M ATHEM ATICS (M ATH) - Rice Universityalgebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the

Mathematics (MATH) 1

MATHEMATICS (MATH)MATH 101 - SINGLE VARIABLE CALCULUS IShort Title: SINGLE VARIABLE CALCULUS IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Limits, continuity, differentiation, integration, and theFundamental Theorem of Calculus. Mutually Exclusive courses mayonly be taken with instructor permission. May substitute MATH 111-112or take MATH 101 after completing MATH 111. Should not be takenif student already has credit for MATH 102, MATH 211, MATH 212, orMATH 221, without permission. Mutually Exclusive: Cannot register forMATH 101 if student has credit for MATH 105/MATH 112.Course URL: math.rice.edu (http://math.rice.edu)

MATH 102 - SINGLE VARIABLE CALCULUS IIShort Title: SINGLE VARIABLE CALCULUS IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Continuation of MATH 101. Includes further techniques ofintegration, as well as infinite sequences and series, Taylor polynomialsand Taylor series, parametric equations, arc length, polar coordinates,complex numbers, and Fourier polynomials. Should not be taken ifstudent already has credit for MATH 211, MATH 212, or MATH 221,without permission. Mutually Exclusive: Cannot register for MATH 102 ifstudent has credit for MATH 106.Course URL: math.rice.edu (http://math.rice.edu)

MATH 105 - AP/OTH CREDIT IN CALCULUS IShort Title: AP/OTH CREDIT IN CALCULUS IDepartment: MathematicsGrade Mode: Transfer CoursesCourse Type: TransferCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Provides transfer credit based on student performance onapproved examinations in calculus, such as the AB Calculus AdvancedPlacement exam or the International Baccalaureate higher-level calculusexams. This credit counts toward the total credit hours required forgraduation, and satisfies major requirements in lieu of MATH 101, butdoes not count for distribution. Mutually Exclusive: Cannot register forMATH 105 if student has credit for MATH 101/MATH 111/MATH 112.

MATH 106 - AP/OTH CREDIT IN CALCULUS IIShort Title: AP/OTH CREDIT IN CALCULUS IIDepartment: MathematicsGrade Mode: Transfer CoursesCourse Type: TransferCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Provides transfer credit based on student performance onapproved examinations in calculus, such as the BC Calculus AdvancedPlacement exam or the International Baccalaureate higher-level calculusexams. This credit counts toward the total credit hours required forgraduation, and satisfies major requirements in lieu of MATH 102, butdoes not count for distribution. Mutually Exclusive: Cannot register forMATH 106 if student has credit for MATH 102.

MATH 111 - CALCULUS: DIFFERENTIATION AND ITS APPLICATIONSShort Title: CALCULUS: DIFFERENTIATIONDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Study of calculus, forming with MATH 112 a version ofMATH 101/102 that does not cover infinite series. MATH 111 coversfunctions, 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 withoutpermission. Mutually Exclusive: Cannot register for MATH 111 if studenthas credit for MATH 105.Course URL: math.rice.edu (http://math.rice.edu)

MATH 112 - CALCULUS: INTEGRATION AND ITS APPLICATIONSShort Title: CALCULUS: INTEGRATION + APPSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Continuation of the study of calculus from MATH 111.Integration, the Fundamental Theorem of Calculus, techniques ofintegration and applications. Should not be taken if student alreadyhas credit for MATH 102, MATH 211, MATH 212, MATH 221, withoutpermission. Mutually Exclusive: Cannot register for MATH 112 if studenthas credit for MATH 101/MATH 105.Course URL: math.rice.edu (http://math.rice.edu)

http://math.rice.edu








2 Mathematics (MATH)

MATH 115 - THE ART OF MATHEMATICSShort Title: THE ART OF MATHDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Math 115 is intended primarily for students majoring in non-STEM fields seeking knowledge of the nature of mathematics as well astraining in mathematical thinking and problem-solving. The goal of thecourse is to demonstrate that math is not necessarily about formulas, butis rather a process of thinking which is relevant to them on a daily basis.Instructor Permission Required.

MATH 211 - ORDINARY DIFFERENTIAL EQUATIONS AND LINEARALGEBRAShort Title: ORD DIFFERENTIAL EQUATIONSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Study of ordinary differential equations (e.g., solutionsto separable and linear first-order equations and to higher-order linearequations with constant coefficients, the properties of solutions todifferential equations, and numerical solution methods) and linearalgebra (e.g., vector spaces and solutions to algebraic linear equations,dimension, eigenvalues, and eigenvectors of a matrix), as well asthe application of linear algebra to first-order systems of differentialequations and the qualitative theory of nonlinear systems and phaseportraits. Mutually Exclusive: Cannot register for MATH 211 if student hascredit for MATH 220.

