**Note:** Mathematics 016A, 016B, and 016C are intended for students who will take no more Mathematics courses. Mathematics 017A, 017B, and 017C have the same level of rigor as 016A, 016B, and 016C, yet are much

**Courses in MAT:**

**Note:** Mathematics 016A, 016B, and 016C are intended for students who will take no more Mathematics courses. Mathematics 017A, 017B, and 017C have the same level of rigor as 016A, 016B, and 016C, yet are much

**Courses in MAT:**

MAT 000B—Elementary Algebra (no credit) (0) Active

Lecture—3 hour(s). Not open to Concurrent student enrollment. Basic concepts of algebra, including polynomials, factoring, equations, graphs, and inequalities. Offered only if sufficient number of students enroll. (P/NP grading only.) Effective: 1997 Winter Quarter.

MAT 000C—Trigonometry (no credit) (0) Active

Lecture—2 hour(s). Not open to Concurrent student enrollment. Basic concepts of trigonometry, including trigonometric functions, identities, inverse functions, and applications. Offered only if sufficient number of students enroll. (P/NP grading only.) Effective: 1997 Winter Quarter.

MAT 000D—Intermediate Algebra (no credit) (0) Active

Lecture—3 hour(s). Not open to Concurrent student enrollment. Basic concepts of algebra, prepares student for college work in mathematics, such as course 16A or 21A. Functions, equations, graphs, logarithms, and systems of equations. Offered only if sufficient number of students enroll. (P/NP grading only.) Effective: 1997 Winter Quarter.

MAT 012—Precalculus (3) Active

Lecture—3 hour(s). Prerequisite(s): Two years of high school algebra, plane geometry, plane trigonometry; and obtaining required score on the Precalculus Diagnostic Examination. Topics selected for their use in calculus, including functions and their graphs, slope, zeroes of polynomials, exponential, logarithmic and trigonometric functions, sketching surfaces and solids. Not open for credit to students who have completed any of courses MAT 016A, MAT 016B, MAT 016C, MAT 017A, MAT 017B, MAT 017C, MAT 021A, MAT 021B, or MAT 021C with a C- or better. (Letter.) GE credit: QL, SE, SL. Effective: 2012 Winter Quarter.

MAT 016A—Short Calculus (3) Active

Lecture—3 hour(s). Prerequisite(s): Two years of high school algebra, plane geometry, plane trigonometry, and satisfying the Mathematics Placement Requirement. Limits; differentiation of algebraic functions; analytic geometry; applications, in particular to maxima and minima problems. Not open for credit to students who have completed MAT 017B, MAT 017C, MAT 021A, MAT 021B, or MAT 021C; only 2 units of credit to students who have completed MAT 17A. (Letter.) GE credit: QL, SE, SL. Effective: 2012 Winter Quarter.

MAT 016B—Short Calculus (3) Active

Lecture—3 hour(s). Prerequisite(s): MAT 016A C- or better or MAT 017A C- or better or MAT 021A C- or better or MAT 021AH C- or better. Integration; calculus for trigonometric, exponential, and logarithmic functions; applications. Not open for credit to students who have completed MAT 017C, MAT 021B, or MAT 021C; only 2 units of credit to students who have completed MAT 017B. (Letter.) GE credit: QL, SE, SL. Effective: 2017 Winter Quarter.

MAT 016C—Short Calculus (3) Active

Lecture—3 hour(s). Prerequisite(s): MAT 016B C- or better or MAT 017B C- or better or MAT 021B C- or better or MAT 021BH C- or better. Differential equations; partial derivatives; double integrals; applications; series. Not open for credit to students who have completed MAT 021C; only 2 units of credit to students who have completed MAT 017C. (Letter.) GE credit: QL, SE, SL. Effective: 2017 Winter Quarter.

MAT 017A—Calculus for Biology & Medicine (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfying the Mathematics Placement Requirement. Introduction to differential calculus via applications in biology and medicine. Limits, derivatives of polynomials, trigonometric, and exponential functions, graphing, applications of the derivative to biology and medicine. Not open for credit to students who have completed MAT 016B, MAT 016C, MAT 021A, MAT 021B, or MAT 021C; only 2 units of credit to students who have completed MAT 016A. (Letter.) GE credit: QL, SE, SL. Effective: 2014 Fall Quarter.

MAT 017B—Calculus for Biology & Medicine (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 016A C- or better or MAT 017A C- or better or MAT 021A C- or better or MAT 021AH C- or better. Introduction to integral calculus and elementary differential equations via applications to biology and medicine. Fundamental theorem of calculus, techniques of integration including integral tables and numerical methods, improper integrals, elementary first order differential equations, applications in biology and medicine.
Not open for credit to students who have completed MAT 016C, MAT 021B, or MAT 021C; only 2 units of credit for students who have completed MAT 016B. (Letter.) GE credit: QL, SE, SL. Effective: 2017 Winter Quarter.

MAT 017C—Calculus for Biology & Medicine (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 017B C- or better. Matrix algebra, functions of several variables, partial derivatives, systems of differential equations, and applications to biology and medicine. Not open for credit to students who have completed MAT 21C; only 2 units of credit to students who have completed MAT 16C. (Letter.) GE credit: SE, SL. Effective: 2016 Fall Quarter.

MAT 021A—Calculus (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfying the Mathematics Placement Requirement. Functions, limits, continuity. Slope and derivative. Differentiation of algebraic and transcendental functions. Applications to motion, natural growth, graphing, extrema of a function. Differentials. L'Hopital's rule. Not open for credit to students who have completed MAT 016B, MAT 016C, MAT 017B, or MAT 017C; only 2 units of credit to students who have completed MAT 016A or MAT 017A. (Letter.) GE credit: QL, SE, SL. Effective: 2012 Winter Quarter.

MAT 021AH—Honors Calculus (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): A Precalculus Diagnostic Examination score significantly higher than the minimum for MAT 021A is required. More intensive treatment of material covered in course 21A. (Letter.) GE credit: QL, SE. Effective: 1997 Winter Quarter.

MAT 021AL—Emerging Scholars Program Calculus Workshop (2) Active

Workshop—6 hour(s). Prerequisite(s): MAT 021A (can be concurrent); MAT 021A required concurrently. Functions, limits, continuity. Slope and derivative. Same course content as course 21A. Enrollment for students in the Emerging Scholars Program by instructor's invitation only. (P/NP grading only.) GE credit: SE. Effective: 2006 Fall Quarter.

MAT 021B—Calculus (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): (MAT 021A C- or better or MAT 021AH C- or better) or MAT 017A B or better. Continuation of course 21A. Definition of definite integral, fundamental theorem of calculus, techniques of integration. Application to area, volume, arc length, average of a function, improper integral, surface of revolution. Only 2 units of credit to students who have completed MAT 016B, MAT 016C, MAT 017B, or MAT 017C. (Letter.) GE credit: QL, SE. Effective: 2017 Winter Quarter.

