Mathematics

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. Pre-Calculus Diagnostic Test is required for registration. Mutually Exclusive: Cannot register for MATH 101 if student has credit for 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: Cannot register for MATH 102 if student has credit for 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

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

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: Cannot register for MATH 105 if student has credit for 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

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

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: Cannot register for MATH 106 if student has credit for MATH 102.

MATH 110 - MATH DISCUSSION SESSIONS

Short Title: MATH DISCUSSION SESSIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Laboratory

Credit Hour: 1

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

Course Level: Undergraduate Lower-Level

Prerequisite(s): MATH 101 (may be taken concurrently) or MATH 111 (may be taken concurrently)

Description: This course is a discussion and practice section for students to review and reinforce concepts needed in single variable calculus. Students will work in small groups under the guidance of the instructor. Repeatable for Credit.

MATH 111 - CALCULUS: DIFFERENTIATION AND ITS APPLICATIONS

Short Title: CALCULUS: DIFFERENTIATION

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

Corequisite: MATH 110

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 already has credit for MATH 101, MATH 102, MATH 112, MATH 211, MATH 212, or MATH 221 without permission. Pre-Calculus Diagnostic Test is required for registration. Mutually Exclusive: Cannot register for MATH 111 if student has credit for 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: Cannot register for MATH 112 if student has credit for MATH 101/MATH 105.

Course URL: math.rice.edu

MATH 115 - THE ART OF MATHEMATICS

Short Title: THE ART OF MATH

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: Math 115 is intended primarily for students majoring in non-STEM fields seeking knowledge of the nature of mathematics as well as training in mathematical thinking and problem-solving. The goal of the course is to demonstrate that math is not necessarily about formulas, but is rather a process of thinking which is relevant to them on a daily basis. Instructor Permission Required.

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: Cannot register for MATH 211 if student has credit for 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: Cannot register for MATH 212 if student has credit for MATH 222/MATH 232.

Course URL: math.rice.edu

MATH 215 - MATHEMATICS UNDERGRADUATE RESEARCH LABORATORY

Short Title: MATH UNDERGRAD LAB

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture/Laboratory

Credit Hours: 3

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

Course Level: Undergraduate Lower-Level

Description: The main objective of this course is to offer students a research experience in mathematics by exploring research labs in science and engineering at Rice University. This Math lab is an inclusive and diverse research environment on mathematics for our undergraduate students. Instructor Permission Required. Repeatable for Credit.

MATH 220 - HONORS ORDINARY DIFFERENTIAL EQUATIONS

Short Title: HONORS ORD DIFFERENTIAL EQNS

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: 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: Cannot register for MATH 220 if student has credit for 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

Prerequisite(s): MATH 221

Description: This course and MATH 221 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. A student may not receive credit for both MATH 222 and MATH 212, or MATH 222 and MATH 232. Mutually Exclusive: Cannot register for MATH 222 if student has credit for MATH 212/MATH 232.

MATH 232 - HONORS MULTIVARIABLE CALCULUS

Short Title: HONORS 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

Prerequisite(s): MATH 220 or MATH 354 or MATH 355 or MATH 221

Description: Calculus of several variables (partial derivatives and gradients, double and triple integrals, vector fields, line and surface integrals, Green's theorem, Stokes's theorem, Gauss's theorem). Content is similar to that of MATH 212, but MATH 232 will use linear algebra to extend results to R^n. There will also be an emphasis on rigorous mathematical arguments. Recommended Prerequisite(s): MATH 290 is recommended as a corequisite for students who have not taken MATH 220 or MATH 354. Mutually Exclusive: Cannot register for MATH 232 if student has credit for MATH 212/MATH 222.

MATH 238 - SPECIAL TOPICS

Short Title: SPECIAL TOPICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Laboratory, Lecture, Internship/Practicum, Seminar, Independent Study, Lecture/Laboratory

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 280 - UNDERGRADUATE MATH TEACHING PRACTICUM

Short Title: UG MATH TEACHING PRACTICUM

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Internship/Practicum

Credit Hours: 1-3

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

Course Level: Undergraduate Lower-Level

Description: In this course, undergraduates who have previously excelled in MATH courses will develop teaching skills while supporting faculty as teaching assistants (TAs) in a particular MATH course for the benefit of the students taking that particular course. This course is open only to undergraduates with special permission of the course instructor and can be repeated for credit. Instructor Permission Required. Repeatable for Credit.

