2025-26 Edition

Department of Mathematics

undefined

Zhiqin Lu, Department Chair
340E Rowland Hall
949-824-5503
http://www.math.uci.edu/

The Department of Mathematics is engaged in teaching and in fundamental research in a wide variety of basic mathematical disciplines, and offers undergraduate and graduate students the opportunity to fashion a thorough program of study leading to professional competence in mathematical research or in an area of application.

The curriculum in mathematics includes opportunities for supervised individual study and research and is augmented by seminars and colloquia. It is designed to be compatible with curricular structures at other collegiate institutions in California in order to enable students transferring to UCI to continue their programs of mathematics study.

Faculty

Jun F. Allard, Ph.D. University of British Columbia, Professor of Mathematics; Physics and Astronomy (mathematical and computational biology)
Kenneth Ascher, Ph.D. Brown University, Associate Professor of Mathematics (algebraic and arithmetic geometry)
Vladimir Baranovsky, Ph.D. University of Chicago, Professor of Mathematics (algebra and number theory)
Paul Carter, Ph.D. Brown University, Assistant Professor of Mathematics (analysis and partial differential equations, applied and computational mathematics)
Long Chen, Ph.D. Pennsylvania State University, Professor of Mathematics (applied and computational mathematics)
Michael C. Cranston, Ph.D. University of Minnesota, Professor of Mathematics (probability)
Christopher J. Davis, Ph.D. Massachusetts Institute of Technology, Professor of Teaching of Mathematics (algebra and number theory)
Neil Donaldson, Ph.D. University of Bath, Lecturer of Mathematics (differential geometry)
German A. Enciso Ruiz, Ph.D. Rutgers, the State University of New Jersey, Professor of Mathematics; Developmental and Cell Biology (applied and computational mathematics, mathematical and computational biology)
Asaf Ferber, Ph.D. Tel Aviv University, Associate Professor of Mathematics (probabilistic combinatorics)
Aleksandr Figotin, Ph.D. Tashkent University of Information Technologies, Professor of Mathematics; Electrical Engineering and Computer Science (applied and computational mathematics, mathematical physics)
Alexandra Florea, Ph.D. Stanford University, Assistant Professor of Mathematics (number theory)
Matthew Foreman, Ph.D. University of California, Berkeley, Distinguished Professor of Mathematics; Logic and Philosophy of Science (ergodic theory and dynamical systems, logic and foundations)
Isaac Goldbring, Ph.D. University of Illinois at Urbana-Champaign, Professor of Mathematics; Logic and Philosophy of Science (logic and foundations)
Anton Gorodetski, Ph.D. Moscow State University, Professor of Mathematics (ergodic theory and dynamical systems)
Patrick Q. Guidotti, Ph.D. University of Zurich, Professor of Mathematics (analysis and partial differential equations, applied and computational mathematics)
Hamid Hezari, Ph.D. Johns Hopkins University, Professor of Mathematics (analysis and partial differential equations)
Kenneth B. Huber, Ph.D. University of California, Irvine, Lecturer of Mathematics (probability)
Paata Ivanisvili, Ph.D. Michigan State University, Associate Professor of Mathematics (analysis and partial differential equations, probability)
Svetlana Jitomirskaya, Ph.D. Moscow State University, Adjunct Professor of Mathematics (mathematical physics)
Nathan Kaplan, Ph.D. Harvard University, Professor of Mathematics (algebra and number theory)
Natalia Komarova, Ph.D. University of Arizona, UCI Chancellor's Professor of Mathematics (applied and computational mathematics, mathematical and computational biology, mathematics of complex social phenomena)
Katsiaryna Krupchyk, Ph.D. Belarusian State University, Professor of Mathematics (analysis and partial differential equations, inverse problems, and imaging)
Yi Lai, Ph.D. University of California, Berkeley, Assistant Professor of Mathematics (geometric analysis)
Rachel Lehman, Ph.D. University of California, Irvine, Lecturer of Mathematics (mathematics education and probability)
Song-Ying Li, Ph.D. University of Pittsburgh, Professor of Mathematics (analysis and partial differential equations)
John S. Lowengrub, Ph.D. Courant Institute of Mathematical Sciences, Distinguished Professor of Mathematics; Biomedical Engineering; Chemical and Biomolecular Engineering (applied and computational mathematics, mathematical and computational biology)
