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UCSB 2009-2010 General Catalog

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Search by subject area and course number. Refer to this list of subject areas and their corresponding department.

Tip: A search for the subject area, for example, querying just "HIST" (without quotes), will return all courses of the queried subject area. Searching using subject area and number, such as "HIST 17" (without quotes), would return all courses in the series; in this example that would include HIST 17A, 17AH, 17B, etc.

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MATH 3A - Calculus with Applications, First Course
(4) STAFF
Prerequisites: Algebra Diagnostic Test.
Differential Calculus including analytic geometry, functions and limits, derivatives, techniques and applications of differentiation, logarithmic and trigonometric functions.



MATH 3B - Calculus with Applications, Second Course
(4) STAFF
Prerequisites: Mathematics 3A with a minimum grade of C.
Integral calculus including definite and indefinite integrals, techniques of integration, with applications in mathematics and physics.



MATH 3BI - Inquiry Based Calculus I
(4) STAFF
Prerequisites: AP score of 3 or higher; consent of instructor.
Honors version of Mathematics 3B. Mathematical inquiry is developed through problem solving and discovery.



MATH 3BS - Calculus With Applications
(4) STAFF
Prerequisites: Mathematics 3AS with a grade of C or better.
Integral calculus, with applications to mathematics and physics. Equivalentcourse to Mathematics 3B but may involve different textbook and teaching methods.



MATH 3C - Differential Equations and Linear Algebra, First Course
(4) STAFF
Prerequisites: Mathematics 3B with a minimum grade of C.
First order ODEs including direction fields, separation of variables, first order linear equations, growth and decay, nonlinear models. Linear algebra including systems of linear equations, matrix inverses, determinants, vector spaces and subspaces, basis and dimension.



MATH 3CI - Inquiry Based Calculus II
(4) STAFF
Prerequisites: Mathematics 3B or Mathematics 3BI with a minimum grade of C.
Honors version of Mathematics 3C. Mathematical inquiry course is developed through problem solving and discovery.



MATH 3CS - Calculus with Applications
(4) STAFF
Prerequisites: Mathematics 3BS with a grade of C or better.
Continuation of Mathematics 3AS-BS, including differential equations, multivariable calculus, and Taylor approximations. Equivalent course to Mathematics 3C but may involve different textbook and teaching methods.



MATH 3H - Honors Seminar-Calculus
(1) STAFF
Prerequisites: Concurrent enrollment in Mathematics 3A or 3B or 3BI or 3C or 3CI.
Emphasizing fundamental concepts and applications. Intended for highly motivated and well prepared students.



MATH 5A - Differential Equations and Linear Algebra, Second Course
(4) STAFF
Prerequisites: Mathematics 3C or 3CI with a grade of C or better.
Second order linear ODEs, linear transformations including eigenvalues, eigenvectors and diagonalization. Linear systems of ODEs. Nonlinear systems and linearization.



MATH 5AI - Inquiry Based Calculus III
(4) STAFF
Prerequisites: Mathematics 3C or 3CI with a minimum grade of C.
Honors version of Mathematics 5A. Mathematical inquiry course is developed through problem solving and discovery.



MATH 5B - Vector Calculus with Applications, First Course
(4) STAFF
Prerequisites: Mathematics 5A or Mathematics 5AI with a grade of C or better.
Differential Calculus of Functions of Several Variables. Gradient, Divergence, Curl. Double Integrals and Triple Integrals. Line Integrals in the Plane. Green's Theorem and Independence of Path.



MATH 5BI - Inquiry Based Calculus IV
(4) STAFF
Prerequisites: Mathematics 5A or Mathematics 5AI with a minimum grade of C.
Honors version of Mathematics 5B. Mathematical inquiry course is developed through problem solving and discovery.



MATH 5C - Vector calculus with Applications, Second Course
(4) STAFF
Prerequisites: Mathematics 5B or 5BI with a grade of C or better.
Line Integrals in Space, Surface Integrals. Divergence Theorem, Stokes's Theorem. Infinite Series, Fourier Series. Introduction to PDE.



MATH 5H - Honors Seminar, Advanced Calculus and Linear Algebra
(1) STAFF
Prerequisites: Concurrent enrollment in Mathematics 5A or 5AI or 5B or 5BI or 5C.
A supplement to the Mathematics 5 sequence emphasizing fundamental concepts and applications. Intended for highly motivated and well prepared students.



MATH 8 - Transition to Higher Mathematics
(5) STAFF
Prerequisites: Mathematics 3B with a grade of C or better.
Introduction to the elements of propositional logic, techniques of mathematical proof, and fundamental mathematical structures, including sets, functions, relations, and other topics as time permits. Mastery of this material is essential for students planning to major in mathematics.



MATH 9 - Sophomore Seminar in Mathematics
(3) STAFF
Prerequisites: Mathematics 3B.
Team-taught seminar which aims to give students exposure to a wide range of interesting topics outside the traditional calculus sequence.



MATH CS 10 - Mathematics Colloquium
(1-6) STAFF
Prerequisites: Consent of instructor.
Students receiving credit will present talks in thei field on material arranged in consultation with the instructor. Credit assigned by the instructor will reflect the extent and quality of participation.