MAT 021BH—Honors Calculus (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021A B or better or MAT 021AH B or better. More intensive treatment of material covered in course 21B. Students completing 21BH can continue with course 21CH or the regular 21C. (Letter.) GE credit: SE. Effective: 1997 Winter Quarter.

MAT 021BL—Emerging Scholars Program Calculus Workshop (2) Active

Workshop—6 hour(s). Prerequisite(s): MAT 021B (can be concurrent); Concurrent enrollment in MAT 021B. Continuation of course 21A. Same course content as 21B. Enrollment for students in the Emerging Scholars Program by instructor's invitation only. (P/NP grading only.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 021C—Calculus (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 016C C- or better or MAT 017C C- or better or MAT 021B C- or better or MAT 021BH C- or better or MAT 017B B or better;. Continuation of course 21B. Sequences, series, tests for convergence, Taylor expansions. Vector algebra, vector calculus, scalar and vector fields. Partial derivatives, total differentials. Applications to maximum and minimum problems in two or more variables. Applications to physical systems. (Letter.) GE credit: QL, SE. Effective: 2017 Winter Quarter.

MAT 021CH—Honors Calculus (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021B B or better or MAT 021BH B or better. More intensive treatment of material covered in course 21C. (Letter.) GE credit: SE. Effective: 1997 Winter Quarter.

MAT 021CL—Emerging Scholars Program Calculus Workshop (2) Active

Workshop—6 hour(s). Prerequisite(s): MAT 021C (can be concurrent); Concurrent enrollment in MAT 021C. Continuation of course 21B. Same course content as course 21C. Enrollment for students in the Emerging Scholars Program by instructor's invitation only. (P/NP grading only.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 021D—Vector Analysis (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): (MAT 021C C- or better or MAT 021CH C- or better) or MAT 017C B or better. Continuation of course 21C. Definite integrals over plane and solid regions in various coordinate systems. Line and surface integrals. Green's theorem, Stoke's theorem, divergence theorem. (Letter.) GE credit: QL, SE. Effective: 2017 Winter Quarter.

MAT 021M—Accelerated Calculus (5) Active

Lecture/Discussion—4 hour(s); Discussion/Laboratory—1 hour(s). Prerequisite(s): Grade of B or higher in both semesters of high school calculus or a score of 4 or higher on the Advanced Placement Calculus AB exam, and obtaining the required score on the Precalculus Diagnostic Examination and its trigonometric component. Accelerated treatment of material from courses 21A and 21B, with detailed presentation of theory, definitions, and proofs, and treatment of computational aspects of calculus at a condensed but sophisticated level. Not open for credit to students who have completed MAT 021A or MAT 021B. (Letter.) GE credit: SE. Effective: 1997 Winter Quarter.

MAT 022A—Linear Algebra (3) Active

Lecture—3 hour(s). Prerequisite(s): (MAT 016C C- or better or MAT 017C C- or better or MAT 021C C- or better or MAT 021CH C- or better); (ENG 006 or EME 005 or ECH 060 or MAT 022AL (can be concurrent)). Matrices and linear transformations, determinants, eigenvalues, eigenvectors, diagonalization, factorization. Not open for credit to students who have completed course 67. (Letter.) GE credit: QL, SE. Effective: 2018 Summer Session 1.

MAT 022AL—Linear Algebra Computer Laboratory (1) Active

Laboratory—3 hour(s). Prerequisite(s): MAT 016C or MAT 017C or MAT 021C or MAT 021CH. Introduction to Matlab and its use in linear algebra. (P/NP grading only.) GE credit: QL, SE. Effective: 2017 Winter Quarter.

MAT 022B—Differential Equations (3) Active

Lecture—3 hour(s). Prerequisite(s): (MAT 022A C- or better or MAT 067 C- or better). Solutions of elementary differential equations. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 025—Advanced Calculus (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021C C- or better or MAT 021CH C- or better. Introduction to the rigorous treatment of abstract mathematical analysis. Proofs in mathematics, induction, sets, cardinality; real number system, theory of convergence of sequences. Not open for credit to students who have completed former MAT 127A. (Letter.) GE credit: SE. Effective: 2017 Spring Quarter.

MAT 027A—Linear Algebra with Applications to Biology (4) Active

Lecture—3 hour(s); Laboratory—2 hour(s). Prerequisite(s): MAT 017C C- or better or MAT 021C C- or better or MAT 021CH C- or better. Introduction to linear algebra with biological, medical, and bioengineering applications. Matrix algebra, vector spaces, orthogonality, determinants, eigenvalues, eigenvectors, principal component analysis, singular value decomposition, and linear transformations. Computer labs cover mathematical and computational techniques for modeling biological systems. Only one unit of credit for students who have completed MAT 022A. (Same course as BIS 027A.) (Letter.) GE credit: SE. Effective: 2019 Winter Quarter.

MAT 027B—Differential Equations with Applications to Biology (4) Active

Lecture—3 hour(s); Laboratory—2 hour(s). Prerequisite(s): MAT 027A C- or better or (MAT 022A C- or better, (MAT 022AL C- or better or ENG 006 C- or better or EME 005 C- or better)). Solutions of differential equations with biological, medical, and bioengineering applications. First and second order linear equations, phase plane analysis, nonlinear dynamics, Laplace transforms, and the diffusion equation. Computer labs cover mathematical and numerical techniques for modeling biological systems. Only one unit of credit for students who have completed MAT 022B. (Same course as BIS 027B.) (Letter.) GE credit: SE. Effective: 2019 Spring Quarter.

MAT 036—Fundamentals of Mathematics (3) Active

Lecture—3 hour(s). Prerequisite(s): Satisfaction of the Mathematics Placement Requirement. Introduction to fundamental mathematical ideas selected from the principal areas of modern mathematics. Properties of the primes, the fundamental theorems of arithmetic, properties of the rationals and irrationals, binary and other number systems. Not open for credit to students who have taken MAT 108. (Letter.) Effective: 2001 Winter Quarter.

MAT 067—Modern Linear Algebra (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021C C- or better or MAT 021CH C- or better. Rigorous treatment of linear algebra; topics include vector spaces, bases and dimensions, orthogonal projections, eigenvalues and eigenvectors, similarity transformations, singular value decomposition and positive definiteness. Only one unit of credit to students who have completed MAT 022A. (Letter.) GE credit: SE. Effective: 2017 Winter Quarter.

MAT 071A—Explorations in Elementary Mathematics (3) Active

Lecture—2 hour(s); Laboratory—3 hour(s). Prerequisite(s): Two years of high school mathematics. Weekly explorations of mathematical ideas related to the elementary school curriculum will be carried out by cooperative learning groups. Lectures will provide background and synthesize the results of group exploration. (Letter.) Effective: 1997 Winter Quarter.