Zhiqin Lu, Ph.D. Courant Institute of Mathematical Sciences, Professor of Mathematics (geometry and topology)
Jeffrey Ludwig, Ph.D. Massachusetts Institute of Technology, Associate Professor of Teaching of Mathematics (probability)
Anna Ma, Ph.D. Claremont Graduate University, Assistant Professor of Mathematics (mathematical data science, numerical linear algebra)
Christopher Miles, Ph.D. University of Utah, Assistant Professor of Mathematics (applied and computational mathematics, mathematical and computational biology)
Connor Mooney, Ph.D. Columbia University, Associate Professor of Mathematics (partial differential equations)
Qing Nie, Ph.D. Ohio State University, Director of the NSF-Simons Center for Multiscale Cell Fate Research and UC Presidential Chair and Distinguished Professor of Mathematics; Biomedical Engineering; Developmental and Cell Biology (applied and computational mathematics, mathematical and computational biology)
Alessandra Pantano, Ph.D. Princeton University, Professor of Teaching of Mathematics (algebra and number theory)
Roberto Pelayo, Ph.D. California Institute of Technology, Associate Professor of Teaching of Mathematics (algebra and data science)
Manuel Reyes, Ph.D. University of California, Berkeley, Associate Professor of Mathematics; Logic and Philosophy of Science (algebra and number theory)
Donald G. Saari, Ph.D. Purdue University, UCI Distinguished Professor Emeritus of Economics; Mathematics
Luke Smith, Ph.D. University of California, Irvine, Lecturer of Mathematics (algebra and number theory)
Knut Solna, Ph.D. Stanford University, Professor of Mathematics (applied and computational mathematics, inverse problems and imaging, probability)
Jeffrey D. Streets, Ph.D. Duke University, Professor of Mathematics (geometric analysis)
Li Sheng Tseng, Ph.D. University of Chicago, Associate Professor of Mathematics (geometry and topology, mathematical physics)
Roman Vershynin, Ph.D. University of Missouri-Columbia, Professor of Mathematics (applied and computational mathematics)
Jeffrey Viaclovsky, Ph.D. Princeton University, Professor of Mathematics (geometric analysis)
Jesse Wolfson, Ph.D. Northwestern University, Associate Professor of Mathematics; Logic and Philosophy of Science (topology)
Jack Xin, Ph.D. New York University, Chancellor's Professor of Mathematics (applied and computational mathematics)
Hamed Youssefpour, Ph.D. University of California, Irvine, Lecturer of Mathematics (mathematical modeling of biological systems)
Yifeng Yu, Ph.D. University of California, Berkeley, Professor of Mathematics (analysis and partial differential equations, applied and computational mathematics)
Martin Zeman, Ph.D. Humboldt University of Berlin, Professor of Mathematics; Logic and Philosophy of Science (logic and foundations)
Xiangwen Zhang, Ph.D. McGill University, Professor of Mathematics (geometric analysis)
Weian Zheng, Ph.D. University of Strasbourg, Professor Emeritus of Mathematics (probability theory and financial engineering)

Affiliate Faculty

Pierre F. Baldi, Ph.D. California Institute of Technology, Director of the Institute for Genomics and Bioinformatics and Distinguished Professor of Computer Science; Biological Chemistry; Biomedical Engineering; Mathematics (algorithms and theory, artificial intelligence and machine learning, biomedical informatics, databases and data mining, environmental informatics, statistics and statistical theory)
Eric D. Mjolsness, Ph.D. California Institute of Technology, Professor of Computer Science; Mathematics (artificial intelligence and machine learning, biomedical informatics and computational biology, applied mathematics, mathematical biology, modeling languages)

Courses

MATH 1A.  Pre-Calculus I.  0 Units.  4 Workload Units.  
Basic equations and inequalities, linear and quadratic functions, and systems of simultaneous equations.
MATH 1B.  Pre-Calculus II.  4 Units.  
Preparation for calculus and other mathematics courses. Exponentials, logarithms, trigonometry, polynomials, and rational functions. Satisfies no requirements other than contribution to the 180 units required for graduation.
Prerequisite: Recommended: A passing score on the Pre-Calculus Self-Assessment exam, or a score of 450 or higher on the Mathematics section of the SAT Reasoning Test. Not for students with a score of 3 or higher on the AP Calc AB exam. Not for students with a score of 3 or higher on the AP Calc BC exam.   