MATH 13 - Mathematics Appreciation
(3) STAFF
A course for the non-major intended to promote a better understanding of the nature of mathematics, the character and origin of different subject fields in mathematics, and the sources of mathematical research.



MATH 15 - Precalculus
(4) STAFF
Prerequisites: Algebra Diagnostic Test.
A function approach integrating algebra and trigonometry. Topics include: one-on-one and onto functions; inverse functions; properties and graphs of polynomial, rational, exponential, and logarithmic functions; properties and graphs of inverse trigonometric identities and trignometric equations.



MATH 34A - Calculus for Social and Life Sciences
(4) STAFF
Introduction to differential and integral calculus with applications to modeling in the biological sciences.



MATH 34B - Calculus for Social and Life Sciences
(4) STAFF
Prerequisites: Mathematics 3A or 3AS or 34A with a Grade of C or better.
Continued study of differential and integral calculus with differential andintegral calculus with applications. Introduction to mathematical modeling with differential equations. Calculus of several variables including an introduction to partial derivatives.



MATH 91 - Workshops in Mathematics
(1) STAFF
Group workshops affiliated with selected lower-division mathematics courses.



MATH 94 - Group Studies in Mathematics
(1-4) STAFF
Prerequisites: Consent of instructor.
Lectures and discussions on special topics.



MATH 100A - Mathematics for Elementary Teaching, I
(3) STAFF
Prerequisites: Upper-division standing.
This class teaches ways to think about and explain elementary school mathematics. Topics include: cultural and base-n number systems, algorithms, elementary number theory, probability, and graphing.



MATH 100B - Mathematics for Elementary Teaching, II
(3) STAFF
Prerequisites: Mathematics 100A.
Completes the explanation of elementary school mathematics by discussing geometry and algebra. Discusses the pedagogy with the California mathematics framework, the NCTM standards, and "replacement units".



MATH 101A - Classical Number Systems
(4) STAFF
Prerequisites: Mathematics 3A; and Mathematics 8.
Especially suitable for prospective teachers. A conceptual rather than an axiomatic development starting with the natural numbers and progressing through the integral, rational, real, and complex number systems. The historical implications of these developments in number systems.



MATH 101B - Mathematical Systems
(4) STAFF
Prerequisites: Mathematics 101A.
Especially suitable for prospective teachers. The theory of operations within rings and fields and the foundations of the real number system. Ideals, quotient rings, and factorization theorems. The history and the historical implications of these developments in mathematical systems.



MATH CS 101 - Problem Solving
(1-6) STAFF
Prerequisites: Consent of instructor.
Discussion and solution of nonroutine mathematical problems



MATH 102A - Modern Euclidean and Noneuclidean Geometry
(4) STAFF
Prerequisites: Mathematics 3B.
Especially suitable for prospective teachers. Topics in plane and solid geometry. The axioms of pure, euclidean, projective, and noneuclidean geometry. Transformational geometry (isometries, dilitations, involutions, perspectivities, and projectivities). The history and the historical implications of these developments in geometry.



MATH 102B - Modern Euclidean and Noneuclidean Geometry
(4) STAFF
Prerequisites: Mathematics 102A.
Especially suitable for prospective teachers. Topics in plane and solid geometry. The axioms of pure, euclidean, projective, and noneuclidean geometry. Transformational geometry (isometries, dilitations, involutions, perspectivities, and projectivities). The history and the historical implications of these developments in geometry.



MATH CS 102 - Project
(1-6) STAFF
Prerequisites: Consent of instructor.
Set up by the student in consultation with the instructor, and concluding with the student's report of progress.



MATH 103 - Introduction to Group Theory
(4) STAFF
Prerequisites: Mathematics 8.
Intended primarily for prospective teachers. Permutation groups, cyclic groups, theory of finite groups, group homomorphisms and isomorphisms, and Abelian groups. Applications to number theory and geometry.



MATH CS 103 - Topics in Modern Algebra
(1-6) STAFF
Prerequisites: Consent of instructor.
Topics may include groups; modules; vector spaces; algebras; metric structures on vector spaces; representation theory; multilinear algebra; graded structures; universal properties; a survey of important algebraic structures.



MATH 104A - Introduction Into Numerical Analysis
(4) STAFF
Prerequisites: Mathematics 5A-B-C; and, Computer Science 5AA-ZZ or 10 or Engineering 3 with a grade of C or above.
Numerical methods for the solution of nonlinear equations (Newton method), for integration (quadrature formulas and composite integration), and for the initial value problem for ordinary differential equations (Euler and Kutta methods).



MATH 104B - Numerical Analysis
(4) STAFF
Prerequisites: Mathematics 104A.
Numerical methods for the solution of systems of linear equations (direct and iteractive methods), and the finite difference methods for boundary value problems for (ordinary and partial) differential equations.



MATH 104C - Advanced Topics in Numerical Analysis
(4) STAFF
Prerequisites: Mathematics 104B.
Topics in approximation theory; numerical methods for finding eigenvalues of a matrix; and advanced topics in numerical methods for ordinary and partial differential equations.



MATH CS 105 - Computer Applications
(1-6) STAFF
Prerequisites: Consent of instructor.
Applications of the various campus computers and departmental microcomputers to problems in mathematics, biology, chemistry, and physics.



