Some courses displayed may not be offered every year. For actual course offerings by quarter, please consult the Quarterly Class Search
or GOLD (for current students). To see the historical record of when a particular course has been taught in the past, please visit the Course Enrollment Histories.
MATH 201A.
Real Analysis
(4)
STAFF
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: Consent of instructor.
Enrollment Comments: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Same course as Computer Science 211A, ME 210A, ECE 210A, Geology 251A, and Chemical Engineering 211A.
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
Prerequisite: Consent of instructor.
Enrollment Comments: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Same course as Computer Science 211B, ME 210B, ECE 210B, Geology 251B, and Chemical Engineering 211B.
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
Prerequisite: Consent of instructor.
Enrollment Comments: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Same course as Computer Science 211C, ME 210C, ECE 210C, Geology 251C, and Chemical Engineering 211C.
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
Prerequisite: Consent of instructor.
Enrollment Comments: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. Same course as Computer Science 211D, ME 210D, ECE 210D, Geology 251D, and Chemical Engineering 211D.
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 214A.
Ordinary Differential Equations
(4)
STAFF
Prerequisite: 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
Prerequisite: 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
Prerequisite: Not open to mathematics majors.
Wave, heat, and potential equations.
MATH 215B.
Fourier Series and Numerical Methods
(4)
STAFF
Prerequisite: Not open to mathematics majors.
Fourier series; generalized functions; and numerical methods.
MATH 220A.
Modern Algebra
(4)
STAFF
Prerequisite: Mathematics 108A-B and 111A-B.
Group theory, ring and module theory, field theory, Galois theory, other topics.
MATH 220B.
Modern Algebra
(4)
STAFF
Prerequisite: Mathematics 108A-B and 111A-B.
Group theory, ring and module theory, field theory, Galois theory, other topics.
MATH 220C.
Modern Algebra
(4)
STAFF
Prerequisite: 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
Prerequisite: 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
Prerequisite: Mathematics 221A.
Homotopy groups, exact sequences, fiber spaces, covering spaces, van Kampen Theorem.
MATH 221C.
Differential Topology
(4)
STAFF
Prerequisite: Mathematics 221A.
Topological manifolds, differentiable manifolds, transversality, tangent bundles, Borsuk-Ulam theorem, orientation and intersection number, Lefschetz fixed point theorem, vector fields.
MATH 225A.
Topics in Number Theory
(4)
STAFF
Prerequisite: Mathematics 220A-B-C.
Enrollment Comments: May be repeated for credit with instructor and department approval.
Selected topics in number theory.
MATH 225B.
Topics in Number Theory
(4)
STAFF
Prerequisite: Mathematics 220A-B-C.
Enrollment Comments: May be repeated for credit with instructor and department approval.
Selected topics in number theory.
MATH 225C.
Topics in Number Theory
(4)
STAFF
Prerequisite: Mathematics 220A-B-C.
Enrollment Comments: May be repeated for credit with instructor and department approval.
Selected topics in number theory.
MATH 227A.
Advanced Topics in Geometric and Algebraic Topology
(4)
STAFF
Prerequisite: Consent of instructor.
Enrollment Comments: May be repeated for credit with instructor and department approval.
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
Prerequisite: Consent of instructor.
Enrollment Comments: May be repeated for credit with instructor and department approval.
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
Prerequisite: Consent of instructor.
Enrollment Comments: May be repeated for credit with instructor and department approval.
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
Prerequisite: 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
Prerequisite: Mathematics 201A-B-C.
Topics in functional analysis such as operators on Hilbert space, convex analysis, fixed point theorems, distribution theory, unbounded operators.
MATH 231A.
Lie Groups and Lie Algebras
(4)
STAFF
Prerequisite: 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
Prerequisite: 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
Prerequisite: Mathematics 108A-B and 145.
Singular homology and cohomology, exact sequences, Hurewicz theorem, Poincare duality.
MATH 232B.
Algebraic Topology
(4)
STAFF
Prerequisite: Mathematics 108A-B and 145.
Singular homology and cohomology, exact sequences, Hurewicz theorem, Poincare duality.
MATH 236A.
Homological Algebra
(4)
STAFF
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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
Prerequisite: 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 260AAZZ.