MATH 290 - FOUNDATIONS OF MATHEMATICAL WRITING

Short Title: MATHEMATICAL WRITING SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hour: 1

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

Course Level: Undergraduate Lower-Level

Description: Half-semester course aimed at students concurrently taking their first mathematical proofs course. The course will cover foundational topics in mathematics such as logic, sets, relations, and functions, while providing students with detailed feedback on expressing mathematics in writing. Should not be taken if student already has credit for MATH 220, 221, 222, 302, or 354. Instructor Permission Required. Mutually Exclusive: Cannot register for MATH 290 if student has credit for COMP 181.

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

Description: Treatment of topics in undergraduate mathematics. Topics vary by year. May be repeated for credit with permission of department. Instructor Permission Required. Repeatable for Credit.

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 or MATH 106

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.

Course URL: math.rice.edu

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 220 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: Cannot register for MATH 306 if student has credit for 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 220 or 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: Cannot register for MATH 321 if student has credit for 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, including analysis in higher dimensions. Possible additional topics include Hilbert spaces, Fourier series, Sturm-Liouville theory.

Course URL: math.rice.edu

MATH 331 - HONORS ANALYSIS

Short Title: HONORS 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 220 or 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: Cannot register for MATH 331 if student has credit for 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): MATH 102 or MATH 106. Mutually Exclusive: Cannot register for MATH 354 if student has credit for 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: Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner products, eigenvalues and eigenvectors, and the Spectral Theorem for real symmetric matrices. Mutually Exclusive: Cannot register for MATH 355 if student has credit for 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 220 or MATH 221)

Description: An introduction to algebraic structures. Covers basic group theory (including subgroups and quotients, permutation and matrix groups, group actions) and basic ring theory (including ideals and quotients, polynomial rings, unique factorization). Mutually Exclusive: Cannot register for MATH 356 if student has credit for MATH 306.

Course URL: math.rice.edu

MATH 357 - 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: Fields and field extensions, modules over rings, further topics in groups, rings, fields, and their applications.

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 220 or MATH 221 or MATH 302 or MATH 354 or COMP 182

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

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

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

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: Cannot register for MATH 382 if student has credit for 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

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. Distribution Credit for MATH 390 no longer eligible beginning Fall 2019. 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

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 355) and (MATH 321 or MATH 331)

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. Recommended Prerequisite(s): MATH 211 or MATH 220 or familiarity with ODEs

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 444 or MATH 539

Description: MATH 402 is the undergraduate version of the graduate class MATH 500 (being generic for all related instances of dual enrollment classes). This is a course in smooth and Riemannian manifolds. Tensors, Riemannian metrics, differential forms. Lie derivatives. Distributions and foliations, including the Frobenius Theorem and an introduction to contact structures. Lie groups and the exponential map. Connections on Vector Bundles. Geodesics and completeness. Curvature. First and second variations of length and area. Jacobi Fields. Additional topics may vary from year to year. Graduate/Undergraduate Equivalency: MATH 500. Mutually Exclusive: Cannot register for MATH 402 if student has credit for MATH 500.

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 or MATH 105) and (MATH 102 or MATH 106) 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 412 - PROBABILITY THEORY

Short Title: PROBABILITY 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: A simultaneous introduction to probability theory and measure theory, from basic definitions to the central limit theorem. The selection of topics in measure theory is in the service of probability theory, and the course carefully examines interplay between the analytic and probabilistic notions.

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: CMOR 405. Graduate/Undergraduate Equivalency: MATH 513. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Cannot register for MATH 423 if student has credit for 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: Cannot register for MATH 424 if student has credit for 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: Cannot register for MATH 425 if student has credit for 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: Cannot register for MATH 426 if student has credit for MATH 516. Repeatable for Credit.

MATH 427 - COMPLEX ANALYSIS

Short Title: 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 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. Graduate/Undergraduate Equivalency: MATH 517. Recommended Prerequisite(s): MATH 321 or MATH 331. Mutually Exclusive: Cannot register for MATH 427 if student has credit for 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: Cannot register for MATH 428 if student has credit for 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: CMOR 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: Cannot register for MATH 443 if student has credit for 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. Elementary homotopy theory. Covering spaces. Graduate/Undergraduate Equivalency: MATH 539. Mutually Exclusive: Cannot register for MATH 444 if student has credit for MATH 539.