MATH 108A - Introduction to Linear Algebra
(4) STAFF
Prerequisites: Mathematics 5A and 8.
Abstract vector spaces subspaces. Span and linear independence. Basis and dimension. Linear maps. Eigenvalues and eigenvectors.



MATH 108B - Introduction to Linear Algebra
(4) STAFF
Prerequisites: Mathematics 108A.
Diagonalization, inner product spaces, projections, least-squares approximations, invariant factors and elementary divisors, canonical forms, topics from advanced matrix theory, applied linear algebra, and group representation theory.



MATH 108C - Introduction to Linear Algebra
(4) STAFF
Prerequisites: Mathematics 108B.
Diagonalization, inner product spaces, projections, least-squares approximations, invariant factors and elementary divisors, canonical forms, topics from advanced matrix theory, applied linear algebra, and group representation theory.



MATH 109A - Introduction to Mathematical Logic
(4) STAFF
Prerequisites: Mathematics 8 or Computer Science 40.
An introduction to mathematical logic with applications in computer scienceand mathematics. Topics include propositional and predicate calculi; models; proof systems, decidability and undecidability, automated theorem-proving, unification, logic programming, and program verification.



MATH CS 109 - Advanced Independent Research
(1-6) STAFF
Prerequisites: Consent of instructor.
Independent research on an original subject under faculty supervision carried out in a mathematics faculty reserach group. These advanced projects will attempt research of publishable quality; generally resulting in the preparation of a written report or manuscript for publication.



MATH 111A - Introduction to Abstract Algebra
(4) STAFF
Prerequisites: Mathematics 108A.
An introduction to algebraic structures with an emphasis on groups.



MATH 111B - Abstract Algebra
(4) STAFF
Prerequisites: Mathematics 111A.
Rings, fields, Galois theory.



MATH 111C - Abstract Algebra
(4) STAFF
Prerequisites: Mathematics 111B.
Rings, fields, Galois theory.



MATH 113 - Non-euclidean Geometry
(4) STAFF
Prerequisites: Mathematics 8.
An introduction to hyperbolic geometry with some discussion of other non-euclidean systems.



MATH 115A - Introduction to Number Theory
(4) STAFF
Prerequisites: Mathematics 8.
Divisibility, congruences, primitive roots an indices, quadratic residues and the quadratic reciprocity law, number-theoretic functions, Diophantine equations, the distribution of primes, number-theorhetic methods in cryptography, quadratic forms, continued fractions, and the approximation of real numbers, algebraic number theory, partitions.



MATH 115B - Introduction to Number Theory
(4) STAFF
Prerequisites: Mathematics 115A.
Divisibility, congruences, primitive roots and indices, quadratic residues and the quadradic reciprocity law, number-theorhetic functions, Diophantine equations, the distribution of primes, number-theorhetic methods in cryptography, quadratic forms, continued fractions, and the approximation of real numbers, algebraic number theory, partitions.



MATH 115C - Topics in Number Theory
(4) STAFF
Prerequisites: Consent of instructor.
Selected topics in number theory at the direction of the instructor.



MATH 116 - Combinatorial Analysis
(4) STAFF
Prerequisites: Mathematics 8.
Elementary counting principles, binomial coefficients, generating functions, recurrence relations, the principle of inclusion and exclusion, distributions and partitions, systems of distinct representatives, applications to computation.



MATH 117 - Methods of Analysis
(4) STAFF
Prerequisites: Mathematics 8.
Introduction to methods of proof in analysis. topics include limits, sequences and series, continuity, compactness, as well as other topics. This course is intended to follow Mathematics 8 and to introduce students to the level of sophistication of upper-division mathematics.



MATH 118A - Introduction to Real Analysis
(4) STAFF
Prerequisites: Mathematics 5A-B and 108A-B and 117.
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.



MATH 118B - Introduction to Real Analysis
(4) STAFF
Prerequisites: Mathematics 118A.
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.



MATH 118C - Introduction to Real Analysis
(4) STAFF
Prerequisites: Mathematics 118B.
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.



MATH 119A - Ordinary Differential Equations
(4) STAFF
Prerequisites: Mathematics 5A-B or equivalent.
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.



MATH 119B - Chaotic Dynamics and Bifurcation Theory
(4) STAFF
Prerequisites: Mathematics 5C or equivalent, and 119A or consent of instructor.
Hyperbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and Ruelle-Takens cascades to strange attractors.



MATH CS 120 - Special Topics
(1-6) STAFF
Prerequisites: Consent of instructor.
Lectures on a coherent body of mathematical topics which are not usually presented in standard mathematics courses.



MATH 122A - Introduction to Theory of Complex Variables
(4) STAFF
Prerequisites: Mathematics 5A-B.
Complex numbers, functions, differentiability, series extensions of elementary functions, complex integration, calculus of residues, conformal maps, mapping functions, applications.



MATH 122B - Introduction to Theory of Complex Variables
(4) STAFF
Prerequisites: Mathematics 122A.
Complex numbers, functions, differentiability, series extensions of elementary functions, complex integration, calculus of residues, conformal maps, mapping functions, applications.



MATH 124A - Partial Differential Equations
(4) STAFF
Prerequisites: Mathematics 5A-B-C or equivalent.
Wave, heat, and potential equations.