MAT 071B—Explorations in Elementary Mathematics (3) Active

Lecture—2 hour(s); Laboratory—3 hour(s). Prerequisite(s): Two years of high school mathematics. Weekly explorations of mathematical ideas related to the elementary school curriculum will be carried out by cooperative learning groups. Lectures will provide background and synthesize the results of group exploration. (Letter.) Effective: 1997 Winter Quarter.

MAT 089—Elementary Problem Solving (1) Active

Lecture—1 hour(s). Prerequisite(s): High school mathematics through precalculus. Solve and present solutions to challenging and interesting problems in elementary mathematics. May be repeated up to 1 Time(s). (P/NP grading only.) Effective: 2001 Winter Quarter.

MAT 098—Directed Group Study (1-5) Active

Variable. Prerequisite(s): Consent of Instructor. (P/NP grading only.) Effective: 1997 Winter Quarter.

MAT 099—Special Study for Undergraduates (1-5) Active

Variable. Prerequisite(s): Consent of Instructor. (P/NP grading only.) Effective: 1997 Winter Quarter.

MAT 107—Probability & Stochastic Processes with Applications to Biology (4) Active

Lecture—3 hour(s); Laboratory—2 hour(s). Prerequisite(s): (MAT 027A C- or better or BIS 027A C- or better) or (MAT 022A C- or better, (MAT 022AL C- or better or ENG 006 C- or better or EME 005 C- or better)). Introduction to probability theory and stochastic processes with biological, medical, and bioengineering applications. Combinatorics, discrete and continuous random variables, Bayes’ formula, conditional probability, Markov chains, Poisson processes, and Brownian motion. Computer labs cover mathematical and computational modeling techniques. Only 2 units of credit for students who have completed MAT 135A or STA 131A. (Same course as BIS 107.) (Letter.) GE credit: SE. Effective: 2019 Spring Quarter.

MAT 108—Introduction to Abstract Mathematics (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021B. A rigorous treatment of mathematical concepts with emphasis on developing the ability to understand abstract mathematical ideas, to read and write mathematical concepts, and to prove theorems. Designed to serve as preparation for the more rigorous upper division courses. (Letter.) GE credit: SE. Effective: 2008 Spring Quarter.

MAT 111—History of Mathematics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 025 or MAT 127A or MAT 067 or MAT 108 or MAT 114 or MAT 115A or MAT 141 or MAT 145; Eight units of upper division Mathematics. History of mathematics from ancient times through the development of calculus. Mathematics from Arab, Hindu, Chinese and other cultures. Selected topics from the history of modern mathematics. (Letter.) GE credit: SE. Effective: 2018 Fall Quarter.

MAT 114—Convex Geometry (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021C; (MAT 022A or MAT 067). Topics selected from the theory of convex bodies, convex functions, geometric inequalities, combinatorial geometry, and integral geometry. Designed to serve as preparation for the more rigorous upper-division courses. (Letter.) GE credit: SE. Effective: 2007 Winter Quarter.

MAT 115A—Number Theory (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021B. Divisibility and related topics, diophantine equations, selected topics from the theory of prime numbers. Designed to serve as preparation for the more rigorous upper division courses. (Letter.) GE credit: QL, SE. Effective: 2006 Fall Quarter.

MAT 115B—Number Theory (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 115A; (MAT 022A or MAT 067). Euler function, Moebius function, congruences, primitive roots, quadratic reciprocity law. (Letter.) GE credit: QL, SE, SL. Effective: 2016 Fall Quarter.

MAT 116—Differential Geometry (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 021D; MAT 022B; (MAT 022A or MAT 067). Vector analysis, curves, and surfaces in three dimensions. (Letter.) GE credit: SE. Effective: 2017 Winter Quarter.

MAT 118A—Partial Differential Equations: Elementary Methods (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 021D; MAT 022B; (MAT 022A or MAT 067). Derivation of partial differential equations; separation of variables; equilibrium solutions and Laplace's equation; Fourier series; method of characteristics for the one dimensional wave equation. Solution of nonhomogeneous equations. (Letter.) GE credit: QL, SE. Effective: 2006 Fall Quarter.

MAT 118B—Partial Differential Equations: Eigenfunction Expansions (4) Active

Lecture—3 hour(s). Prerequisite(s): MAT 118A. Sturm-Liouville Theory; selfadjoint operators; mixed boundary conditions; partial differential equations in two and three dimensions;
Eigenvalue problems in circular domains; nonhomogeneous problems and the method of eigenfunction expansions; Poisson's Equations. (Letter.) GE credit: QL, SE. Effective: 2000 Fall Quarter.

MAT 118C—Partial Differential Equations: Green's Functions & Transforms (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 118B. Green's functions for one-dimensional problems and Poisson's equation; Fourier transforms; Green's Functions for time dependent problems; Laplace transform and solution of partial differential equations. (Letter.) GE credit: QL, SE. Effective: 2000 Fall Quarter.

MAT 119A—Ordinary Differential Equations (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 021D; MAT 022B; (MAT 022A or MAT 067). Scalar and planar autonomous systems; nonlinear systems and linearization; existence and uniqueness of solutions; matrix solution of linear systems; phase plane analysis; stability analysis; bifurcation theory; Liapunov's method; limit cycles; Poincare Bendixon theory. (Letter.) GE credit: QL, SE. Effective: 2007 Winter Quarter.

MAT 119B—Ordinary Differential Equations (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 119A. Lorentz equations; Poincare maps; center manifolds and normal forms; scalar and planar maps; phase space analysis for iterated maps; period-doubling bifurcation; Lyapunov exponent; chaos and symbolic dynamics; strange attractors; fractals. (Letter.) GE credit: QL, SE. Effective: 2007 Spring Quarter.

MAT 124—Mathematical Biology (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): MAT 022B; (MAT 022A or MAT 067). Methods of mathematical modeling of biological systems including difference equations, ordinary differential equations, stochastic and dynamic programming models. Computer simulation methods applied to biological systems. Applications to population growth, cell biology, physiology, evolutionary ecology and protein clustering. MATLAB programming required. (Letter.) GE credit: QL, SE. Effective: 2007 Spring Quarter.

MAT 125A—Real Analysis (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 025. Functions, limits of functions, continuity and uniform continuity, sequences of functions, series of real numbers, series of functions, power series. Not open for credit to students who have completed former MAT 127B. (Letter.) GE credit: SE. Effective: 2006 Fall Quarter.

MAT 125B—Real Analysis (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 125A; (MAT 067 or (MAT 022A, MAT 108)). Theory of the derivative, Taylor series, integration, partial derivatives, Implicit Function Theorem. Not open for credit to students who have completed former MAT 127C. (Letter.) GE credit: SE. Effective: 2017 Winter Quarter.