Restrictions: MATH 1B may not be taken for credit if taken after MATH 2A.  
MATH 2A.  Single-Variable Calculus I.  4 Units.  
Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
Prerequisite: MATH 1B with a minimum grade of C- or SAT Mathematics with a minimum score of 650 or ACT Mathematics with a minimum score of 29. Placement via the Calculus Placement exam (fee required) is also accepted.  
Overlaps with MATH 5A, MATH 7A.  
Restrictions: School of Physical Sciences students, School of Engineering students, and School of Information and Computer Sciences students have the first consideration for enrollment.   
(Vb)  
MATH 2AX.  Calculus Preparation.  1 Unit.  
Group activities designed to review and reinforce fundamental concepts essential for success in Calculus. Linear functions, quadratic functions, polynomials, and rational functions; exponentials and logarithms; trigonometry; absolute values. Graphs of functions.
Corequisite: MATH 2A.  
Grading Option: Pass/Not Pass only  
MATH 2B.  Single-Variable Calculus II.  4 Units.  
Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series.
Prerequisite: MATH 2A or MATH 5A or MATH 7A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP69 with a minimum score of 3.   
Overlaps with MATH 7B.  
Restrictions: School of Physical Sciences students, School of Engineering students, and School of Information and Computer Sciences students have the first consideration for enrollment.   
(Vb)  
MATH 2D.  Multivariable Calculus I.  4 Units.  
Differential and integral calculus of real-valued functions of several real variables, including applications. Polar coordinates.
Prerequisite: MATH 2B or MATH 5B or MATH 7B or AP Calculus BC with a minimum score of 4.   
Overlaps with MATH H2D.  
Restrictions: Unaffiliated Undeclared majors, School of Physical Sciences students, School of Engineering students, and School of Information and Computer Sciences students have the first consideration for enrollment.   
(Vb)  
MATH 2E.  Multivariable Calculus II.  4 Units.  
The differential and integral calculus of vector-valued functions. Implicit and inverse function theorems. Line and surface integrals, divergence and curl, theorems of Greens, Gauss, and Stokes.
Prerequisite: MATH 2D or MATH H2D.   
Restrictions: School of Physical Sciences students and School of Engineering students have the first consideration for enrollment.   
MATH 3A.  Introduction to Linear Algebra.  4 Units.  
Systems of linear equations, matrix operations, determinants, eigenvalues and eigenvectors, vector spaces, subspaces, and dimension.
Prerequisite: MATH 2B or MATH 5B or MATH 7B or AP Calculus BC with a minimum score of 4.   
Overlaps with I&C SCI 6N, MATH H3A.  
Restrictions: Unaffiliated Undeclared majors, School of Physical Sciences students, and School of Engineering students have the first consideration for enrollment.   
(Vb)  
MATH 3D.  Elementary Differential Equations.  4 Units.  
Linear differential equations, variation of parameters, constant coefficient cookbook, systems of equations, Laplace transforms, series solutions.
Prerequisite: (MATH 3A or MATH H3A) and (MATH 2D or MATH H2D).   
Restrictions: School of Physical Sciences students and School of Engineering students have the first consideration for enrollment.   
MATH 5A.  Calculus for Life Sciences I.  4 Units.  
Differential calculus with applications to life sciences. Exponential, logarithmic, and trigonometric functions. Limits, differentiation techniques, optimization and difference equations.
Prerequisite: MATH 1B with a minimum grade of C- or SAT Mathematics with a minimum score of 650 or ACT Mathematics with a minimum score of 29. Placement via the Calculus Placement exam (fee required) is also accepted.  
Overlaps with MATH 2A, MATH 7A.  
Restrictions: School of Biological Sciences students have the first consideration for enrollment.   
(Vb)  
MATH 5B.  Calculus for Life Sciences II.  4 Units.  
Integral calculus and multivariable calculus with applications to life sciences. Integration techniques, applications of the integral, phase plane methods and basic modeling, basic multivariable methods.
Prerequisite: MATH 5A or MATH 2A or MATH 7A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP69 with a minimum score of 3.   
Restrictions: School of Biological Sciences students have the first consideration for enrollment. Cannot be taken for credit after MATH 2B.  
(Vb)  
MATH 8.  Explorations in Functions and Modeling.  4 Units.  