MATH 124B - Fourier Series and Numerical Methods
(4) STAFF
Prerequisites: Mathematics 5A-B-C or equivalent and 124A or consent of instructor.
Fourier series; generalized functions; and numerical methods.



MATH 130 - Introduction to Mathematical Modeling
(4) STAFF
Prerequisites: Mathematics 5A-B.
Introduction to the principles of mathematical modeling, both discrete and continuous.



MATH 132A - Introduction to Operations Research
(4) STAFF
Prerequisites: Mathematics 5A.
Linear programming, the simplex method, duality, applications to the transportation and assignment problems, sensitivity analysis, problem formulation.



MATH 132B - Introduction to Operations Research
(4) STAFF
Prerequisites: Mathematics 5B and 132A.
Network analysis: shortest route, minimal spanning tree and maximal flow problems; PERT including the critical path method; dynamic programming; game theory; integer programming, nonlinear programming.



MATH 137A - Graph and Network Theory
(4) STAFF
Prerequisites: Mathematics 5A and 8.
Elements of graph and network theory including paths, circuits, trees, coloring, planarity, matching theory, Hall's theorem, applications to scheduling theory, flows in networks, Menger's theorem, and other topics astime permits.



MATH 137B - Graph and Network Theory
(4) STAFF
Prerequisites: Mathematics 137A.
Elements of graph and network theory including paths, circuits, trees, coloring, planarity, matching theory, Hall's theorem, applications to scheduling theory, flows in networks, Menger's theorem, and other topics astime permits.



MATH CS 140 - Introduction to Mathematical Problems
(1-6) STAFF
Prerequisites: Consent of instructors.
Several nontrivial solved and unsolve mathematical problems are considered which require a minimal background. These include tiling and network problems, the solutions of which are ultimately useful in the natural sciences.



MATH 144A - Discrete and Probabilistic Mathematical Modeling
(4) STAFF
Prerequisites: Mathematics 5A.
Fundamental modeling principles. Topics selected from: simulation, optimization, networks, decision trees, random walks and differential equations, Markovian Analysis, game theoretic models, applications.



MATH 144B - Continuous Mathematical Modeling
(4) STAFF
Prerequisites: Mathematics 5A.
Differential equation, partial differential equation, and integral equationmodels. Topics selected from: derivation of model equations from first principles, conservation, solution techniques, both analytical and numerical, perturbation analysis, applications.



MATH 145 - Introduction to Topology
(4) STAFF
Prerequisites: Mathematics 8.
Metric spaces, continuity, compactness, classification of surfaces, Euler characteristics, and fundamental groups. Additional topics at the discretion of the instructor.



MATH 147A - Introductory Differential Geometry
(4) STAFF
Prerequisites: Mathematics 5B; and, Mathematics 108A or 117.
Curves and surfaces in three-dimensional Euclidean space, first and second fundamental forms, Gaussian and mean curvature, geodesics, Gauss-Bonnet theorem, and non-Euclidean geometry.



MATH 147B - Introductory Differential Geometry
(4) STAFF
Prerequisites: Mathematics 147A.
Curves and surfaces in three-dimensional Euclidean space, first and second fundamental forms, Gaussian and mean curvature, geodesics, Gauss-Bonnet theorem, and non-Euclidean geometry.



MATH 170 - Introduction to Mathematical Finance
(4) STAFF
Prerequisites: PSTAT 120A-B, 160A.
Describes mathematical methods for estimating and evaluating asset pricing models, equilibrium and derivative pricing, options, bonds, and the term-structure of interest rates. Also introduces finance optimization models for risk management and financial engineering.



MATH 178 - Introduction to Cryptography
(4) STAFF
Prerequisites: Computer Science 10; and, PSTAT 120A or 121A or equivalent courses.
An introduction to the basic concepts and techniques of cryptography and cryptanalysis. Topics include: The Shannon Theory, classical systems, the enigma machine, the data encryption standard, public key systems, digital signatures, file security.



MATH 181A - Advanced Problem Solving: Mathematical, Historical, and Pedagogical Contexts
(4) STAFF
Prerequisites: Mathematics 5A; an upper-division mathematics course.
Designed for prospective middle and high school teachers. Focuses on the representations, strategies, and language learners use to conceptualize and develop fundamental ideas of mathematics. Includes advanced problem solving and its implications for teaching and learning at the secondary level.



MATH 181B - Advanced Problem Solving: Mathematical, Historical, and Pedagogical Contexts
(4) STAFF
Prerequisites: Consent of instructor.
Continuation of Math 181A.



MATH 190 - Special Topics in Mathematics
(4) STAFF
Prerequisites: Consent of instructor.
Information about the special topics to be presented may be obtained from the office of the Department of Mathematics.



MATH 193 - Internship in Mathematics
(1-4) STAFF
Prerequisites: Consent of instructor and department.
Faculty sponsored academic internship in industrial or research firms.



MATH 194GS - Group Studies for Advanced Students
(1) STAFF
Prerequisites: Consent of instructor.
Participants will select a math-related book or papers, read the section before the next meeting and discuss reading at the meeting. Readings may include biographies of mathematicians, histories or popularizations of mathematics, textbooks, and readings in mathematical physics or biology.



