be earned for MATH 516 and MATH 426. Repeatable for Credit.

**MATH 517 - COMPLEX ANALYSIS**

**Short Title: **COMPLEX ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 518 - TOPICS IN COMPLEX ANALYSIS**

**Short Title: **TOPICS IN COMPLEX ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 382 or MATH 427

**Description: **. Graduate/Undergraduate Equivalency: MATH 428. Mutually Exclusive: Credit cannot be earned for MATH 518 and MATH 428. Repeatable for Credit.

**MATH 521 - ADVANCED TOPICS IN REAL ANALYSIS**

**Short Title: **ADV TOPIC: REAL ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 522 - TOPICS IN ANALYSIS**

**Short Title: **TOPICS IN ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 523 - FUNCTIONAL ANALYSIS**

**Short Title: **FUNCTIONAL ANALYSIS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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 PARTIAL DIFFERENTIAL EQUATIONS**

**Short Title: **TOPICS IN PDE

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 527 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICS**

**Short Title: **ERGODIC THRY&TOP DYNAMICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 528 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICS**

**Short Title: **ERGODIC THRY&TOPOLOGICAL DYN

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Repeatable for Credit.

**MATH 538 - GENERAL TOPOLOGY**

**Short Title: **GENERAL TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **. Graduate/Undergraduate Equivalency: MATH 443. Mutually Exclusive: Credit cannot be earned for MATH 538 and MATH 443.

**MATH 539 - GEOMETRIC TOPOLOGY**

**Short Title: **GEOMETRIC TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 356 and MATH 443

**Description: **. Graduate/Undergraduate Equivalency: MATH 444. Mutually Exclusive: Credit cannot be earned for MATH 539 and MATH 444.

**MATH 540 - ALGEBRAIC TOPOLOGY**

**Short Title: **ALGEBRAIC TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 539

**Description: **. Graduate/Undergraduate Equivalency: MATH 445. Mutually Exclusive: Credit cannot be earned for MATH 540 and MATH 445.

**MATH 541 - TOPICS IN TOPOLOGY**

**Short Title: **TOPICS IN TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 542 - TOPICS IN ADVANCED TOPOLOGY**

**Short Title: **TOPICS IN ADVANCED TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Topic to be announced. Repeatable for Credit.

**MATH 543 - TOPICS IN LOW-DIMENSIONAL TOPOLOGY**

**Short Title: **TOPICS IN L-D TOPOLOGY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Repeatable for Credit.

**MATH 563 - ABSTRACT ALGEBRA II**

**Short Title: **ABSTRACT ALGEBRA II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 356

**Description: **. Graduate/Undergraduate Equivalency: MATH 463. Mutually Exclusive: Credit cannot be earned for MATH 563 and MATH 463.

**MATH 564 - ABSTRACT ALGEBRA III**

**Short Title: **ABSTRACT ALGEBRA III

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Prerequisite(s): **MATH 563

**Description: **. Graduate/Undergraduate Equivalency: MATH 464. Mutually Exclusive: Credit cannot be earned for MATH 564 and MATH 464.

**MATH 565 - TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAIC GEOMETRY**

**Short Title: **TOPICS IN ALGEBRA

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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 MATH 565 and MATH 465. Repeatable for Credit.

**MATH 566 - TOPICS IN ALGEBRA II**

**Short Title: **TOPICS IN ALGEBRA II

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **. Graduate/Undergraduate Equivalency: MATH 466. Mutually Exclusive: Credit cannot be earned for MATH 566 and MATH 466. Repeatable for Credit.

**MATH 567 - TOPICS IN ALGEBRAIC GEOMETRY**

**Short Title: **TOPICS IN ALGEBRAIC GEOMETRY

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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 571 - MATHEMATICS OF APERIODIC ORDER**

**Short Title: **MATHEMATICS OF APERIODIC ORDER

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Lecture

**Credit Hours: **3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**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. Graduate/Undergraduate Equivalency: MATH 471. Recommended Prerequisite(s): MATH 356 Mutually Exclusive: Credit cannot be earned for MATH 571 and MATH 471.

**MATH 590 - CURRENT MATHEMATICS SEMINAR**

**Short Title: **CURRENT MATHEMATICS SEMINAR

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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**

**Short Title: **GRADUATE TEACHING SEMINAR

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 677 - SPECIAL TOPICS**

**Short Title: **SPECIAL TOPICS

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Internship/Practicum, Seminar, Lecture, Laboratory

**Credit Hours: **1-4

**Restrictions: ** Enrollment is limited to Graduate or Visiting Graduate level students.

**Course Level: **Graduate

**Description: **Topics and credit hours vary each semester. Contact department for current semester's topic(s). Repeatable for Credit.

**MATH 680 - MATHEMATICS COLLOQUIUM**

**Short Title: **MATHEMATICS COLLOQUIUM

**Department: **Mathematics

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Lecture

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 681 - TOPOLOGY SEMINAR**

**Short Title: **TOPOLOGY SEMINAR

**Department: **Mathematics

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Seminar

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 682 - ALGEBRAIC GEOMETRY SEMINAR**

**Short Title: **ALGEBRAIC GEOMETRY SEMINAR

**Department: **Mathematics

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Seminar

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 683 - GEOMETRY AND ANALYSIS SEMINAR**

**Short Title: **GEOMETRY AND ANALYSIS SEMINAR

**Department: **Mathematics

**Grade Mode: **Satisfactory/Unsatisfactory

**Course Type: **Seminar

**Credit Hour: **1

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

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

**MATH 690 - SUPERVISED READING**

**Short Title: **SUPERVISED READING

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Independent Study

**Credit Hours: **1-6

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Repeatable for Credit.

**MATH 698 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCES**

**Short Title: **RESEARCH THEMES IN MATH. SCI.

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-3

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **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 MATH 698 and MATH 498. Repeatable for Credit.

**MATH 699 - MATHEMATICAL SCIENCES VIGRE SEMINAR**

**Short Title: **MATHEMATICAL SCIENCES

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Seminar

**Credit Hours: **1-9

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Repeatable for Credit.

**MATH 800 - GRADUATE THESIS AND RESEARCH**

**Short Title: **GRADUATE THESIS AND RESEARCH

**Department: **Mathematics

**Grade Mode: **Standard Letter

**Course Type: **Research

**Credit Hours: **1-15

**Restrictions: ** Enrollment is limited to Graduate level students.

**Course Level: **Graduate

**Description: **Repeatable for Credit.