MAT 127A—Real Analysis (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): (MAT 021C or MAT 021CH); (MAT 067 or (MAT 022A, MAT 108). Real numbers, sequences, series, and continuous functions. (Letter.) Effective: 2017 Fall Quarter.

MAT 127B—Real Analysis (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 127A. Derivatives, integrals, sequences of functions, and power series. (Letter.) Effective: 2017 Fall Quarter.

MAT 127C—Real Analysis (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 127B. Metric spaces and multi-variable calculus. (Letter.) Effective: 2017 Fall Quarter.

MAT 128A—Numerical Analysis (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): MAT 021C; (ECS 032A or ENG 006 or EME 005 or ECS 030). Error analysis, approximation, interpolation, numerical differentiation and integration. Programming in language such as Pascal, Fortran, or BASIC required. (Letter.) GE credit: QL, SE. Effective: 2019 Winter Quarter.

MAT 128B—Numerical Analysis in Solution of Equations (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): (MAT 022A or MAT 067); (ECS 032A or ENG 006 or EME 005 or ECS 030). Solution of nonlinear equations and nonlinear systems. Minimization of functions of several variables. Simultaneous linear equations. Eigenvalue problems. Linear programming. Programming in language such as Pascal, Fortran, or BASIC required. (Letter.) GE credit: QL, SE. Effective: 2019 Winter Quarter.

MAT 128C—Numerical Analysis in Differential Equations (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): (MAT 022A or MAT 067); MAT 022B; (ECS 032A or ENG 006 or EME 005 or ECS 030). Difference equations, operators, numerical solutions of ordinary and partial differential equations. Programming in language such as Pascal, Fortran, or BASIC required. (Letter.) GE credit: QL, SE. Effective: 2019 Winter Quarter.

MAT 129—Fourier Analysis (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 021D; MAT 022B; (MAT 022A or MAT 067); MAT 025. Fourier series and integrals, orthogonal sets of functions. Topics selected from trigonometric approximation, orthogonal polynomials, applications to signal and image processing, numerical analysis, and differential equations. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 133—Mathematical Finance (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): (MAT 067 or (MAT 022A, MAT 108)), MAT 135A. Analysis and evaluation of deterministic and random cash flow streams, yield and pricing of basic financial instruments, interest rate theory, mean-variance portfolio theory, capital asset pricing models, utility functions and general principles. MATLAB programming required. (Letter.) GE credit: QL, SE, SL. Effective: 2016 Fall Quarter.

MAT 135A—Probability (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021C; (MAT 108 or MAT 025). Probability space; discrete probability, combinatorial analysis; independence, conditional probability; random variables, discrete and continuous distributions, probability mass function, joint and marginal density functions; expectation, moments, variance, Chebyshev inequality; sums of random variables, random walk, large number law, central limit theorem. Not open for credit to students who have completed former MAT 131. (Letter.) GE credit: SE. Effective: 2018 Spring Quarter.

MAT 135B—Stochastic Processes (4) Active

Discussion/Laboratory—4 hour(s). Prerequisite(s): MAT 135A; (MAT 022A or MAT 067). Generating functions, branching processes, characteristic function; Markov chains; convergence of random variables, law of iterated logarithm; random processes, Brownian motion, stationary processes, renewal processes, queueing theory, martingales. Not open for credit to students who have completed former MAT 132A. (Letter.) GE credit: QL, SE. Effective: 2009 Spring Quarter.

MAT 141—Euclidean Geometry (4) Active

Lecture—3 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 021B; (MAT 022A or MAT 067). Axiomatic and analytic examination of Euclidean geometry from an advanced point of view. In particular, a discussion of its relation to other geometries. Designed to serve as preparation for the more rigorous upper division courses. (Letter.) GE credit: SE. Effective: 2018 Winter Quarter.

MAT 145—Combinatorics (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 021C. Combinatorial methods using basic graph theory, counting methods, generating functions, and recurrence relations. Designed to serve as preparation for the more rigorous upper division courses. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 146—Algebraic Combinatorics (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): ((MAT 022A, MAT 108) or MAT 067)); MAT 145. Enumeration, Polya theory, generating functions, current topics in algebraic combinatorics. Not open for credit to students who have completed former MAT 149A. (Letter.) GE credit: SE. Effective: 2018 Fall Quarter.

MAT 147—Topology (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 025. Basic notions of point-set and combinatorial topology. (Letter.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 148—Discrete Mathematics (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 067 or (MAT 022A, MAT 108). Coding theory, error correcting codes, finite fields and the algebraic concepts needed in their development. Not open for credit to students who have completed former MAT 149B. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 150A—Modern Algebra (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 067 or (MAT 022A, MAT 108). Basic concepts of groups, symmetries of the plane. Emphasis on the techniques used in the proof of the ideas (Lemmas, Theorems, etc.) developing these concepts. Precise thinking, proof writing, and the ability to deal with abstraction. (Letter.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 150B—Modern Algebra (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 150A. Bilinear forms, rings, factorization, modules. (Letter.) GE credit: SE. Effective: 2007 Winter Quarter.

MAT 150C—Modern Algebra (4) Active

Lecture/Discussion—4 hour(s). Prerequisite(s): MAT 150B. Group representations, fields, Galois theory.
(Letter.) GE credit: SE. Effective: 2007 Spring Quarter.

MAT 160—Mathematics for Data Analytics & Decision Making (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): MAT 167. Relational model; relational algebra, relational calculus, normal forms, functional and multivalued dependencies, separability. Cost benefit analysis of physical database design and reorganization. Performance via analytical modeling, simulation, and queueing theory. Block accesses; buffering; operating system contention; CPU intensive operations. (Letter.) GE credit: SE. Effective: 2018 Spring Quarter.

MAT 165—Mathematics & Computers (4) Active

Lecture—3 hour(s); Project (Term Project). Prerequisite(s): MAT 022A or MAT 067; (MAT 025 or MAT 108 or MAT 114 or MAT 115A or MAT 145). Introduction to computational mathematics, symbolic computation, and computer generated/verified proofs in algebra, analysis and geometry. Investigation of rigorous new mathematics developed in conjunction with modern computational questions and the role that computers play in mathematical conjecture and experimentation. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 167—Applied Linear Algebra (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 022A or MAT 067. Applications of linear algebra; LU and QR matrix factorizations, eigenvalue and singular value matrix decompositions. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 168—Optimization (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 021C; ((MAT 022A, MAT 108) or MAT 067)). Linear programming, simplex method. Basic properties of unconstrained nonlinear problems, descent methods, conjugate direction method. Constrained minimization. Programming language required. (Letter.) GE credit: QL, SE. Effective: 2016 Fall Quarter.