MATH 195A - Internship in Mathematics Teaching
(4) STAFF
Prerequisites: Upper-division standing in the major; two upper-division mathematics courses.
Supervised mathematics internship in local schools and participation in themathematics teaching seminar on mathematics learning and teaching. A paper on mathematics and its teaching required.



MATH 195B - Internship in Mathematics Teaching
(4) STAFF
Prerequisites: Upper-division standing in the major; two upper-division mathematics courses.
Supervised mathematics internship in local schools and participation in themathematics teaching seminar on mathematics learning and teaching. A paper on mathematics and its teaching required.



MATH 197A - Senior Thesis
(1-4) STAFF
Prerequisites: Open to senior majors only; consent of department and instructor.
Independent research under the supervision of a faculty member which will result in a senior thesis. Student will concentrate on reading and gathering material for a thesis.



MATH 197B - Senior Thesis
(1-4) STAFF
Prerequisites: Mathematics 197A. Open to senior majors only; consent of department and instructor.
Independent research under the supervision of a faculty member which will result in a senior thesis. Student will concentrate on writing a thesis.



MATH 199 - Independent Studies in Mathematics
(1-5) STAFF
Prerequisites: Upper-division standing; completion of 2 upper-division courses in math; consent of instructor and department.
Coursework shall consist of academic research supervised by a faculty member on a topic not available in established course offerings.



MATH 199RA - Independent Research Assistance
(1-4) STAFF
Prerequisites: Upper-division standing; completion of 2 upper-division courses in math; consent of instructor and department.
Coursework shall consist of faculty supervised research assistance.



MATH CS 199 - Independent Studies
(1-6) STAFF
Prerequisites: Consent of instructor.
Serious independent study in mathematics with consenting faculty member.



MATH 201A - Real Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Measure theory and integration. Point set topology. Principles of functional analysis. Lp-spaces. The Riesz representation theorem. Topics in real and functional analysis.



MATH 201B - Real Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Measure theory and integration. Point set topology. Principles of functional analysis. Lp-spaces. The Riesz representation theorem. Topics in real and functional analysis.



MATH 201C - Real Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Measure theory and integration. Point set topology. Principles of functional analysis. Lp-spaces. The Riesz representation theorem. Topics in real and functional analysis.



MATH 202A - Complex Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C or 122A.
Analytic functions. Complex integration. Cauchy's theorem. Series and product developments. Entire functions. Conformal mappings. Topics in complex analysis.



MATH 202B - Complex Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C or 122A.
Analytic functions. Complex integration. Cauchy's theorem. Series and product developments. Entire functions. Conformal mappings. Topics in complex analysis.



MATH 202C - Complex Analysis
(4) STAFF
Prerequisites: Mathematics 118A-B-C or 122A.
Analytic functions. Complex integration. Cauchy's theorem. Series and product developments. Entire functions. Conformal mappings. Topics in complex analysis.



MATH 206A - Matrix Analysis and Computation
(4) STAFF
Prerequisites: Consent of instructor.
Graduate level-matrix theory with introduction to matrix computations. SVD's, pseudoinverses, variational characterization of eigenvalues, perturbation theory, direct and iterative methods for matrix computations.



MATH 206B - Numerical Simulation
(4) STAFF
Prerequisites: Consent of instructor.
Linear multistep methods and Runge-Kutta methods for ordinary differential equations: stability, order and convergence. Stiffness. Differential algebraic equations. Numerical solution of boundary value problems.



MATH 206C - Numerical Solution of Partial Differential Equations--Finite Difference Methods
(4) STAFF
Prerequisites: Consent of instructor.
Finite difference methods for hyperbolic, parabolic and elliptic PDE's, with application to problems in science and engineering. Convergence, consistency, order and stability of finite difference methods. Dissipation and dispersion. Finite volume methods. Software design and adaptivity.



MATH 206D - Numerical Solution of Partial Differential Equations - Finite Element Methods
(4) STAFF
Prerequisites: Consent of instructor.
Weighted residual and finite element methods for the solution of hyperbolic, parabolic and elliptic partial differential equations, with application to problems in science and engineering. Error estimates. Standard and discontinuous Galerkin methods.



MATH 209 - Set Theory
(4) STAFF
Prerequisites: Consent of instructor.
Study of axiomic set theory; topics include relations and functions, orderings, ordinal and cardinal numbers and their arithmetic, transfinite constructible sets, consistency and independence results of Godel and Cohen.



MATH 212A - Harmonic Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Fourier transformation. Interpolation theorems. Riesz-Thorin and Marcinriewicz theorems. Hardy-Littlewood maximal function. Singular integrals. Calderon-Zygmund theory. H1&BMO. Mulitipliers. Pseudo-differential operators.



MATH 212B - Harmonic Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Fourier transformation. Interpolation theorems. Riesz-Thorin and Marcinriewicz theorems. Hardy-Littlewood maximal function. Singular integrals. Calderon-Zygmund theory. H1&BMO. Mulitipliers. Pseudo-differential operators.



MATH 212C - Harmonic Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Fourier transformation. Interpolation theorems. Riesz-Thorin and Marcinriewicz theorems. Hardy-Littlewood maximal function. Singular integrals. Calderon-Zygmund theory. H1&BMO. Mulitipliers. Pseudo-differential operators.