MATH 212 - MULTIVARIABLE CALCULUSShort Title: MULTIVARIABLE CALCULUSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Calculus of multiple variables. Vectors, partial derivativesand gradients, double and triple integrals, vector fields, line and surfaceintegrals, Green's theorem, Stokes's theorem, and Gauss's theorem. Maysubstitute Math 221 and 222. Mutually Exclusive: Cannot register forMATH 212 if student has credit for MATH 222.Course URL: math.rice.edu (http://math.rice.edu)

MATH 220 - HONORS ORDINARY DIFFERENTIAL EQUATIONSShort Title: HONORS ORD DIFFERENTIAL EQNSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: A rigorous introduction to the study of ordinary differentialequations, including results about the existence, uniqueness and stabilityof solutions. Some concepts from multi-variable calculus and linearalgebra will be introduced along the way. This course will introducestudents 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 IIIShort Title: HONORS CALCULUS IIIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: This course and MATH 222 include the material ofMATH 212 and much more. Topology of Rn, calculus for functions ofseveral variables, linear and multilinear algebra, theory of determinants,inner product spaces, integration on manifolds.

MATH 222 - HONORS CALCULUS IVShort Title: HONORS CALCULUS IVDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: See MATH 221. A student may not receive credit for bothMATH 222 and MATH 212. Mutually Exclusive: Cannot register forMATH 222 if student has credit for MATH 212.

MATH 238 - SPECIAL TOPICSShort Title: SPECIAL TOPICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: Internship/Practicum, Lecture, Laboratory, SeminarCredit Hours: 1-4Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: Topics and credit hours may vary each semester. ContactDepartment for current semester's topic(s). Repeatable for Credit.




MATH 280 - UNDERGRADUATE MATH TEACHING PRACTICUMShort Title: UG MATH TEACHING PRACTICUMDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: Internship/PracticumCredit Hours: 1-3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Lower-LevelDescription: In this course, undergraduates who have previously excelledin MATH courses will develop teaching skills while supporting faculty asteaching assistants (TAs) in a particular MATH course for the benefit ofthe students taking that particular course. This course is open only toundergraduates with special permission of the course instructor and canbe repeated for credit. Instructor Permission Required. Repeatable forCredit.

MATH 300 - TOPICS IN UNDERGRADUATE MATHShort Title: TOPICS IN UNDERGRADUATE MATHDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Treatment of topics in undergraduate mathematics. Topicsvary by year. May be repeated for credit with permission of department.Instructor Permission Required. Repeatable for Credit.Course URL: math.rice.edu (http://math.rice.edu)

MATH 302 - ELEMENTS OF ANALYSISShort Title: ELEMENTS OF ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 102 or MATH 106Description: Introductory treatment of topics in analysis and topology,with the real line as a central example. Techniques include connectedand compact sets, sequences and subsequences, continuity, and uniformapproximation. Clear, cogent, and complete mathematical arguments areemphasized.Course URL: math.rice.edu (http://math.rice.edu)

MATH 304 - ELEMENTS OF KNOT THEORYShort Title: ELEMENTS OF KNOT THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 221 or MATH 354 or MATH 355Description: 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 (http://math.rice.edu)

MATH 306 - ELEMENTS OF ABSTRACT ALGEBRAShort Title: ELEMENTS OF ABSTRACT ALGEBRADepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): (MATH 354 or MATH 355) and (MATH 302 or MATH 354or MATH 220 or MATH 221)Description: Introductory treatment of the basic structures ofabstract algebra: groups, rings, and fields. Clear, cogent, and completemathematical arguments are emphasized. A student many not receivecredit for both MATH 306 and MATH 356. Mutually Exclusive: Cannotregister for MATH 306 if student has credit for MATH 356.Course URL: math.rice.edu (http://math.rice.edu)

MATH 321 - INTRODUCTION TO ANALYSIS IShort Title: INTRODUCTION TO ANALYSIS IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 220 or MATH 221 or MATH 354 or MATH 302Description: A thorough treatment of the foundations of real analysissuch as metric spaces, compactness, sequences and series of functions,differentiation, Riemann integration. Mutually Exclusive: Cannot registerfor MATH 321 if student has credit for MATH 331.Course URL: math.rice.edu (http://math.rice.edu)












MATH 322 - INTRODUCTION TO ANALYSIS IIShort Title: INTRODUCTION TO ANALYSIS IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 321 or MATH 331Description: Further study in real analysis. Possible topics includeanalysis in higher dimensions, Hilbert spaces, Fourier series, Sturm-Liouville theory. Repeatable for Credit.Course URL: math.rice.edu (http://math.rice.edu)

MATH 323 - INTRODUCTION TO MATHEMATICAL CRYPTOGRAPHYShort Title: INTRO TO MATH CRYPTOGRAPHYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): COMP 182 or COMP 448 or MATH 306 or MATH 365Description: The course introduces students to modern cryptographictechniques, focusing mainly on mathematical tools. The course coverstopics such as Diffie-Hellman key exchange, the ElGamal public keycrypto system, integer factorization and RSA, and elliptic curves andlattices in cryptography

MATH 331 - HONORS ANALYSISShort Title: HONORS ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 220 or MATH 221 or MATH 302 or MATH 354Description: A careful treatment of basic topics in real analysis, includingmetric spaces and their topology, sequences and series, continuity, anddifferentiation. 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 (http://math.rice.edu)

MATH 354 - HONORS LINEAR ALGEBRAShort Title: HONORS LINEAR ALGEBRADepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Vector spaces, linear transformations and matrices,theory of systems of linear equations, determinants, eigenvalues anddiagonalizability, inner product spaces; and optional material chosenfrom: dual vector spaces, spectral theorem for self-adjoint operators,Jordan canonical form. Content is similar to that of MATH 355, but withmore emphasis on theory. The course will include instruction on how toconstruct mathematical proofs. This course is appropriate for potentialMathematics majors and others interested in learning how to constructrigorous mathematical arguments. Recommended Prerequisite(s): A 200-level math class. Mutually Exclusive: Cannot register for MATH 354 ifstudent has credit for MATH 355.