MAT 180—Special Topics (3) Active

Lecture—3 hour(s). Prerequisite(s): MAT 025; (MAT 067 or (MAT 022A, MAT 108)). Special topics from various fields of modern, pure, and applied mathematics. Some recent topics include Knot Theory, General Relativity, and Fuzzy Sets. May be repeated for credit when topics differs. (Letter.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 185A—Complex Analysis (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): (MAT 067 or (MAT 022A, MAT 108)), MAT 125A. Complex number system, analyticity and the Cauchy-Riemann equations, elementary functions, complex integration, power and Laurent series expansions, residue theory. (Letter.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 185B—Complex Analysis (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 185A. Analytical functions, elementary functions and their mapping properties, applications of Cauchy's integral theorem, conformal mapping and applications to heat flow and fluid mechanics. (Letter.) GE credit: SE. Effective: 2007 Spring Quarter.

MAT 189—Advanced Problem Solving (3) Active

Lecture—3 hour(s). Prerequisite(s): MAT 025; ((MAT 022A, MAT 108) or MAT 067). Solution and presentation of advanced problem solving techniques. Solve and present interesting and challenging problems of all areas of mathematics. (Letter.) GE credit: OL, QL, SE, WE. Effective: 2016 Fall Quarter.

MAT 192—Internship in Applied Mathematics (1-3) Active

Internship. Prerequisite(s): Consent of Instructor. Supervised work experience in applied mathematics. Final report. May be repeated up to 10 Unit(s). (P/NP grading only.) Effective: 2016 Fall Quarter.

MAT 194—Undergraduate Thesis (3) Active

Independent Study. Prerequisite(s): Consent of Instructor. Independent research under supervision of a faculty member. Student will submit written report in thesis form. May be repeated for credit with consent of Vice Chairperson. (P/NP grading only.) GE credit: SE. Effective: 2016 Fall Quarter.

MAT 197TC—Tutoring Mathematics in the Community (1-5) Active

Seminar—1-2 hour(s); Laboratory—2-6 hour(s). Prerequisite(s): Consent of Instructor. Special projects in mathematical education developing techniques for mathematics instruction and tutoring on an individual or small group basis. May be repeated up to 1 Time(s). (P/NP grading only.) Effective: 2016 Fall Quarter.

MAT 198—Directed Group Study (1-5) Active

Variable. Prerequisite(s): Consent of Instructor. (P/NP grading only.) Effective: 2016 Fall Quarter.

MAT 199—Special Study for Advanced Undergraduates (1-5) Active

Variable. (P/NP grading only.) GE credit: SE. Effective: 1997 Winter Quarter.

MAT 200—Problem-Solving in Analysis (3) Active

Lecture—1 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 201A (can be concurrent); MAT 201B (can be concurrent). Problem-solving in graduate analysis: continuous functions, metric spaces, Banach & Hilbert spaces, bounded linear operators, the spectral theorem, distributions, Fourier series & transforms, Lp spaces, Sobolev spaces. (S/U grading only.) Effective: 2019 Fall Quarter.

MAT 201A—Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in Mathematics or Applied Mathematics, or consent of instructor. Metric and normed spaces. Continuous functions. Topological, Hilbert, and Banach spaces. Fourier series. Spectrum of bounded and compact linear operators. Linear differential operators and Green's functions. Distributions. Fourier transform. Measure theory. Lp and Sobolev spaces. Differential calculus and variational methods. (Letter.) Effective: 2004 Fall Quarter.

MAT 201B—Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in Mathematics or Applied Mathematics, or consent of instructor. Metric and normed spaces. Continuous functions. Topological, Hilbert, and Banach spaces. Fourier series. Spectrum of bounded and compact linear operators. Linear differential operators and Green's functions. Distributions. Fourier transform. Measure theory. Lp and Sobolev spaces. Differential calculus and variational methods. (Letter.) Effective: 2005 Winter Quarter.

MAT 201C—Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in Mathematics or Applied Mathematics, or consent of instructor. Metric and normed spaces. Continuous functions. Topological, Hilbert, and Banach spaces. Fourier series. Spectrum of bounded and compact linear operators. Linear differential operators and Green's functions. Distributions. Fourier transform. Measure theory. Lp and Sobolev spaces. Differential calculus and variational methods. (Letter.) Effective: 2005 Spring Quarter.

MAT 202—Functional Analysis (4) Active

Lecture—3 hour(s); Term Paper. Prerequisite(s): MAT 201A; MAT 201B. Hahn-Banach, Open mapping, Closed graph, Banach-Steinhaus, and Krein-Milman. Subspaces and quotient spaces. Projections. Weak and weak-star topologies. Compact and adjoint operators in Banach spaces. Fredholm theory. Functions of operators. Spectral theory of self-adjoint operators. (Letter.) Effective: 2009 Winter Quarter.

MAT 205—Complex Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 185A; Or equivalent to MAT 185A, or consent of instructor. Analytic continuation, Riemann surfaces, conformal mappings, Riemann mapping theorem, entire functions, special functions, elliptic functions.
(Letter.) Effective: 2009 Spring Quarter.

MAT 205A—Complex Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 185A; Or equivalent to MAT 185A, or consent of instructor. Cauchy's theorem, Cauchy's integral formulas, meromorphic functions, complex logarithm, entire functions, Weierstrass infinite product formula, the gamma and zeta functions, and prime number theorem.
No credit given to students who have completed MAT 205. (Letter.) Effective: 2011 Fall Quarter.

MAT 205B—Complex Analysis (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 205A; or Consent of Instructor. Conformal mappings, the Schwarz lemma, analytic automorphisms, the Riemann mapping theorem, elliptic functions, Eisenstein series, the Jacobi theta functions, asymptotics, Bessel functions, the Airy function, topics on special functions and Riemann surfaces. May be repeated up to 2 Time(s) if topic varies. (Letter.) Effective: 2011 Spring Quarter.

MAT 206—Measure Theory (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 125B. Introduction to measure theory. The study of lengths, surface areas, and volumes in general spaces, as related to integration theory. (Letter.) Effective: 2007 Spring Quarter.

MAT 207A—Methods of Applied Mathematics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Ordinary differential equations and dynamical systems. Variational principles. Eigenfunctions, integral equations and Green's functions. Complex analysis and contour integration. Laplace's equation. Diffusion equations. Wave phenomena. Dimensional analysis and scaling. Asymptotic expansions and perturbation theory. Stochastic processes and Brownian motion. (Letter.) Effective: 2010 Fall Quarter.

MAT 207B—Methods of Applied Mathematics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Ordinary differential equations and dynamical systems. Variational principles. Eigenfunctions, integral equations and Green's functions. Complex analysis and contour integration. Laplace's equation. Diffusion equations. Wave phenomena. Dimensional analysis and scaling. Asymptotic expansions and perturbation theory. Stochastic processes and Brownian motion. (Letter.) Effective: 2011 Winter Quarter.