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: Cannot register for MATH 445 if student has credit for 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 323 or COMP 382 or MATH 306 or MATH 323 or MATH 356 or MATH 357 or MATH 365 or MATH 368)

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 451 - DIFFERENTIABLE MANIFOLDS

Short Title: DIFFERENTIABLE MANIFOLDS

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 321 or MATH 331) and MATH 443

Description: This is a course on differentiable manifolds. Topics include: Differential of a smooth map. Transversality. Implicit function theorem, submersions, and immersions. Tangent and Cotangent bundles. Vector fields, flows. Lie derivatives. Lie groups. Differential forms, Integration on manifolds, Stokes theorem. DeRham theory. Additional topics may include distributions and foliations, including the Frobenius Theorem. Graduate/Undergraduate Equivalency: MATH 551. Recommended Prerequisite(s): MATH 444 or MATH 463 or MATH 370 or MATH 401

MATH 452 - RIEMANNIAN GEOMETRY

Short Title: RIEMANNIAN 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 370 or MATH 401 or MATH 451) and (MATH 321 or MATH 331) and MATH 443

Description: This is a course on Riemannian manifolds. Topics will include: Tensors, Riemannian metrics. Connections. The exponential map. Geodesics and completeness. Curvature. First and second variations of length and area. Jacobi Fields. Additional topics may vary from year to year. Graduate/Undergraduate Equivalency: MATH 552. Recommended Prerequisite(s): MATH 444 Mutually Exclusive: Cannot register for MATH 452 if student has credit for MATH 552.

MATH 463 - ADVANCED ALGEBRA I

Short Title: ADVANCED ALGEBRA 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

Prerequisite(s): MATH 357

Description: This course will cover graduate level topics in group theory, ring theory, and module theory. Specific topics include the isomorphism theorems for groups, rings, and modules; group actions; solvable and nilpotent groups; Sylow’s theorems; semi-direct products of groups; ideals; rings of fractions; various unique factorization domains; Hilbert’s Basis Theorem; Gröbner Bases; tensor product of modules and universal property; modules over principal ideal domains; and canonical forms. The course will also include an introduction to category theory as time permits. Graduate/Undergraduate Equivalency: MATH 563. Mutually Exclusive: Cannot register for MATH 463 if student has credit for MATH 563.

MATH 464 - ADVANCED ALGEBRA II

Short Title: ADVANCED 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 463

Description: This course will cover topics in field theory, Galois theory, and advanced topics in commutative algebra and in multilinear algebra. Specific topics include various algebraic field extensions; fundamental theorem of Galois theory; solvable and radical extensions; transcendental extensions; tensor, symmetric, and exterior algebras; projective, injective, and flat modules; advanced ideal theory; localization; and chain conditions for rings and modules. The course will also include additional advanced topics, such as homological algebra, as time permits. Graduate/Undergraduate Equivalency: MATH 564. Mutually Exclusive: Cannot register for MATH 464 if student has credit for 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

Prerequisite(s): MATH 356 and MATH 357 (may be taken concurrently)

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

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

Prerequisite(s): MATH 356 and MATH 357 (may be taken concurrently)

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

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: Cannot register for MATH 471 if student has credit for 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 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

Prerequisite(s): MATH 444 or MATH 539

Description: A graduate course in smooth and Riemannian manifolds. Tensors, Riemannian metrics, differential forms. Lie derivatives. Distributions and foliations, including the Frobenius Theorem and an introduction to contact structures. Lie groups and the exponential map. Connections on Vector Bundles. Geodesics and completeness. Curvature. First and second variations of length and area. Jacobi Fields. Additional topics may vary from year to year. Graduate/Undergraduate Equivalency: MATH 402. Mutually Exclusive: Cannot register for MATH 500 if student has credit for 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: CMOR 505. Graduate/Undergraduate Equivalency: MATH 423. Recommended Prerequisite(s): MATH 321 AND MATH 322 Mutually Exclusive: Cannot register for MATH 513 if student has credit for 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: Cannot register for MATH 514 if student has credit for 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: Cannot register for MATH 515 if student has credit for 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: Cannot register for MATH 516 if student has credit for 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: Graduate/Undergraduate Equivalency: MATH 427. Mutually Exclusive: Cannot register for MATH 517 if student has credit for 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: Cannot register for MATH 518 if student has credit for 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: Cannot register for MATH 538 if student has credit for 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: Cannot register for MATH 539 if student has credit for 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: Cannot register for MATH 540 if student has credit for 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 544 - TOPOLOGY OF MANIFOLDS