Seminars in Mathematics
(1-6)
STAFF
Prerequisite: Consent of instructor.
Enrollment Comments: May be repeated for credit.
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
MATH 260AA.
Seminars in Mathematics
MATH 260B.
Seminars in Mathematics
MATH 260BB.
Seminars in Mathematics
MATH 260C.
Seminars in Mathematics
MATH 260CC.
Seminars in Mathematics
MATH 260D.
Seminars in Mathematics
MATH 260DD.
Seminars in Mathematics
MATH 260E.
Seminars in Mathematics
MATH 260EE.
Seminars in Mathematics
MATH 260ES.
Seminars in Mathematics
MATH 260F.
Seminars in Mathematics
MATH 260G.
Seminars in Mathematics
MATH 260GG.
Seminars in Mathematics
MATH 260H.
Seminars in Mathematics
MATH 260HH.
Seminars in Mathematics
MATH 260I.
Seminars in Mathematics
MATH 260II.
Seminars in Mathematics
MATH 260J.
Seminars in Mathematics
MATH 260JJ.
Seminars in Mathematics
MATH 260K.
Seminars in Mathematics
MATH 260KK.
Seminars in Mathematics
MATH 260L.
Seminars in Mathematics
MATH 260LL.
Seminars in Mathematics
MATH 260M.
Seminars in Mathematics
MATH 260MM.
Seminars in Mathematics
MATH 260N.
Seminars in Mathematics
MATH 260NN.
Seminars in Mathematics
MATH 260O.
Seminars in Mathematics
MATH 260OO.
Seminars in Mathematics
MATH 260P.
Seminars in Mathematics
MATH 260Q.
Seminars in Mathematics
MATH 260QQ.
Seminars in Mathematics
MATH 260R.
Seminars in Mathematics
MATH 260S.
Seminars in Mathematics
MATH 260SS.
Seminars in Mathematics
MATH 260T.
Seminars in Mathematics
MATH 260TT.
Seminars in Mathematics
MATH 260U.
Foundations in Mathematics
MATH 260UU.
Seminars in Mathematics
MATH 260V.
Seminars in Mathematics
MATH 260W.
Seminars in Mathematics
MATH 260X.
Seminars in Mathematics
MATH 260Y.
Seminars in Mathematics
MATH 260Z.
Seminars in Mathematics
MATH 500.
Teaching Assistant Practicum
(1-4)
STAFF
Prerequisite: Appointment as teaching assistant and departmental approval.
Enrollment Comments: No unit credit allowed toward degree.
Supervised teaching of undergraduate mathematics courses.
MATH 501.
Teaching Assistant Training
(1-2)
STAFF
Prerequisite: Departmental and instructor approval.
Enrollment Comments: No unit credit allowed toward degree.
Consideration of ideas about the process of learning mathematics and discussion of approaches to teaching.
MATH 502.
Teaching Associate Practicum
(1-5)
STAFF
Prerequisite: Appointment as associate; departmental approval.
Enrollment Comments: No unit credit allowed toward degree.
Supervised teaching of undergraduate courses.
MATH 510.
Reading for Area Examinations
(2-6)
STAFF
Prerequisite: Enrollment in M.A. or Ph.D. program. Consent of instructor.
Reading for area examinations.
MATH 596AAZZ.
Directed Reading and Research
(1-6)
STAFF
Prerequisite: Graduate standing and consent of instructor.
Enrollment Comments: May be repeated for credit. Only 8 units total in all Mathematics 596, 598,599 courses may be applied toward the degree.
Directed reading and research.
MATH 596AA.
Directed Reading and Research
MATH 598AAZZ.
Master's Thesis Research and Preparation
(1-6)
STAFF
Prerequisite: Graduate standing and consent of instructor.
Enrollment Comments: No unit credit allowed toward degree.
Master's thesis research and preparation.
MATH 598AA.
Master's Thesis Research and Preparation
MATH 599AAZZ.
Dissertation Preparation
(1-6)
STAFF
Prerequisite: Consent of instructor.
Enrollment Comments: May be repeated for credit. Only 8 units total in all Mathematics 596, 598,599 courses may apply toward degree.
Dissertation preparation.