MATH 213A - Operator Theory
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Banach algebras and the spectral theorm for normal operators. Unbounded operators and special classes of operators. Elements of scattering theory. Friedrichs operators. Kato-Rosenblum theorm. Weyl-von Neumann theorm. Toeplitz and Wiener-Hopf operators. Contractive operators and dilation theory.



MATH 213B - Operator Theory
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Banach algebras and the spectral theorm for normal operators. Unbounded operators and special classes of operators. Elements of scattering theory. Friedrichs operators. Kato-Rosenblum theorm. Weyl-von Neumann theorm. Toeplitz and Wiener-Hopf operators. Contractive operators and dilation theory.



MATH 213C - Operator Theory
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Banach algebras and the spectral theorm for normal operators. Unbounded operators and special classes of operators. Elements of scattering theory. Friedrichs operators. Kato-Rosenblum theorm. Weyl-von Neumann theorm. Toeplitz and Wiener-Hopf operators. Contractive operators and dilation theory.



MATH 214A - Ordinary Differential Equations
(4) STAFF
Prerequisites: Not open to mathematics majors.
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.



MATH 214B - Chaotic Dynamics and Bifurcation Theory
(4) STAFF
Prerequisites: Not open to mathematics majors.
Hyberbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and Ruelle-Takens cascades to strange attractors.



MATH 215A - Partial Differential Equations
(4) STAFF
Prerequisites: Not open to mathematics majors.
Wave, heat, and potential equations.



MATH 215B - Fourier Series and Numerical Methods
(4) STAFF
Prerequisites: Not open to mathematics majors.
Fourier series; generalized functions; and numerical methods.



MATH 220A - Modern Algebra
(4) STAFF
Prerequisites: Mathematics 108A-B and 111A-B.
Group theory, ring and module theory, field theory, Galois theory, other topics.



MATH 220B - Modern Algebra
(4) STAFF
Prerequisites: Mathematics 108A-B and 111A-B.
Group theory, ring and module theory, field theory, Galois theory, other topics.



MATH 220C - Modern Algebra
(4) STAFF
Prerequisites: Mathematics 108A-B and 111A-B.
Group theory, ring and module theory, field theory, Galois theory, other topics.



MATH 221A - Foundations of Topology
(4) STAFF
Prerequisites: Mathematics 118A or equivalent.
Metric spaces, topological spaces, continuity, Hausdorff condition, compactness, connectedness, product spaces, quotient spaces. Other topics as time allows.



MATH 221B - Homotopy Theory
(4) STAFF
Prerequisites: Mathematics 221A.
Homotopy groups, exact sequences, fiber spaces, covering spaces, van Kampen Theorem.



MATH 221C - Differential Topology
(4) STAFF
Prerequisites: Mathematics 221A.
Topological manifolds, differentiable manifolds, transversality, tangent bundles, Borsuk-Ulam theorem, orientation and intersection number, Lefschetz fixed point theorem, vector fields.



MATH 223A - Topics in Ring Theory
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Selected topics in ring theory.



MATH 225A - Topics in Number Theory
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Selected topics in number theory.



MATH 225B - Topics in Number Theory
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Selected topics in number theory.



MATH 227A - Advanced Topics in Geometric and Algebraic Topology
(4) STAFF
Prerequisites: Consent of instructor.
Topics, varying from year to year, include piecewise linear and differential topology, manifolds, fiber bundles and fiber spaces, homotopy theory, and spectral sequences.



MATH 227B - Advanced Topics in Geometric and Algebraic Topology
(4) STAFF
Prerequisites: Consent of instructor.
Topics, varying from year to year, include piecewise linear and differential topology, manifolds, fiber bundles and fiber spaces, homotopy theory, and spectral sequences.



MATH 227C - Advanced Topics in Geometric and Algebraic Topology
(4) STAFF
Prerequisites: Consent of instructor.
Topics, varying from year to year, include piecewise linear and differential topology, manifolds, fiber bundles and fiber spaces, homotopy theory, and spectral sequences.



MATH 228A - Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in functional analysis such as operators on Hilbert space, convex analysis, fixed point theorems, distribution theory, unbounded operators.



MATH 228B - Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in functional analysis such as operators on Hilbert space, convex analysis, fixed point theorems, distribution theory, unbounded operators.



MATH 228C - Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in functional analysis such as operators on Hilbert space, convex analysis, fixed point theorems, distribution theory, unbounded operators.



MATH 229A - Operator Algebras
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Bananch algebras. The Gelfand transform. C*-algebras and von Neumann algebras. Positivity. States. The Gelfand-Naimark-Segal construction, *-representations of C*-algebras. Von Neumann's bicommutant theorem. Comparison of projections. Examples and applications. Advanced topics in the theory of operator algebras.



MATH 229B - Operator Algebras.
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Bananch algebras. The Gelfand transform. C*-algebras and von Neumann algebras. Positivity. States. The Gelfand-Naimark-Segal construction, *-representations of C*-algebras. Von Neumann's bicommutant theorem. Comparison of projections. Examples and applications. Advanced topics in the theory of operator algebras.