Explorations of applications and connections in topics in algebra, geometry, calculus, and statistics for future secondary math educators. Emphasis on nonstandard modeling problems.
Corequisite: MATH 2A or MATH 5A or MATH 7A.  
Prerequisite: MATH 2A or MATH 5A or MATH 7A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3.   
MATH 9.  Introduction to Programming for Numerical Analysis.  4 Units.  
Introduction to computers and programming using Matlab and Python. Representation of numbers and precision, input/output, functions, custom data types, testing/debugging, reading exceptions, plotting data, numerical differentiation, basics of algorithms. Analysis of random processes using computer simulations.
Prerequisite: MATH 2A or MATH 5A or MATH 7A or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP69 with a minimum score of 3.   
Restrictions: Applied and Computational Mathematics majors and Mathematics majors have the first consideration for enrollment.   
(II and Vb.)  
MATH 10.  Introduction to Programming for Data Science.  4 Units.  
Introduction to Python for data science. Selecting appropriate data types; functions and methods; plotting; the libraries NumPy, pandas, scikit-learn. Foundations of machine learning.
Corequisite: (MATH 2D or MATH H2D) and (MATH 3A or MATH H3A).  
Prerequisite: (MATH 2D or MATH H2D) and (MATH 3A or MATH H3A) and MATH 9.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
(II and VB.)  
MATH 13.  Introduction to Abstract Mathematics.  4 Units.  
Introduction to formal definition and rigorous proof writing in mathematics. Topics include basic logic, set theory, equivalence relations, and various proof techniques such as direct, induction, contradiction, contrapositive, and exhaustion.
Prerequisite: MATH 2A or MATH 5A or MATH 7A or I&C SCI 6D or AP Calculus AB with a minimum score of 3 or AP Calculus BC with a minimum score of 3 or AP69 with a minimum score of 3.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 13X.  Skills for Success in Abstract Math .  1 Unit.  
Group activities designed to practice fundamental concepts used in abstract mathematics. Logic and reasoning; functions; sets. Proof techniques. Most coursework is done in class in collaboration with peers.
Corequisite: MATH 13.  
Grading Option: Pass/Not Pass only  
MATH 99.  New Math Major Seminar for First-Year and Transfer Students.  1 Unit.  
A series of presentations and activities to help first-year and transfer students transition to the UCI mathematics majors. Presentations are given by faculty, current students, and school staff to ensure that students make the most of the math major.
Grading Option: Pass/Not Pass only  
Restrictions: New math majors only, including transfer students majoring in math.  
MATH 105A.  Numerical Analysis I.  4 Units.  
Introduction to the theory and practice of numerical computation with an emphasis on solving equations. Solving transcendental equations; linear systems, Gaussian elimination, QR factorization, iterative methods, eigenvalue computation, power method.
Corequisite: MATH 105LA.  
Prerequisite: (MATH 3A or MATH H3A) and MATH 9.   
Overlaps with ENGRMAE 185.  
MATH 105B.  Numerical Analysis II.  4 Units.  
Introduction to the theory and practice of numerical computation with an emphasis on topics from calculus and approximation theory. Lagrange interpolation; Gaussian quadrature; Fourier series and transforms; Methods from data science including least squares and L1 regression.
Corequisite: MATH 105LB.  
Prerequisite: MATH 105A.   
MATH 105LA.  Numerical Analysis Laboratory.  1 Unit.  
Provides practical experience to complement the theory developed in Mathematics 105A.
Corequisite: MATH 105A.  
MATH 105LB.  Numerical Analysis Laboratory.  1 Unit.  
Provides practical experience to complement the theory developed in Mathematics 105B.
Corequisite: MATH 105B.  
MATH 107.  Numerical Differential Equations.  4 Units.  
Theory and applications of numerical methods to initial and boundary-value problems for ordinary and partial differential equations.
Corequisite: MATH 107L.  
Prerequisite: MATH 3D and MATH 105B.   
MATH 107L.  Numerical Differential Equations Laboratory.  1 Unit.  
Provides practical experience to complement the theory developed in Mathematics 107.
Corequisite: MATH 107.  
MATH 110A.  Optimization I.  4 Units.  
Introduction to optimization, linear search method, trust region method, Newton method, linear programming, linear, and non-linear least square methods.
Corequisite: MATH 121B.  