MATH 355 - LINEAR ALGEBRAShort Title: LINEAR ALGEBRADepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Linear transformations and matrices, solution of linearequations, inner products eigenvalues and eigenvectors, the spectraltheorem for real symmetric matrices, applications of Jordan canonicalform. Mutually Exclusive: Cannot register for MATH 355 if student hascredit for MATH 354.

MATH 356 - ABSTRACT ALGEBRA IShort Title: ABSTRACT ALGEBRA IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): (MATH 354 or MATH 355) and (MATH 302 or MATH 354or MATH 220 or MATH 221)Description: An introduction to algebraic structures. Covers basic grouptheory (including subgroups and quotients, permutation and matrixgroups, group actions) and basic ring theory (including ideals andquotients, polynomial rings, unique factorization). Mutually Exclusive:Cannot register for MATH 356 if student has credit for MATH 306.Course URL: math.rice.edu (http://math.rice.edu)








MATH 357 - ABSTRACT ALGEBRA IIShort Title: ABSTRACT ALGEBRA IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 356Description: Fields and field extensions, modules over rings, furthertopics in groups, rings, fields, and their applications.

MATH 365 - NUMBER THEORYShort Title: NUMBER THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 220 or MATH 221 or MATH 302 or MATH 354 orCOMP 182Description: Prime numbers and factorization, modular arithmetic,Diophantine equations, quadratic reciprocity, and other topics such ascryptography or continued fractions.Course URL: math.rice.edu (http://math.rice.edu)

MATH 366 - GEOMETRYShort Title: GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Topics chosen from Euclidean, spherical, hyperbolic, andprojective geometry, with emphasis on the similarities and differencesfound in various geometries. Isometries and other transformationsare studied and used throughout. The history of the development ofgeometric ideas is discussed. This course is strongly recommended forprospective high school teachers.

MATH 368 - TOPICS IN COMBINATORICSShort Title: TOPICS IN COMBINATORICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Study of combinatorics and discrete mathematics.Topics that may be covered include graph theory, Ramsey theory, finitegeometries, combinatorial enumeration, combinatorial games.

MATH 370 - CALCULUS ON MANIFOLDSShort Title: CALCULUS ON MANIFOLDSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): (MATH 302 or MATH 321 or MATH 331) and (MATH 354or MATH 355)Description: Differentiation and integration on manifolds: calculus onRn, exterior differentiation, differentiation forms, vector fields, Stokes'theorem.Course URL: math.rice.edu (http://math.rice.edu)

MATH 371 - LIE THEORYShort Title: LIE THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 306 or MATH 356Description: Study of classical groups as symmentries of Euclideanspaces. Geometry of complex numbers and quaternions, rotationsand 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 takenthe same semester).Course URL: math.rice.edu (http://math.rice.edu)

MATH 373 - ELLIPTIC CURVESShort Title: ELLIPTIC CURVESDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 306 or MATH 356Description: Elliptic curves are central to modern number theoryand instrumental in the proof of Fermat's Last Theorem. Topics willinclude: The addition law, solutions over the rational numbers, explicitcomputations, applications to factorization and cryptography; iftime permits, infinite series attached to elliptic curves and the Birch-Swinnerton-Dyer conjecture. Recommended Prerequisite(s): 200 LevelMath CourseCourse URL: math.rice.edu (http://math.rice.edu)










MATH 374 - INTRODUCTION TO REPRESENTATION THEORYShort Title: INTRO TO REPRESENTATION THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 306 or MATH 356Description: First course in representation theory, with an emphasison concrete examples, especially the symmetric group. Topics includerepresentations of finite groups, characters, classification, symmetricfunctions, Young symmetrizers, and Schur-Weyl duality. Prior experiencewith proofs is necessary; some familiarity with linear or abstract algebrawould be helpful, but can be acquired along the way. RecommendedPrerequisite(s): Linear Algebra (MATH 221, MATH 354, or MATH 355) andMATH 356.Course URL: math.rice.edu (http://math.rice.edu)

MATH 376 - ALGEBRAIC GEOMETRYShort Title: ALGEBRAIC GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): (MATH 354 or MATH 355) and (MATH 306 or MATH 356)Description: An introduction to algebraic geometry, with an emphasison algorithms. Topics include: polynomial rings and ideals, Groebnerbases and elimination theory, affine varieties, Hilbert's Nullstellensatz,and the Algebra-Geometry correspondence. Projective varieties; Bezout'sTheorem.