MATH 229C - Operator Algebras
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Bananch algebras. The Gelfand transform. C*-algebras and von Neumann algebras. Positivity. States. The Gelfand-Naimark-Segal construction, *-representations of C*-algebras. Von Neumann's bicommutant theorem. Comparison of projections. Examples and applications. Advanced topics in the theory of operator algebras.



MATH 231A - Lie Groups and Lie Algebras
(4) STAFF
Prerequisites: Consent of instructor.
Differentiable manifolds, definition and examples of lie groups, lie group-lie algebra correspondence, nilpotent and solvable lie algebras, classification of semi-simple lie algebras over the complexes, representations of lie groups and lie algebras, special topics.



MATH 231B - Lie Groups and Lie Algebras
(4) STAFF
Prerequisites: Consent of instructor.
Differentiable manifolds, definition and examples of lie groups, lie group-lie algebra correspondence, nilpotent and solvable lie algebras, classification of semi-simple lie algebras over the complexes, representations of lie groups and lie algebras, special topics.



MATH 232A - Algebraic Topology
(4) STAFF
Prerequisites: Mathematics 108A-B and 145.
Singular homology and cohomology, exact sequences, Hurewicz theorem, Poincare duality.



MATH 232B - Algebraic Topology
(4) STAFF
Prerequisites: Mathematics 108A-B and 145.
Singular homology and cohomology, exact sequences, Hurewicz theorem, Poincare duality.



MATH 232C - Algebraic Topology
(4) STAFF
Prerequisites: Mathematics 108A-B and 145.
Singular homology and cohomology, exact sequences, Hurewicz theorem, Poincare duality.



MATH 233A - Applied Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in applied functional analysis such as convex analysis, optimization, minimax theorems, variational analysis, distribution theory and harmonic analysis, global analysis (pseudo-differential operators and index theorems).



MATH 233B - Applied Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in applied functional analysis such as convex analysis, optimization, minimax theorems, variational analysis, distribution theory and harmonic analysis, global analysis (pseudo-differential operators and index theorems).



MATH 233C - Applied Functional Analysis
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
Topics in applied functional analysis such as convex analysis, optimization, minimax theorems, variational analysis, distribution theory and harmonic analysis, global analysis (pseudo-differential operators and index theorems).



MATH 236A - Homological Algebra
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Algebraic construction of homology and cohomology theories, aimed at applications to topology, geometry, groups and rings. Special emphasis on hom and tensor functors; projective, injective and flat modules; exact sequences; chain complexes; derived functors, in particular, ext and tor.



MATH 236B - Homological Algebra
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Algebraic construction of homology and cohomology theories, aimed at applications to topology, geometry, groups and rings. Special emphasis on hom and tensor functors; projective, injective and flat modules; exact sequences; chain complexes; derived functors, in particular, ext and tor.



MATH 237A - Algebraic Geometry
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Affine/projective varieties, Hilbert's Nullstellensatz, morphisms of varieties, rational maps, dimension, singular/nonsingular points, blowing up of varieties, tanent spaces, divisors, differentials, Riemann-Roch theorem. Special topics may include: elliptic curves, intersection numbers, Bezout's theorem, Max Noether's theorem.



MATH 237B - Algebraic Geometry
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Affine/projective varieties, Hilbert's Nullstellensatz, morphisms of varieties, rational maps, dimension, singular/nonsingular points, blowing up of varieties, tangent spaces, divisors, differentials, Riemann-Roch theorem. Special topics may include: elliptic curves, intersection numbers,Bezout's theorem, Max Noether's theorem.



MATH 237C - Algebraic Geometry
(4) STAFF
Prerequisites: Mathematics 220A-B-C.
Affine/projective varieties, Hilbert's Nullstellensatz, morphisms of varieties, rational maps, demension, singular/nonsingular points, blowing up of varieties, tanent spaces, divisors, differentials Riemann-Roch theorem. Special topics may include: elliptic curves, intersection numbers,Bezout's theorem, Max Noether's theorem.



MATH 240A - Introduction to Differential Geometry and Riemannian Geometry
(4) STAFF
Topics include geometry of surfaces, manifolds, differential forms, Lie groups, Riemannian manifolds, Levi-Civita connection and curvature, curvature and topology, Hodge theory. Additional topics such as bundles and characteristic classes, spin structures, and Dirac operator, comparison theorems in Riemannian geometry.



MATH 240B - Introduction to Differential Geometry and Riemannian Geometry
(4) STAFF
Topics include geometry of surfaces, manifolds, differential forms, Lie groups, Riemannian manifolds, Levi-Civita connection and curvature, curvature and topology, Hodge theory. Additional topics such as bundles and characteristic classes, spin structures, and Dirac operator, comparison theorems in Riemannian geometry.



MATH 240C - Introduction to Differential Geometry and Riemannian Geometry
(4) STAFF
Topics include geometry of surfaces, manifolds, differential forms, Lie groups, Riemannian manifolds, Levi-Civita connection and curvature, curvature and topology, Hodge theory. Additional topics such as bundles and characteristic classes, spin structures, and Dirac operator, comparison theorems in Riemannian geometry.



MATH 241A - Topics in Differential Geometry
(4) STAFF
Prerequisites: Mathematics 240A-B-C..
Various topics are covered including sectional curvature and Ricci curvature, minimal submanifolds, Atiyah-Singer index theorem and eta invariant, Einstein manifold, symplectic geometry, geometry of gauge theories, geometric PDE, Morse theory and Floer theory.