Prerequisite: (MATH 2D or MATH H2D) and MATH 10 and MATH 121B.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 110B.  Optimization II.  4 Units.  
The simplex method, interior point method, penalty barrier method, primal dual method, augmented Lagrangian method, and stochastic gradient method.
Prerequisite: MATH 110A with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 112A.  Introduction to Partial Differential Equations and Applications I.  4 Units.  
Introduction to ordinary and partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Classification of PDEs, separation of variables and series expansions, special functions, eigenvalue problems.
Prerequisite: (MATH 2E or MATH H2E) and MATH 3D.   
MATH 112B.  Introduction to Partial Differential Equations and Applications II.  4 Units.  
Introduction to partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Green functions and integral representations, method of characteristics.
Prerequisite: MATH 112A.   
MATH 112C.  Introduction to Partial Differential Equations and Applications III.  4 Units.  
Nonhomogeneous problems and Green's functions, Sturm-Liouville theory, general Fourier expansions, applications of partial differential equations in different areas of science.
Prerequisite: MATH 112B.   
MATH 113A.  Mathematical Modeling in Biology I.  4 Units.  
Discrete mathematical and statistical models; difference equations, population dynamics, Markov chains, and statistical models in biology.
Prerequisite: MATH 2B or MATH 5B or MATH 7B or AP Calculus BC with a minimum score of 4.   
MATH 113B.  Mathematical Modeling in Biology II.  4 Units.  
Linear algebra; differential equations models; dynamical systems; stability; hysteresis; phase plane analysis; applications to cell biology, viral dynamics, and infectious diseases.
Prerequisite: MATH 113A.   
MATH 115.  Mathematical Modeling.  4 Units.  
Mathematical modeling and analysis of phenomena that arise in engineering physical sciences, biology, economics, or social sciences.
Prerequisite: MATH 112A.   
MATH 117.  Dynamical Systems.  4 Units.  
Introduction to the modern theory of dynamical systems including contraction mapping principle, fractals and chaos, conservative systems, Kepler problem, billiard models, expanding maps, Smale's horseshoe, topological entropy.
Prerequisite: MATH 3D and MATH 140A.   
MATH 118.  The Theory of Differential Equations.  4 Units.  
Existence and uniqueness of solutions, continuous dependence of solutions on initial conditions and parameters, Lyapunov and asymptotic stability, Floquet theory, nonlinear systems, and bifurcations.
Prerequisite: MATH 3D and MATH 140A.   
MATH 120A.  Introduction to Abstract Algebra: Groups.  4 Units.  
Axioms for group theory; permutation groups, matrix groups. Isomorphisms, homomorphisms, quotient groups. Advanced topics as time permits. Special emphasis on doing proofs.
Prerequisite: (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 120B.  Introduction to Abstract Algebra: Rings and Fields.  4 Units.  
Basic properties of rings; ideals, quotient rings; polynomial and matrix rings. Elements of field theory.
Prerequisite: MATH 120A with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 120C.  Introduction to Abstract Algebra: Galois Theory.  4 Units.  
Galois Theory: proof of the impossibility of certain ruler-and-compass constructions (squaring the circle, trisecting angles); nonexistence of analogues to the "quadratic formula" for polynomial equations of degree 5 or higher.
Prerequisite: MATH 120B.   
MATH H120A.  Honors Introduction to Graduate Algebra I.  5 Units.  
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of A and (MATH 120A with a minimum grade of A or MATH 121A with a minimum grade of A).   
Restrictions: Mathematics Honors students only.  
Concurrent: MATH 206A  
MATH H120B.  Honors Introduction to Graduate Algebra II.  5 Units.  
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH H120A.   
Restrictions: Mathematics Honors students only.  
Concurrent: MATH 206B  
MATH H120C.  Honors Introduction to Graduate Algebra III.  5 Units.  
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH H120B.   
Restrictions: Mathematics Honors students only.  
Concurrent: MATH 206C  
MATH 121A.  Linear Algebra I.  4 Units.  
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Vector spaces, linear independence, bases, dimension. Linear transformations and their matrix representations. Theory of determinants.
Prerequisite: (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 121B.  Linear Algebra II.  4 Units.  
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Canonical forms; inner products; similarity of matrices.
Prerequisite: MATH 121A with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 130A.  Probability I.  4 Units.  