MATH 381 - INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONSShort Title: INTRO PARTIAL DIFF EQUATIONSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Laplace transform: inverse transform, applications toconstant coefficient differential equations. Boundary value problems:Fourier series, Bessel functions, Legendre polynomials. RecommendedPrerequisite(s): MATH 211.

MATH 382 - COMPUTATIONAL COMPLEX ANALYSISShort Title: COMPUTATIONAL COMPLEX ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Study of the Cauchy integral theorem, Taylor series, residues,as well as the evaluation of integrals by means of residues, conformalmapping, and application to two-dimensional fluid flow. RecommendedPrerequisite(s): MATH 212 OR 221. Mutually Exclusive: Cannot registerfor MATH 382 if student has credit for MATH 427/MATH 517.Course URL: math.rice.edu (http://math.rice.edu)

MATH 390 - UNDERGRADUATE COLLOQUIUMShort Title: UNDERGRADUATE COLLOQUIUMDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hour: 1Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Lectures by undergraduate students on mathematical topicsnot usually covered in other courses. Presentation of one lecture andattendance at all sessions required. Distribution Credit for MATH 390 nolonger eligible beginning Fall 2019. Repeatable for Credit.

MATH 401 - DIFFERENTIAL GEOMETRY OF CURVES AND SURFACESShort Title: DIFF GEOM OF CURVES/SURFACESDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): (MATH 222 or MATH 354 or MATH 355) and (MATH 321or MATH 331)Description: Study of the differential geometry of curves and surfaces inR3. Includes an introduction to the concept of curvature and thoroughtreatment of the Gauss-Bonnet theorem. Recommended Prerequisite(s):MATH 211 or MATH 220 or familiarity with ODEsCourse URL: math.rice.edu (http://math.rice.edu)








MATH 402 - DIFFERENTIAL GEOMETRYShort Title: DIFFERENTIAL GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 444 or MATH 539Description: MATH 402 is the undergraduate version of the graduateclass MATH 500 (being generic for all related instances of dualenrollment classes). This is a course in smooth and Riemannianmanifolds. Tensors, Riemannian metrics, differential forms. Liederivatives. Distributions and foliations, including the FrobeniusTheorem and an introduction to contact structures. Lie groups andthe exponential map. Connections on Vector Bundles. Geodesics andcompleteness. 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: Cannotregister for MATH 402 if student has credit for MATH 500.

MATH 410 - CALCULUS OF VARIATIONSShort Title: CALCULUS OF VARIATIONSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(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 functionshaving some integral expression which is maximal, minimal, or critical.Geodesics, brachistochrone problem, minimal surfaces, and numerousapplications to physics. Euler-Lagrange equations, 1st and 2nd variations,Hamilton's Principle.

MATH 412 - PROBABILITY THEORYShort Title: PROBABILITY THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureDistribution Group: Distribution Group IIICredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 321 or MATH 331Description: A simultaneous introduction to probability theory andmeasure theory, from basic definitions to the central limit theorem. Theselection of topics in measure theory is in the service of probabilitytheory, and the course carefully examines interplay between the analyticand probabilistic notions.

MATH 423 - PARTIAL DIFFERENTIAL EQUATIONS IShort Title: PARTIAL DIFFERENTIAL EQNS IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: First order of partial differential equations. The method ofcharacteristics. Analysis of the solutions of the wave equation, heatequation 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 singularperturbation methods. Cross-list: CAAM 423. Graduate/UndergraduateEquivalency: MATH 513. Recommended Prerequisite(s): MATH 321 ANDMATH 322 Mutually Exclusive: Cannot register for MATH 423 if studenthas credit for MATH 513.

MATH 424 - TOPICS IN PARTIAL DIFFERENTIAL EQUATIONSShort Title: TOPICS IN PARTIAL DIFF EQNSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 423Description: Continuation of MATH 423. Analysis of the solutions ofsecond order differential equations. Integral relations and Green'sfunctions. Potential theory, Dirichlet and Neumann problems. Asymptoticmethods: the method of stationary phase, geometrical optics, regularand 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 (http://math.rice.edu)

MATH 425 - INTEGRATION THEORYShort Title: INTEGRATION THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 321 or MATH 331Description: Lebesgue theory of measure and integration. Graduate/Undergraduate Equivalency: MATH 515. Mutually Exclusive: Cannotregister for MATH 425 if student has credit for MATH 515.Course URL: math.rice.edu (http://math.rice.edu)






MATH 426 - TOPICS IN REAL ANALYSISShort Title: TOPICS IN REAL ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 425Description: Content varies from year to year. May include Fourier series,harmonic analysis, probability theory, advanced topics in measuretheory, ergodic theory, and elliptic integrals. Graduate/UndergraduateEquivalency: MATH 516. Mutually Exclusive: Cannot register forMATH 426 if student has credit for MATH 516. Repeatable for Credit.