MAT 207C—Methods of Applied Mathematics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Ordinary differential equations and dynamical systems. Variational principles. Eigenfunctions, integral equations and Green's functions. Complex analysis and contour integration. Laplace's equation. Diffusion equations. Wave phenomena. Dimensional analysis and scaling. Asymptotic expansions and perturbation theory. Stochastic processes and Brownian motion. (Letter.) Effective: 2011 Spring Quarter.

MAT 215A—Topology (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Fundamental group and covering space theory. Homology and cohomology. Manifolds and duality. CW complexes. Fixed point theorems.
(Letter.) Effective: 2002 Fall Quarter.

MAT 215B—Topology (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Fundamental group and covering space theory. Homology and cohomology. Manifolds and duality. CW complexes. Fixed point theorems. (Letter.) Effective: 2002 Fall Quarter.

MAT 215C—Topology (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Fundamental group and covering space theory. Homology and cohomology. Manifolds and duality. CW complexes. Fixed point theorems. (Letter.) Effective: 2002 Fall Quarter.

MAT 216—Geometric Topology (4) Active

Lecture—3 hour(s); Extensive Problem Solving—1 hour(s). Prerequisite(s): MAT 215A. Topology of two- and three-dimensional manifolds. Surfaces and their diffeomorphisms. Dehn twists. Heegaard surfaces. Theory of 3-dimensional manifolds. Knots and knot theory. Hyperbolic manifolds and geometric structures. May be repeated up to 1 Time(s). (Letter.) Effective: 2010 Spring Quarter.

MAT 218A—Partial Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 201A; MAT 201B; MAT 201C; or Consent of Instructor. Year-long sequence on PDEs which covers linear transport, Laplace, heat, and wave equations, maximum principles, method of characteristics, Sobelev and Hölder space theory, weak derivatives, semilinear, quasilinear, and fully nonlinear elliptic/parabolic equations, nonlinear hyperbolic equations, and compensated compactness. (Letter.) Effective: 2009 Fall Quarter.

MAT 218B—Partial Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 218A; or Consent of Instructor. Year-long sequence on PDEs which covers linear transport, Laplace, heat, and wave equations, maximum principles, method of characteristics, Sobelev and Hölder space theory, weak derivatives, semilinear, quasilinear, and fully nonlinear elliptic/parabolic equations, nonlinear hyperbolic equations, and compensated compactness. (Letter.) Effective: 2010 Winter Quarter.

MAT 218C—Partial Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 218B; or Consent of Instructor. Year-long sequence on PDEs which covers linear transport, Laplace, heat, and wave equations, maximum principles, method of characteristics, Sobelev and Hölder space theory, weak derivatives, semilinear, quasilinear, and fully nonlinear elliptic/parabolic equations, nonlinear hyperbolic equations, and compensated compactness. (Letter.) Effective: 2010 Spring Quarter.

MAT 221A—Mathematical Fluid Dynamics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 118B; or Consent of Instructor. Kinematics and dynamics of fluids. The Euler and Navier-Stokes equations. Vorticity dynamics. Irrotational flow. Low Reynolds number flows and the Stokes equations. High Reynolds number flows and boundary layers. Compressible fluids. Shock waves. (Letter.) Effective: 2002 Fall Quarter.

MAT 221B—Mathematical Fluid Dynamics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 118B; or Consent of Instructor. Kinematics and dynamics of fluids. The Euler and Navier-Stokes equations. Vorticity dynamics. Irrotational flow. Low Reynolds number flows and the Stokes equations. High Reynolds number flows and boundary layers. Compressible fluids. Shock waves. (Letter.) Effective: 2003 Winter Quarter.

MAT 226A—Numerical Methods: Fundamentals (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 128A; MAT 128B; Or equivalent, or consent of instructor; familiarity with some programming language. Fundamental principles and methods in numerical analysis, including the concepts of stability of algorithms and conditioning of numerical problems, numerical methods for interpolation and integration, eigenvalue problems, singular value decomposition and its applications. (Letter.) Effective: 2009 Fall Quarter.

MAT 226B—Numerical Methods: Large-Scale Matrix Computations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 167; Or equivalent, or consent of instructor; familiarity with some programming language. Numerical methods for large-scale matrix computations, including direct and iterative methods for the solution of linear systems, the computation of eigenvalues and singular values, the solution of least-squares problems, matrix compression, methods for the solution of linear programs. (Letter.) Effective: 2010 Winter Quarter.

MAT 226C—Numerical Methods: Ordinary Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 022B; Or equivalent, or consent of instructor; familiarity with some programming language. Numerical methods for the solution of ordinary differential equations, including methods for initial-value problems and two-point boundary-value problems, theory of and methods for differential algebraic equations, dimension reduction of large-scale dynamical systems. (Letter.) Effective: 2010 Spring Quarter.

MAT 227—Mathematical Biology (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing or consent of instructor. Nonlinear ordinary and partial differential equations and stochastic processes of cell and molecular biology. Scaling, qualitative, and numerical analysis of mathematical models. Applications to nerve impulse, chemotaxis, muscle contraction, and morphogenesis.
(Letter.) Effective: 2002 Fall Quarter.

MAT 228A—Numerical Solution of Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s); Discussion. Prerequisite(s): MAT 128C. Numerical solutions of initial-value, eigenvalue and boundary-value problems for ordinary differential equations. Numerical solution of parabolic and hyperbolic partial differential equations. (Letter.) Effective: 1998 Fall Quarter.

MAT 228B—Numerical Solution of Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s); Discussion. Prerequisite(s): MAT 128C. Numerical solutions of initial-value, eigenvalue and boundary-value problems for ordinary differential equations. Numerical solution of parabolic and hyperbolic partial differential equations. (Letter.) Effective: 1998 Fall Quarter.

MAT 228C—Numerical Solution of Differential Equations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s); Discussion. Prerequisite(s): MAT 128C. Numerical solutions of initial-value, eigenvalue and boundary-value problems for ordinary differential equations. Numerical solution of parabolic and hyperbolic partial differential equations. (Letter.) Effective: 1998 Fall Quarter.

MAT 235A—Probability Theory (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 125B; (MAT 135A or STA 131A); or Consent of Instructor. Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. (Same course as STA 235A.) (Letter.) Effective: 2007 Fall Quarter.

MAT 235B—Probability Theory (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 235A or STA 235A; or Consent of Instructor. Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. (Same course as STA 235B.) (Letter.) Effective: 2008 Spring Quarter.

MAT 235C—Probability Theory (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 235B or STA 235B; or Consent of Instructor. Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. (Same course as STA 235C.) (Letter.) Effective: 2008 Spring Quarter.

MAT 236A—Stochastic Dynamics & Applications (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 201C or (MAT 235B or STA 235B); MAT 235A, MAT 235B, MAT 235C/ STA 235A, STA 235B, STA 235C recommended. Stochastic processes, Brownian motion, Stochastic integration, martingales, stochastic differential equations. Diffusions, connections with partial differential equations, mathematical finance. (Letter.) Effective: 2002 Fall Quarter.