Combinatorial probability, conditional probabilities, independence, discrete and continuous random variables, expectation and variance, common probability distributions.
Prerequisite: MATH 3A or MATH H3A.   
MATH 130B.  Probability II.  4 Units.  
Joint distributions, sums of independent random variables, conditional distributions and conditional expectation, covariances, moment generating functions, limit theorems.
Prerequisite: MATH 130A or STATS 120A.   
MATH 130C.  Stochastic Processes.  4 Units.  
Markov chains, Brownian motion, Gaussian processes, applications to option pricing and Markov chain Monte Carlo methods.
Prerequisite: MATH 130B.   
MATH 134A.  Fixed Income.  4 Units.  
Overview of interest theory, time value of money, annuities/cash flows with payments that are not contingent, loans, sinking funds, bonds, general cash flow and portfolios, immunization, duration and convexity, swaps.
Prerequisite: MATH 130A or STATS 120A.   
Overlaps with MATH 133C.  
MATH 134B.  Mathematics of Financial Derivatives.  4 Units.  
General derivatives; call/put options; hedging and investment strategies: spreads and collars; risk management; forwards and futures; bonds.
Prerequisite: MATH 130A with a minimum grade of C-.   
Overlaps with MATH 133A.  
MATH 134C.  Mathematical Models for Finance.  4 Units.  
General properties of options: option contracts (call and put options, European, American and exotic options); binomial option pricing model, Black-Scholes option pricing model; risk-neutral pricing formula using Monte-Carlo simulation; option greeks and risk management; interest rate derivatives, Markowitz portfolio theory.
Prerequisite: MATH 134B or MATH 133A.   
Overlaps with MATH 133B.  
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 140A.  Elementary Analysis I.  4 Units.  
Introduction to real analysis, including convergence of sequence, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
Prerequisite: (MATH 2D or MATH H2D) and (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 140B.  Elementary Analysis II.  4 Units.  
Introduction to real analysis including convergence of sequences, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
Prerequisite: MATH 140A with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 140C.  Analysis in Several Variables .  4 Units.  
Rigorous treatment of multivariable differential calculus. Jacobians, Inverse and Implicit Function theorems.
Prerequisite: MATH 140B.   
MATH H140A.  Honors Introduction to Graduate Analysis I.  5 Units.  
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: (MATH 2E with a minimum grade of A or MATH H2E with a minimum grade of A) and (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of A and MATH 121A with a minimum grade of A and MATH 140A with a minimum grade of A.   
Concurrent: MATH 205A  
MATH H140B.  Honors Introduction to Graduate Analysis II.  5 Units.  
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH H140A with a minimum grade of C-.   
Concurrent: MATH 205B  
MATH H140C.  Honors Introduction to Graduate Analysis III.  5 Units.  
Construction of the real number system; topology of the real line; concepts of continuity, differential, and integral calculus; sequences and series of functions, equicontinuity, metric spaces, multivariable differential, and integral calculus; implicit functions, curves and surfaces.
Prerequisite: MATH H140B with a minimum grade of C-.   
Concurrent: MATH 205C  
MATH 141.  Introduction to Topology.  4 Units.  
The elements of naive set theory and the basic properties of metric spaces. Introduction to topological properties.
Prerequisite: MATH 140A.   
MATH 147.  Complex Analysis.  4 Units.  
Rigorous treatment of basic complex analysis: analytic functions, Cauchy integral theory and its consequences, power series, residue calculus, harmonic functions, conformal mapping. Students are expected to do proofs.
Prerequisite: MATH 140B (may be taken concurrently).   
MATH 150.  Introduction to Mathematical Logic.  4 Units.  
First order logic through the Completeness Theorem for predicate logic.
Prerequisite: MATH 13 with a minimum grade of C- or (I&C SCI 6B with a minimum grade of C- and I&C SCI 6D with a minimum grade of C-).   
Overlaps with LPS 105B, PHILOS 105B.  
MATH 161.  Modern Geometry.  4 Units.  
Euclidean Geometry; Hilbert's Axioms; Absolute Geometry; Hyperbolic Geometry; the Poincare Models; and Geometric Transformations.
Prerequisite: MATH 13 with a minimum grade of C- or (I&C SCI 6B with a minimum grade of C- and I&C SCI 6D with a minimum grade of C-).   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 162A.  Introduction to Differential Geometry I.  4 Units.  