MATH 427 - COMPLEX ANALYSISShort Title: COMPLEX ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 354 or MATH 222 or MATH 302Description: 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 forMATH 382/MATH 517.Course URL: math.rice.edu (http://math.rice.edu)

MATH 428 - TOPICS IN COMPLEX ANALYSISShort Title: TOPICS IN COMPLEX ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 382 or MATH 427Description: Special topics include Riemann mapping theorem, Runge'sTheorem, elliptic function theory, prime number theorem, Riemannsurfaces, et al. Graduate/Undergraduate Equivalency: MATH 518.Mutually Exclusive: Cannot register for MATH 428 if student has credit forMATH 518. Repeatable for Credit.

MATH 435 - DYNAMICAL SYSTEMSShort Title: DYNAMICAL SYSTEMSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Existence and uniqueness for solutions of ordinarydifferential equations and difference equations, linear systems, nonlinearsystems, stability, periodic solutions, bifurcation theory. Theory andtheoretical examples are complemented by computational, model drivenexamples from biological and physical sciences. Cross-list: CAAM 435.Recommended Prerequisite(s): (MATH 212 or MATH 221) and (CAAM 335or MATH 355 or MATH 354) and (MATH 302 or MATH 321 or MATH 331)Course URL: math.rice.edu (http://math.rice.edu)

MATH 443 - GENERAL TOPOLOGYShort Title: GENERAL TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 321 or MATH 331Description: Study of basic point set topology. Includes a treatmentof cardinality and well ordering, as well as metrization. Graduate/Undergraduate Equivalency: MATH 538. Mutually Exclusive: Cannotregister for MATH 443 if student has credit for MATH 538.Course URL: math.rice.edu (http://math.rice.edu)

MATH 444 - GEOMETRIC TOPOLOGYShort Title: GEOMETRIC TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 356 and MATH 443 and (MATH 322 or MATH 370or MATH 401)Description: Introduction to algebraic methods in topology anddifferential topology. Elementary homotopy theory. Covering spaces.Differentiable Manifolds. Graduate/Undergraduate Equivalency:MATH 539. Mutually Exclusive: Cannot register for MATH 444 if studenthas credit for MATH 539.Course URL: math.rice.edu/~jkn3/geotop.html (http://math.rice.edu/~jkn3/geotop.html)







http://math.rice.edu/~jkn3/geotop.html




MATH 445 - ALGEBRAIC TOPOLOGYShort Title: ALGEBRAIC TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 444Description: Introduction to the theory of homology. Includes simplicialcomplexes, cell complexes and cellular homology and cohomology,as well as manifolds, and Poincare duality. Graduate/UndergraduateEquivalency: MATH 540. Mutually Exclusive: Cannot register forMATH 445 if student has credit for MATH 540.

MATH 448 - CONCRETE MATHEMATICSShort Title: CONCRETE MATHEMATICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): COMP 182 or MATH 220 or MATH 221 or MATH 302 orMATH 354Description: Concrete mathematics is a blend of continuous and discretemathematics. 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 - ADVANCED ALGEBRA IShort Title: ADVANCED ALGEBRA IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 357Description: A first graduate course in Algebra. Advanced topics in grouptheory: semi-direct products, dual groups, inverse limits and completions.Galois Theory, including infinite Galois xtensions. Advanced topicsin ring theory: radicals, local rings, primary decomposition, the primespectrum of a ring. Groebner Bases; elimination theory. Modules: theCayley-Hamilton Theorem and Nakayama's lemma; localization and localproperties; composition series and the Jordan-Hölder theorem; structuretheorem for finitely generated modules over a PID. Tensor products:universal properties, multilinear algebra. Introduction to categories andfunctors. Graduate/Undergraduate Equivalency: MATH 563. MutuallyExclusive: Cannot register for MATH 463 if student has credit forMATH 563.

MATH 464 - ADVANCED ALGEBRA IIShort Title: ADVANCED ALGEBRA IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 463Description: Continuation of MATH 463. Tensor and exterior algebra,introductory commutative algebra, structure of modules, and elementsof homological algebra. Additional advanced topics may includerepresentations of finite groups and affine algebraic geometry. Graduate/Undergraduate Equivalency: MATH 564. Mutually Exclusive: Cannotregister for MATH 464 if student has credit for MATH 564.

MATH 465 - TOPICS IN ALGEBRA: INTRODUCTION TO ALGEBRAICGEOMETRYShort Title: TOPICS IN ALGEBRADepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Varieties as solution sets of systems of polynomialequations, varieties in projective space, rational and regular functions,maps of varieties, local properties and singularities. Graduate/Undergraduate Equivalency: MATH 565. Mutually Exclusive: Cannotregister for MATH 465 if student has credit for MATH 565. Repeatable forCredit.

MATH 466 - TOPICS IN ALGEBRA IIShort Title: TOPICS IN ALGEBRA IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Content varies from year to year. Graduate/UndergraduateEquivalency: MATH 566. Mutually Exclusive: Cannot register forMATH 466 if student has credit for MATH 566.

MATH 468 - POTPOURRIShort Title: POTPOURRIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: This course deals with miscellaneous special topics notcovered in other courses. Repeatable for Credit.