Short Title: TOPOLOGY OF MANIFOLDS

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 444 or MATH 539) and (MATH 445 or MATH 540)

Description: A graduate course on the topology of fiber bundles, especially vector bundles and principal bundles, as well as their characteristic classes. It will cover differential forms as well as Stiefel-Whitney, Euler, Chern, and Pontryagin classes. If time allows, other topics may be included. The prerequisites for the class are the material from Math 444/539 and Math 445/540. In particular, the student should be familiar with smooth manifolds, the tangent spaces, homotopy groups, covering spaces, and homology groups.

MATH 551 - DIFFERENTIABLE MANIFOLDS

Short Title: DIFFERENTIABLE MANIFOLDS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Restrictions: Enrollment is limited to Graduate level students.

Course Level: Graduate

Description: This is a course on differentiable manifolds. Topics include: Differential of a smooth map. Transversality. Implicit function theorem, submersions, and immersions. Tangent and Cotangent bundles. Vector fields, flows. Lie derivatives. Lie groups. Differential forms, Integration on manifolds, Stokes theorem. DeRham theory. Additional topics may include distributions and foliations, including the Frobenius Theorem. Graduate/Undergraduate Equivalency: MATH 451. Recommended Prerequisite(s): MATH 539

MATH 552 - RIEMANNIAN GEOMETRY

Short Title: RIEMANNIAN 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: This is a course on Riemannian manifolds. Topics will include: Tensors, Riemannian metrics. Connections. The exponential map. Geodesics and completeness. Curvature. First and second variations of length and area. Jacobi Fields. Additional topics may vary from year to year. Graduate/Undergraduate Equivalency: MATH 452. Recommended Prerequisite(s): MATH 451/551 or MATH 401/500 Mutually Exclusive: Cannot register for MATH 552 if student has credit for MATH 452.

MATH 563 - ADVANCED ALGEBRA I

Short Title: ADVANCED ALGEBRA 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: This course will cover graduate level topics in group theory, ring theory, and module theory. Specific topics include the isomorphism theorems for groups, rings, and modules; group actions; solvable and nilpotent groups; Sylow’s theorems; semi-direct products of groups; ideals; rings of fractions; various unique factorization domains; Hilbert’s Basis Theorem; Gröbner Bases; tensor product of modules and universal property; modules over principal ideal domains; and canonical forms. The course will also include an introduction to category theory as time permits. Graduate/Undergraduate Equivalency: MATH 463. Mutually Exclusive: Cannot register for MATH 563 if student has credit for MATH 463.

MATH 564 - ADVANCED ALGEBRA II

Short Title: ADVANCED 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 463 or MATH 563

Description: This course will cover graduate level topics in field theory, Galois theory, and advanced topics in commutative algebra and in multilinear algebra. Specific topics include various algebraic field extensions; fundamental theorem of Galois theory; solvable and radical extensions; transcendental extensions; tensor, symmetric, and exterior algebras; projective, injective, and flat modules; advanced ideal theory; localization; and chain conditions for rings and modules. The course will also additional advanced topics, such as homological algebra, as time permits. Graduate/Undergraduate Equivalency: MATH 464. Mutually Exclusive: Cannot register for MATH 564 if student has credit for 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: Cannot register for MATH 565 if student has credit for 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: Cannot register for MATH 566 if student has credit for 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: Cannot register for MATH 571 if student has credit for 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, Laboratory, Lecture, Seminar, Independent Study

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 SEMINAR

Short Title: 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: Research in geometry and related areas will be presented by both external and internal speakers. The participation in this course will support the learning experience of students enrolled in the MATH PhD program at Rice who work with a faculty member whose primary research interests intersect geometry and related areas. Repeatable for Credit.

MATH 684 - ANALYSIS SEMINAR

Short Title: 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 analysis 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 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 700 - SUMMER RESEARCH FOR PHD STUDENTS

Short Title: SUMMER RESEARCH

Department: Mathematics

Grade Mode: Satisfactory/Unsatisfactory

Course Type: Research

Credit Hours: 9

Restrictions: Enrollment is limited to Graduate level students. Enrollment limited to students in a Doctor of Philosophy degree. Enrollment limited to students in the Mathematics department.

Course Level: Graduate

Description: Summer research for MATH PhD students. Can be repeated for credit. 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.