MAT 236B—Stochastic Dynamics & Applications (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 201C or (MAT 235B or STA 235B); MAT 235A, MAT 235B, MAT 235C/ STA 235A, STA 235B, STA 235C recommended. Stochastic processes, Brownian motion, Stochastic integration, martingales, stochastic differential equations. Diffusions, connections with partial differential equations, mathematical finance. (Letter.) Effective: 2002 Fall Quarter.

MAT 239—Differential Topology (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 201A; or Consent of Instructor. Vector calculus, point-set topology; MAT 250A and MAT 250B is highly recommended. Topics include: differentiable manifolds, vector fields, transversality, Sard's theorem, examples of differentiable manifolds; orientation, intersection theory, index of vector fields; differential forms, integration, Stokes' theorm, deRham cohomology; Morse functions, Morse lemma, index of critical points. (Letter.) Effective: 2007 Spring Quarter.

MAT 240A—Differential Geometry (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 201A; MAT 239; MAT 250A and MAT 250B highly recommended; intended primarily for second-year graduate students. Riemannian metrics, connections, geodesics, Gauss lemma, convex neighborhoods, curvature tensor, Ricci and scalar curvature, connections and curvature on vector bundles. (Letter.) Effective: 2008 Fall Quarter.

MAT 240B—Differential Geometry (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 240A; Intended primarily for second-year graduate students. Jacobi fields, conjugate points, completeness, Hopf-Rinow theorem, Cartan-Hadamard theorem, energy, variation theorems and their applications, Rauch comparison theorem and its applications. (Letter.) Effective: 2009 Winter Quarter.

MAT 245—Enumerative Combinatorics (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 145; MAT 150; or the equivalent, or consent of instructor. Introduction to modern combinatorics and its applications. Emphasis on enumerative aspects of combinatorial theory. (Letter.) Effective: 2004 Fall Quarter.

MAT 246—Algebraic Combinatorics (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 245; or Consent of Instructor. Algebraic and geometric aspects of combinatorics. The use of structures such as groups, polytopes, rings, and simplicial complexes to solve combinatorial problems. (Letter.) Effective: 2005 Winter Quarter.

MAT 248A—Algebraic Geometry (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 250A; MAT 250B; MAT 250C. Affine varieties and radical ideals. Projective varieties. Abstract varieties. Morphisms and rational maps. Smoothness. Algebraic curves and the Riemann-Roch theorem. Special topics. (Letter.) Effective: 2009 Fall Quarter.

MAT 248B—Algebraic Geometry (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 248A. Complex varieties and the analytic topology. Sheaves and schemes.
Fiber products. Separatedness and properness. Applications of scheme
theory.
(Letter.) Effective: 2010 Winter Quarter.

MAT 249—Problem-Solving in Algebra (3) Active

Lecture—1 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 250A (can be concurrent); MAT 250B (can be concurrent). Problem-solving in graduate algebra: groups, rings, modules, matrices, tensor products, representations, Galois theory, ring extensions, commutative algebra and homological algebra. (S/U grading only.) Effective: 2019 Fall Quarter.

MAT 249B—Problem-Solving in Algebra (2) Review all entries Historical

Lecture—1 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 250A; MAT 250B. Problem-solving in graduate algebra: groups, rings, modules, matrices, tensor products, representations, Galois theory, ring extensions, commutative algebra and homological algebra. May be repeated up to 2 Time(s). (Letter.) Effective: 2011 Fall Quarter.

MAT 249B—Problem-Solving in Algebra (2) Review all entries Discontinued

Lecture—1 hour(s); Extensive Problem Solving. Prerequisite(s): MAT 250A; MAT 250B. Problem-solving in graduate algebra: groups, rings, modules, matrices, tensor products, representations, Galois theory, ring extensions, commutative algebra and homological algebra. May be repeated up to 2 Time(s). (Letter.) Effective: 2019 Fall Quarter.

MAT 250A—Algebra (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in mathematics or consent of instructor. Group and rings. Sylow theorems, abelian groups, Jordan-Holder theorem. Rings, unique factorization. Algebras, and modules. Fields and vector spaces over fields. Field extensions. Commutative rings. Representation theory and its applications. (Letter.) Effective: 2002 Fall Quarter.

MAT 250B—Algebra (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in mathematics or consent of instructor. Group and rings. Sylow theorems, abelian groups, Jordan-Holder theorem. Rings, unique factorization. Algebras, and modules. Fields and vector spaces over fields. Field extensions. Commutative rings. Representation theory and its applications. (Letter.) Effective: 2002 Fall Quarter.

MAT 250C—Algebra (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): Graduate standing in mathematics or consent of instructor. Group and rings. Sylow theorems, abelian groups, Jordan-Holder theorem. Rings, unique factorization. Algebras, and modules. Fields and vector spaces over fields. Field extensions. Commutative rings. Representation theory and its applications.
(Letter.) Effective: 2002 Fall Quarter.

MAT 258A—Numerical Optimization (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 025; MAT 167. Numerical methods for infinite dimensional optimization problems. Newton and Quasi-Newton methods, linear and sequential quadratic programming, barrier methods; large-scale optimization; theory of approximations; infinite and semi-infinite programming; applications to optimal control, stochastic optimization and distributed systems. (Letter.) Effective: 2007 Fall Quarter.

MAT 258B—Discrete & Mixed-Integer Optimization (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 025; MAT 167; or Consent of Instructor. Combinatorial, integer, and mixed-integer linear optimization problems. Ideal and strong formulations, cutting planes, branch and cut, decomposition methods. (Letter.) Effective: 2014 Fall Quarter.

MAT 261A—Lie Groups & Their Representations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 215A; MAT 240A; MAT 250A; MAT 250B; Or the equivalent, or consent of instructor. Lie groups and Lie algebras. Classification of semi-simple Lie groups. Classical and compact Lie groups. Representations of Lie groups and Lie algebras. Root systems, weights, Weil character formula. Kac-Moody and Virasoro algebras. Applications. (Letter.) Effective: 2002 Fall Quarter.

MAT 261B—Lie Groups & Their Representations (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 215A; MAT 240A; MAT 250A; MAT 250B; Or the equivalent, or consent of instructor. Lie groups and Lie algebras. Classification of semi-simple Lie groups. Classical and compact Lie groups. Representations of Lie groups and Lie algebras. Root systems, weights, Weil character formula. Kac-Moody and Virasoro algebras. Applications.
(Letter.) Effective: 2002 Fall Quarter.

MAT 265—Mathematical Quantum Mechanics (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 201; or Consent of Instructor. Mathematical foundations of quantum mechanics: the Hilbert space and Operator Algebra formulations; the Schrödinger and Heisenberg equations, symmetry in quantum mechanics, basics of spectral theory and perturbation theory. Applications to atoms and molecules. The Dirac equation. (Letter.) Effective: 2003 Fall Quarter.