MATH 471 - MATHEMATICS OF APERIODIC ORDERShort Title: MATHEMATICS OF APERIODIC ORDERDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelPrerequisite(s): MATH 321 or MATH 354 or MATH 355Description: Mathematical models of quasicrystals, whose discoveryin the early 1980's led to a paradigm shift in materials science. Topicsinclude: classical theory of ordered structures (i.e., lattices modelingcrystals), Delone subsets and tilings of Euclidean space, aperiodicallyordered structures generated by inflation or cut-and-project schemes.Graduate/Undergraduate Equivalency: MATH 571. RecommendedPrerequisite(s): MATH 356. Mutually Exclusive: Cannot register forMATH 471 if student has credit for MATH 571.

MATH 477 - SPECIAL TOPICSShort Title: SPECIAL TOPICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: Internship/Practicum, Seminar, Lecture, LaboratoryCredit Hours: 1-4Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Topics and credit hours may vary each semester. Contactdepartment for current semester's topic(s). Repeatable for Credit.

MATH 479 - MATHEMATICS UNDERGRADUATE RESEARCHShort Title: MATH UNDERGRADUATE RESEARCHDepartment: MathematicsGrade Mode: Standard LetterCourse Type: ResearchCredit Hours: 1-3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: In depth investigation of a particular area of mathematicsof mutual interest to the student and the faculty adviser. InstructorPermission Required. Repeatable for Credit.Course URL: math.rice.edu (http://math.rice.edu)

MATH 490 - SUPERVISED READINGShort Title: SUPERVISED READINGDepartment: MathematicsGrade Mode: Standard LetterCourse Type: Independent StudyCredit Hours: 1-6Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Repeatable for Credit.

MATH 498 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCESShort Title: RESEARCH THEMES IN MATH. SCI.Department: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hours: 1-3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: A seminar course that will cover selected theme of generalresearch in the mathematical sciences from the perspectives ofmathematics, computational and applied mathematics and statistics.The course may be repeated multiple times for credit. Cross-list:CAAM 498, STAT 498. Graduate/Undergraduate Equivalency: MATH 698.Mutually Exclusive: Cannot register for MATH 498 if student has credit forMATH 698. Repeatable for Credit.

MATH 499 - MATHEMATICAL SCIENCES VIGRE SEMINARShort Title: MATHEMATICAL SCIENCESDepartment: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hours: 1-3Restrictions: Enrollment is limited to Undergraduate, UndergraduateProfessional or Visiting Undergraduate level students.Course Level: Undergraduate Upper-LevelDescription: Repeatable for Credit.

MATH 500 - DIFFERENTIAL GEOMETRYShort Title: DIFFERENTIAL GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 444 or MATH 539Description: A graduate course in smooth and Riemannian manifolds.Tensors, Riemannian metrics, differential forms. Lie derivatives.Distributions and foliations, including the Frobenius Theorem and anintroduction 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. Additionaltopics may vary from year to year. Graduate/Undergraduate Equivalency:MATH 402. Mutually Exclusive: Cannot register for MATH 500 if studenthas credit for MATH 402. Repeatable for Credit.

MATH 501 - TOPICS IN DIFFERENTIAL GEOMETRYShort Title: TOPICS DIFFERENTIAL GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.




MATH 502 - TOPICS IN DIFFERENTIAL GEOMETRYShort Title: TOPIC DIFFERENTIAL GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 513 - PARTIAL DIFFERENTIAL EQUATIONS IShort Title: PARTIAL DIFFERENTIAL EQNS IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: First order of partial differential equations. The method ofcharacteristics. Analysis of the solutions of the wave equation, heatequation 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 singularperturbation methods. Additional course work is required beyond theundergraduate course requirements. Cross-list: CAAM 523. Graduate/Undergraduate Equivalency: MATH 423. Recommended Prerequisite(s):MATH 321 AND MATH 322 Mutually Exclusive: Cannot register forMATH 513 if student has credit for MATH 423.

MATH 514 - TOPICS IN PARTIAL DIFFERENTIAL EQUATIONSShort Title: TOPICS IN PARTIAL DIFF EQNSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 513 or MATH 423Description: Continuation of MATH 513. Analysis of the solutions ofsecond order differential equations. Integral relations and Green'sfunctions. Potential theory, Dirichlet and Neumann problems. Asymptoticmethods: the method of stationary phase, geometrical optics, regularand 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 (http://math.rice.edu)

MATH 515 - INTEGRATION THEORYShort Title: INTEGRATION THEORYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: . Graduate/Undergraduate Equivalency: MATH 425. MutuallyExclusive: Cannot register for MATH 515 if student has credit forMATH 425.

MATH 516 - TOPICS IN REAL ANALYSISShort Title: TOPICS IN REAL ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 425Description: . Graduate/Undergraduate Equivalency: MATH 426. MutuallyExclusive: Cannot register for MATH 516 if student has credit forMATH 426. Repeatable for Credit.

MATH 517 - COMPLEX ANALYSISShort Title: COMPLEX ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Graduate/Undergraduate Equivalency: MATH 427. MutuallyExclusive: Cannot register for MATH 517 if student has credit forMATH 382/MATH 427.