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
Prerequisite: (MATH 2E or MATH H2E) and MATH 3D.   
MATH 162B.  Introduction to Differential Geometry II.  4 Units.  
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
Prerequisite: MATH 162A with a minimum grade of C-.   
MATH 173A.  Introduction to Cryptology I.  4 Units.  
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. Includes topics from number theory, probability, and abstract algebra.
Prerequisite: (MATH 2B or MATH 5B or MATH 7B or AP Calculus BC with a minimum score of 4) and (MATH 3A or MATH H3A) and (MATH 13 or (I&C SCI 6B and I&C SCI 6D)).   
MATH 173B.  Introduction to Cryptology II.  4 Units.  
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. The mathematics covered includes topics from number theory, probability, and abstract algebra.
Prerequisite: MATH 173A.   
MATH 175.  Combinatorics .  4 Units.  
Introduction to combinatorics including basic counting principles, permutations, combinations, binomial coefficients, inclusion-exclusion, derangements, ordinary and exponential generating functions, recurrence relations, Catalan numbers, Stirling numbers, and partition numbers.
Prerequisite: (MATH 2B or MATH 5B or MATH 7B or AP Calculus BC with a minimum score of 4) and MATH 13 with a minimum grade of C-.   
MATH 176.  Mathematics of Finance.  4 Units.  
After reviewing tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the Blac-Scholes, and other equations are discussed.
Prerequisite: MATH 3A or MATH H3A.   
Same as ECON 135  
Restrictions: Business Economics majors, Economics majors, Mathematics majors, Quantitative Economics majors, and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 178.  Mathematical Machine Learning.  6 Units.  
Theoretical introduction to Mathematical Machine Learning. Mathematical foundations and coding implementations using Python libraries such as scikit-learn and Keras. Supervised and unsupervised learning; regression and classification; loss functions; overfitting and the bias-complexity tradeoff. Prominent algorithms in machine learning.
Prerequisite: MATH 10 and MATH 121A and MATH 130A.   
Overlaps with COMPSCI 178.  
MATH 180A.  Number Theory I.  4 Units.  
Introduction to number theory and applications. Divisibility, prime numbers, factorization. Arithmetic functions. Congruences. Quadratic residue. Diophantine equations. Introduction to cryptography.
Prerequisite: (MATH 3A or MATH H3A) and MATH 13 with a minimum grade of C-.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 180B.  Number Theory II.  4 Units.  
Introduction to number theory and applications. Analytic number theory, character sums, finite fields, discrete logarithm, computational complexity. Introduction to coding theory. Other topics as time permits.
Prerequisite: MATH 180A.   
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 184.  Topics in the History of Mathematics.  4 Units.  
Topics include mathematics in ancient times; the development of modern analysis; the evolution of geometric ideas. Students are assigned individual topics for term papers.
Corequisite: MATH 184L.  
Prerequisite: MATH 120A and MATH 140A.   
Repeatability: May be taken 1 time as topics vary  
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
MATH 184L.  History of Mathematics Lesson Lab.  1 Unit.  
Aspiring math teachers research, design, present, and peer review middle school or high school math lessons that draw from history of mathematics topics.
Corequisite: MATH 184.  
Prerequisite: PHY SCI 5.   
MATH 192.  Studies in the Learning and Teaching of Secondary Mathematics.  2 Units.  
Focus is on historic and current mathematical concepts related to student learning and effective math pedagogy, with fieldwork in grades 6-14.
Grading Option: Pass/Not Pass only  
Repeatability: May be taken unlimited times  
MATH 194.  Problem Solving Seminar.  2 Units.  
Develops ability in analytical thinking and problem solving, using problems of the type found in the Mathematics Olympiad and the Putnam Mathematical Competition. Students taking the course in fall will prepare for and take the Putnam examination in December.
Grading Option: Pass/Not Pass only  
Repeatability: May be taken for credit 2 times  
MATH 195W.  Mathematical Writing.  4 Units.  
Techniques of mathematical writing and communication. Covers effectively writing mathematical papers, creating effective presentations, and communicating mathematics in a variety of media. Focuses on utilizing LaTeX for typesetting mathematics.
Prerequisite: MATH 120A with a minimum grade of C- or MATH 121A with a minimum grade of C- or MATH 140A with a minimum grade of C-. Satisfactory completion of the Lower-Division Writing requirement.  