MAT 266—Mathematical Statistical Mechanics & Quantum Field Theory (4) Active

Lecture—3 hour(s); Term Paper/Discussion—1 hour(s). Prerequisite(s): MAT 265; or Consent of Instructor. Mathematical principles of statistical mechanics and quantum field theory. Topics include classical and quantum lattice systems, variational principles, spontaneous symmetry breaking and phase transitions, second quantization and Fock space, and fundamentals
of quantum field theory.
May be repeated up to 1 Time(s). (Letter.) Effective: 2010 Spring Quarter.

MAT 271—Applied & Computational Harmonic Analysis (4) Active

Lecture—3 hour(s); Extensive Problem Solving. Prerequisite(s): (MAT 125B or MAT 201C); (MAT 128B or MAT 167); MAT 129; Or the equivalent, or consent of instructor. Introduction to mathematical basic building blocks (wavelets, local Fourier basis, and their relatives) useful for diverse fields (signal and image processing, numerical analysis, and statistics). Emphasis on the connection between the continuum and the discrete worlds. (Letter.) Effective: 2007 Fall Quarter.

MAT 280—Topics in Pure & Applied Mathematics (3) Active

Lecture—3 hour(s). Prerequisite(s): Graduate standing. Special topics in various fields of pure and applied mathematics. Topics selected based on the mutual interests of students and faculty. May be repeated for credit when topic differs. (Letter.) Effective: 1997 Winter Quarter.

MAT 290—Seminar (1-6) Active

Seminar—1-6 hour(s). Advanced study in various fields of mathematics, including analysis, applied mathematics, discrete mathematics, geometry, mathematical biology, mathematical physics, optimization, partial differential equations, probability, and topology. May be repeated for credit. (S/U grading only.) Effective: 2003 Spring Quarter.

MAT 298—Group Study (1-5) Active

Variable. (Letter.) Effective: 1997 Winter Quarter.

MAT 299—Individual Study (1-12) Active

Variable. (S/U grading only.) Effective: 1997 Winter Quarter.

MAT 299D—Dissertation Research (1-12) Active

Variable. (S/U grading only.) Effective: 1997 Winter Quarter.

MAT 301A—Mathematics Teaching Practicum (3) Active

Fieldwork—5 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 302A (can be concurrent); MAT 303A (can be concurrent); MAT 302A and MAT 303A required concurrently or consent of instructor. Specialist training in mathematics teaching. Teaching, training, and cross observing classes taught using large group Socratic techniques, small group guided inquiry experiences, and/or other approaches to teaching at various grade levels. Required for advanced degrees in mathematics education. May be repeated up to 1 Time(s). (Letter.) Effective: 2001 Fall Quarter.

MAT 301B—Mathematics Teaching Practicum (3) Active

Fieldwork—5 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 302B (can be concurrent); MAT 303B (can be concurrent); MAT 302B and MAT 303B required concurrently or consent of instructor. Specialist training in mathematics teaching. Teaching, training, and cross observing classes taught using large group Socratic techniques, small group guided inquiry experiences, and/or other approaches to teaching at various grade levels. Required for advanced degrees in mathematics education. May be repeated up to 1 Time(s). (Letter.) Effective: 2002 Winter Quarter.

MAT 301C—Mathematics Teaching Practicum (3) Active

Fieldwork—5 hour(s); Discussion—1 hour(s). Prerequisite(s): MAT 302C (can be concurrent); MAT 303B (can be concurrent); MAT 302C and MAT 303C required concurrently or consent of instructor. Specialist training in mathematics teaching. Teaching, training, and cross observing classes taught using large group Socratic techniques, small group guided inquiry experiences, and/or other approaches to teaching at various grade levels. Required for advanced degrees in mathematics education. May be repeated up to 1 Time(s). (Letter.) Effective: 2002 Spring Quarter.

MAT 302A—Curriculum Development in Mathematics (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 303A (can be concurrent); MAT 303A required concurrently or consent of instructor. Mathematics curriculum development for all grade levels. Required for advanced degrees in mathematics education. May be repeated up to 1 Time(s). (Letter.) Effective: 2001 Fall Quarter.

MAT 302B—Curriculum Development in Mathematics (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 303B (can be concurrent); MAT 303B required concurrently or consent of instructor. Mathematics curriculum development for all grade levels. Required for advanced degrees in mathematics education. May be repeated up to 1 Time(s). (Letter.) Effective: 2002 Winter Quarter.

MAT 302C—Curriculum Development in Mathematics (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 303C (can be concurrent); MAT 303C required concurrently or consent of instructor. Mathematics curriculum development for all grade levels. Required for advanced degrees in mathematics education. May be repeated for credit. (Letter.) Effective: 2002 Spring Quarter.

MAT 303A—Mathematics Pedagogy (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 302A (can be concurrent) or MAT 210AL (can be concurrent); MAT 302A or MAT 210AL required concurrently or consent of instructor. An investigation of the interplay of mathematical pedagogy and mathematical content, including a historical survey of past and present methods in view of some of the influences that shaped their development. May be repeated up to 1 Time(s). (Letter.) Effective: 2001 Fall Quarter.

MAT 303B—Mathematics Pedagogy (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 302B (can be concurrent) or MAT 210BL (can be concurrent); MAT 302A or MAT 210AL required concurrently or consent of instructor. An investigation of the interplay of mathematical pedagogy and mathematical content, including a historical survey of past and present methods in view of some of the influences that shaped their development. May be repeated up to 1 Time(s). (Letter.) Effective: 2002 Winter Quarter.

MAT 303C—Mathematics Pedagogy (1) Active

Lecture/Discussion—1 hour(s). Prerequisite(s): MAT 302C (can be concurrent) or MAT 210CL (can be concurrent); MAT 302C or MAT 210CL required concurrently or consent of instructor. An investigation of the interplay of mathematical pedagogy and mathematical content, including a historical survey of past and present methods in view of some of the influences that shaped their development. May be repeated up to 1 Time(s). (Letter.) Effective: 2002 Spring Quarter.

MAT 390—Teaching Assistantship Training (3) Active

Lecture—3 hour(s). Prerequisite(s): Graduate standing in the Department of Mathematics. Experience in methods of assisting and teaching of mathematics at the university level. Includes discussion of lecturing techniques, running discussion sessions, holding office hours, preparing and grading of examinations, student-teacher interaction, and related topics. Required of departmental teaching assistants. (S/U grading only.) Effective: 2008 Fall Quarter.

MAT 399—Individual Study (2-4) Active

Independent Study—2-3 hour(s); Discussion—1 hour(s). Individual study of some aspect of mathematics education or a focused work on a curriculum design project under supervision of a faculty member in mathematics. May be repeated up to 1 Time(s). (S/U grading only.) Effective: 2002 Spring Quarter.