MATH 518 - TOPICS IN COMPLEX ANALYSISShort Title: TOPICS IN COMPLEX ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 382 or MATH 427Description: . Graduate/Undergraduate Equivalency: MATH 428. MutuallyExclusive: Cannot register for MATH 518 if student has credit forMATH 428. Repeatable for Credit.

MATH 521 - ADVANCED TOPICS IN REAL ANALYSISShort Title: ADV TOPIC: REAL ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 522 - TOPICS IN ANALYSISShort Title: TOPICS IN ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.




MATH 523 - FUNCTIONAL ANALYSISShort Title: FUNCTIONAL ANALYSISDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Banach spaces: review of L^p spaces, linear operators, dualspace, 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), symmetricoperators and self-adjoint extensions; if time allows, distributions andSobolev spaces. Repeatable for Credit.

MATH 524 - TOPICS IN PARTIAL DIFFERENTIAL EQUATIONSShort Title: TOPICS IN PDEDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 527 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICSShort Title: ERGODIC THRY&TOP DYNAMICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 528 - ERGODIC THEORY AND TOPOLOGICAL DYNAMICSShort Title: ERGODIC THRY&TOPOLOGICAL DYNDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Repeatable for Credit.

MATH 538 - GENERAL TOPOLOGYShort Title: GENERAL TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: . Graduate/Undergraduate Equivalency: MATH 443. MutuallyExclusive: Cannot register for MATH 538 if student has credit forMATH 443.

MATH 539 - GEOMETRIC TOPOLOGYShort Title: GEOMETRIC TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 356 and MATH 443Description: . Graduate/Undergraduate Equivalency: MATH 444. MutuallyExclusive: Cannot register for MATH 539 if student has credit forMATH 444.

MATH 540 - ALGEBRAIC TOPOLOGYShort Title: ALGEBRAIC TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 539Description: . Graduate/Undergraduate Equivalency: MATH 445. MutuallyExclusive: Cannot register for MATH 540 if student has credit forMATH 445.

MATH 541 - TOPICS IN TOPOLOGYShort Title: TOPICS IN TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 542 - TOPICS IN ADVANCED TOPOLOGYShort Title: TOPICS IN ADVANCED TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Topic to be announced. Repeatable for Credit.

MATH 543 - TOPICS IN LOW-DIMENSIONAL TOPOLOGYShort Title: TOPICS IN L-D TOPOLOGYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 1-3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Repeatable for Credit.


MATH 544 - TOPOLOGY OF MANIFOLDSShort Title: TOPOLOGY OF MANIFOLDSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(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 theircharacteristic classes. It will cover differential forms as well as Stiefel-Whitney, Euler, Chern, and Pontryagin classes. If time allows, other topicsmay be included. The prerequisites for the class are the material fromMath 444/539 and Math 445/540. In particular, the student should befamiliar with smooth manifolds, the tangent spaces, homotopy groups,covering spaces, and homology groups.

MATH 563 - ADVANCED ALGEBRA IShort Title: ADVANCED ALGEBRA IDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 357Description: A first graduate course in Algebra. Advanced topics in grouptheory: semi-direct products, dual groups, inverse limits and completions.Galois Theory, including infinite Galois Extensions. Advanced topicsin ring theory: radicals, local rings, primary decomposition, the primespectrum of a ring. Groebner Bases; elimination theory. Modules: theCayley-Hamilton Theorem and Nakayama's lemma; localization and localproperties; composition series and the Jordan-Hölder theorem; structuretheorem for finitely generated modules over a PID. Tensor products:universal properties, multilinear algebra. Introduction to categories andfunctors. Graduate/Undergraduate Equivalency: MATH 463. MutuallyExclusive: Cannot register for MATH 563 if student has credit forMATH 463.

MATH 564 - ADVANCED ALGEBRA IIShort Title: ADVANCED ALGEBRA IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduatePrerequisite(s): MATH 463 or MATH 563Description: A continuation of Math 563. Integrality: going up and downtheorems. Noether Normalization and Hilbert's Nullstellensatz. ArtinianRings, Discrete Valuation Rings and Dedekind Domains, with applications:rings of integers in number rings, prime decomposition in number ringextensions. Completions: topologies, filtrations. Graded modules andassociated graded rings. Homological algebra: complexes, homology,homotopies; injective, projective and flat modules. Derived functors:Ext and Tor. Introduction to group cohomology and spectral sequences.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 ALGEBRAICGEOMETRYShort Title: TOPICS IN ALGEBRADepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Varieties as solution sets of systems of polynomialequations, varieties in projective space, rational and regular functions,maps of varieties, local properties and singularities. Graduate/Undergraduate Equivalency: MATH 465. Mutually Exclusive: Cannotregister for MATH 565 if student has credit for MATH 465. Repeatable forCredit.

MATH 566 - TOPICS IN ALGEBRA IIShort Title: TOPICS IN ALGEBRA IIDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: . Graduate/Undergraduate Equivalency: MATH 466. MutuallyExclusive: Cannot register for MATH 566 if student has credit forMATH 466. Repeatable for Credit.