MATH 241B - Topics in Differential Geometry
(4) STAFF
Prerequisites: Mathematics 240A-B-C.
Various topics are covered including sectional curvature and Ricci curvature, minimal submanifolds, Atiyah-Singer index theorem and eta invariant, Einstein manifold, symplectic geometry, geometry of gauge theories, geometric PDE, Morse theory and Floer theory.



MATH 241C - Topics in Differential Geometry
(4) STAFF
Prerequisites: Mathematics 240A-B-C.
Various topics are covered including sectional curvature and Ricci curvature, minimal submanifolds, Atiyah-Singer index theorem and eta invariant, Einstein manifold, symplectic geometry, geometry of gauge theories, geometric PDE, Morse theory and Floer theory.



MATH 243A - Ordinary Differential Equations
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Existence and stability of solutions, Floquet theory, Poincare-Bendixson theorem, invariant manifolds, existence and stability of periodic solutions, Bifurcation theory and normal forms, hyperbolic structure and chaos, Feigenbaum period-doubling cascade, Ruelle-Takens cascade.



MATH 243B - Ordinary Differential Equations
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Existance and stability of solutions, Floq uet theory, Poincare-Bendixson theorem, invariant manifolds, existence and stability of periodic solutions, Bifurcation theory and normal forms, hyperbolic structure and chaos, Feigenbaum period-doubling cascade, Ruelle-Takens cascade.



MATH 243C - Ordinary Differential Equations
(4) STAFF
Prerequisites: Mathematics 118A-B-C.
Existance and stability of solutions, Floquet theory, Poincare-Bendixson theorem, invariant manifolds, existence and stability of periodic solutions, Bifurcation theory and normal forms, hyperbolic structure and chaos, Feigenbaum period-doubling cascade, Ruelle-Takens cascade.



MATH 246A - Partial Differential Equations
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
First-order nonlinear equations; the Cauchy problem, elements of distribution theory an Sobolev spaces; the heat, wave, and Laplace equations; additional topics such as quasilinear symmetric hyperbolic systems, elliptic regularity theory.



MATH 246B - Partial Differential Equations
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
First-order nonlinear equations; the Cauchy problem, elements of distribution theory and Sobolev spaces; the heat, wave, and Laplace equations; additional topics such as quasilinear symmetric hyperbolic systems, elliptic regularity theory.



MATH 246C - Partial Differential Equations
(4) STAFF
Prerequisites: Mathematics 201A-B-C.
First-order nonlinear equations; the Cauchy problem, elements of distribution theory and Sobolev spaces; the heat, wave, and Laplace equations; additional topics such as quasilinear symmetric hyperbolic systems, ellipitic regularity theory.



MATH 260 - Seminars in Mathematics
(1-6) STAFF
Prerequisites: Consent of instructor.
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260A - Seminars in Mathematics
(1-6) STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260AA - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260B - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260BB - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260C - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260CC - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260D - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260DD - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260E - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260EE - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260ES - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260F - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260G - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260GG - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260H - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional alalysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260HH - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260I - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260II - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260J - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260JJ - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260K - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260KK - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260L - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260LL - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260M - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260MM - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260N - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260NN - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260O - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260OO - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260P - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260Q - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260QQ - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260R - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260S - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260SS - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260T - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260TT - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260U - Foundations in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics combinatorial mathematics,functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260UU - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260V - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260W - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260X - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260Y - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 260Z - Seminars in Mathematics
() STAFF
Topics in algebra, analysis, applied mathematics, combinatorial mathematics, functional analysis, geometry, statistics, topology, by means of lectures and informal conferences with members of staff.



MATH 280 - Surveys in Contemporary Mathematics
(2-4) STAFF
Prerequisites: Consent of instructor.
An expository treatment of a topic of current interest in mathematics with sufficient detail to impart the flavor of the field. Where appropriate, applications to other fields of mathematics will be included. The course isdesigned for the nonspecialist in the area treated. The topics will vary from quarter to quarter.



MATH 500 - Teaching Assistant Practicum
(1-4) STAFF
Prerequisites: Appointment as teaching assistant and departmental approval.
Supervised teaching of undergraduate mathematics courses.



MATH 501 - Teaching Assistant Training
(1-2) STAFF
Prerequisites: Departmental and instructor approval.
Consideration of ideas about the process of learning mathematics and discussion of approaches to teaching.



MATH 502 - Teaching Associate Practicum
(1-5) STAFF
Prerequisites: Appointment as associate; departmental approval.
Supervised teaching of undergraduate courses.



MATH 510 - Reading for Area Examinations
(2-6) STAFF
Prerequisites: Enrollment in M.A. or Ph.D. program. Consent of instructor.
Reading for area examinations.



MATH 596 - Directed Reading and Research
(1-6) STAFF
Prerequisites: Graduate standing and consent of instructor.
Directed reading and research.



MATH 598 - Master's Thesis Research and Preparation
(1-6) STAFF
Prerequisites: Graduate standing and consent of instructor.
Master's thesis research and preparation.



MATH 599 - Dissertation Preparation
(1-6) STAFF
Prerequisites: Consent of instructor.
Dissertation preparation.