MATH 567 - TOPICS IN ALGEBRAIC GEOMETRYShort Title: TOPICS IN ALGEBRAIC GEOMETRYDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Possible topics include rational points on algebraic varieties,moduli spaces, deformation theory, and Hodge structures. RecommendedPrerequisite(s): MATH 463 and MATH 464. Repeatable for Credit.

MATH 571 - MATHEMATICS OF APERIODIC ORDERShort Title: MATHEMATICS OF APERIODIC ORDERDepartment: MathematicsGrade Mode: Standard LetterCourse Type: LectureCredit Hours: 3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Mathematical models of quasicrystals, whose discoveryin the early 1980's led to a paradigm shift in materials science. Topicsinclude: classical theory of ordered structures (i.e., lattices modelingcrystals), Delone subsets and tilings of Euclidean space, aperiodicallyordered structures generated by inflation or cut-and-project schemes.Graduate/Undergraduate Equivalency: MATH 471. RecommendedPrerequisite(s): MATH 356 Mutually Exclusive: Cannot register forMATH 571 if student has credit for MATH 471.


MATH 590 - CURRENT MATHEMATICS SEMINARShort Title: CURRENT MATHEMATICS SEMINARDepartment: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Lectures on topics of recent research in mathematicsdelivered by mathematics graduate students and faculty. Repeatable forCredit.

MATH 591 - GRADUATE TEACHING SEMINARShort Title: GRADUATE TEACHING SEMINARDepartment: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Discussion on teaching issues and practice lectures byparticipants as preparation for classroom teaching of mathematics.Repeatable for Credit.

MATH 677 - SPECIAL TOPICSShort Title: SPECIAL TOPICSDepartment: MathematicsGrade Mode: Standard LetterCourse Type: Internship/Practicum, Seminar, Lecture, LaboratoryCredit Hours: 1-4Restrictions: Enrollment is limited to Graduate or Visiting Graduate levelstudents.Course Level: GraduateDescription: Topics and credit hours vary each semester. Contactdepartment for current semester's topic(s). Repeatable for Credit.

MATH 680 - MATHEMATICS COLLOQUIUMShort Title: MATHEMATICS COLLOQUIUMDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: LectureCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Presentations of research topics in mathematics and relatedfields. Repeatable for Credit.

MATH 681 - TOPOLOGY SEMINARShort Title: TOPOLOGY SEMINARDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: SeminarCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Presentations of research in topology and related areas.Repeatable for Credit.

MATH 682 - ALGEBRAIC GEOMETRY SEMINARShort Title: ALGEBRAIC GEOMETRY SEMINARDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: SeminarCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Presentations of research in algebraic geometry and relatedareas. Repeatable for Credit.

MATH 683 - GEOMETRY AND ANALYSIS SEMINARShort Title: GEOMETRY AND ANALYSIS SEMINARDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: SeminarCredit Hour: 1Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Presentations of research in geometric analysis,mathematical physics, dynamics and related areas. Repeatable for Credit.

MATH 690 - SUPERVISED READINGShort Title: SUPERVISED READINGDepartment: MathematicsGrade Mode: Standard LetterCourse Type: Independent StudyCredit Hours: 1-6Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Repeatable for Credit.

MATH 698 - RESEARCH THEMES IN THE MATHEMATICAL SCIENCESShort Title: RESEARCH THEMES IN MATH. SCI.Department: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hours: 1-3Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: A seminar course that will cover selected theme of generalresearch in the mathematical sciences from the perspectives ofmathematics, computational and applied mathematics and statistics.The course may be repeated multiple times for credit. Cross-list:CAAM 698, STAT 698. Graduate/Undergraduate Equivalency: MATH 498.Mutually Exclusive: Cannot register for MATH 698 if student has credit forMATH 498. Repeatable for Credit.

MATH 699 - MATHEMATICAL SCIENCES VIGRE SEMINARShort Title: MATHEMATICAL SCIENCESDepartment: MathematicsGrade Mode: Standard LetterCourse Type: SeminarCredit Hours: 1-9Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Repeatable for Credit.


MATH 700 - SUMMER RESEARCH FOR PHD STUDENTSShort Title: SUMMER RESEARCHDepartment: MathematicsGrade Mode: Satisfactory/UnsatisfactoryCourse Type: ResearchCredit Hours: 9Restrictions: Enrollment is limited to Graduate level students. Enrollmentlimited to students in a Doctor of Philosophy degree.Course Level: GraduateDescription: Summer research for MATH PhD students. Can be repeatedfor credit. Repeatable for Credit.

MATH 800 - GRADUATE THESIS AND RESEARCHShort Title: GRADUATE THESIS AND RESEARCHDepartment: MathematicsGrade Mode: Standard LetterCourse Type: ResearchCredit Hours: 1-15Restrictions: Enrollment is limited to Graduate level students.Course Level: GraduateDescription: Repeatable for Credit.

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M ATHEM ATICS (M ATH) - Rice Universityalgebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the