Restrictions: Mathematics majors and Applied and Computational Mathematics majors have the first consideration for enrollment.   
(Ib)  
MATH 199A.  Special Studies in Mathematics.  1-4 Units.  
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: May be taken unlimited times as topics vary  
MATH 199B.  Special Studies in Mathematics.  1-4 Units.  
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: May be taken unlimited times as topics vary  
MATH 199C.  Special Studies in Mathematics.  1-4 Units.  
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: May be taken unlimited times as topics vary  
MATH 205A.  Introduction to Graduate Analysis.  5 Units.  
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: Recommended: MATH 2E and MATH 3A and MATH 13, or equivalent.  
Concurrent: MATH H140A  
MATH 205B.  Introduction to Graduate Analysis.  5 Units.  
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 205A with a minimum grade of B-.   
Concurrent: MATH H140B  
MATH 205C.  Introduction to Graduate Analysis.  5 Units.  
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 205B with a minimum grade of B-.   
Concurrent: MATH H140C  
MATH 210A.  Real Analysis.  4 Units.  
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
Prerequisite: Recommended: MATH 140C or equivalent.  
MATH 210B.  Real Analysis.  4 Units.  
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
Prerequisite: MATH 210A with a minimum grade of B-.   
MATH 210C.  Real Analysis.  4 Units.  
Measure theory, Lebesgue integral, signed measures, Radon-Nikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the Riesz-Markov theorem, measure and outer measure, product measure spaces.
Prerequisite: MATH 210B with a minimum grade of B-.   
MATH 218A.  Introduction to Manifolds and Geometry.  4 Units.  
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: Recommended: MATH 140C and MATH 121B, or equivalent.  
MATH 218B.  Introduction to Manifolds and Geometry.  4 Units.  
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: MATH 218A with a minimum grade of B-.   
MATH 218C.  Introduction to Manifolds and Geometry.  4 Units.  
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: MATH 218B with a minimum grade of B-.   
MATH 220A.  Analytic Function Theory.  4 Units.  
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: Recommended: MATH 140C or equivalent.  
MATH 220B.  Analytic Function Theory.  4 Units.  
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: MATH 220A with a minimum grade of B-.   
MATH 220C.  Analytic Function Theory.  4 Units.  
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: MATH 220B with a minimum grade of B-.   
MATH 222A.  Topics in Several Complex Variables and Complex Geometry.  4 Units.  
Several Complex variables, d-bar problems, mappings, Kaehler geometry, de Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, Kahler-Einstein geometry, Monge-Ampere.
Prerequisite: MATH 220C with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 222B.  Topics in Several Complex Variables and Complex Geometry.  4 Units.  
Several Complex variables, d-bar problems, mappings, Kaehler geometry, Le Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, Kahler-Einstein geometry, Monge-Ampere.
Prerequisite: MATH 222A with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 222C.  Topics in Several Complex Variables and Complex Geometry.  4 Units.  
Several Complex variables, d-bar problems, mappings, Kaehler geometry, Le Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, Kahler-Einstein geometry, Monge-Ampere.
Prerequisite: MATH 222B with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 225A.  Introduction to Numerical Analysis and Scientific Computing.  4 Units.  
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Error analysis, approximation of functions, nonlinear equations.
Prerequisite: Recommended: MATH 3D and MATH 105B and MATH 140A and MATH 121A and MATH 112A, or equivalent.  
MATH 225B.  Introduction to Numerical Analysis and Scientific Computing.  4 Units.  
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
Prerequisite: MATH 225A with a minimum grade of B-.   
MATH 225C.  Introduction to Numerical Analysis and Scientific Computing.  4 Units.  
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
Prerequisite: Recommended: MATH 3D and MATH 105B and MATH 140A and MATH 121A and MATH 112A, or equivalent.  
MATH 226A.  Computational Differential Equations.  4 Units.  
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
Prerequisite: Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent.  
MATH 226B.  Computational Differential Equations.  4 Units.  
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
Prerequisite: Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent.  
MATH 226C.  Computational Differential Equations.  4 Units.  
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and Petrov-Galerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226A-B-C, respectively.
Prerequisite: Recommended: MATH 3D and MATH 112A and (MATH 140B or MATH 105B), or equivalent.  
MATH 227A.  Mathematical and Computational Biology.  4 Units.  
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Analytical methods.
Prerequisite: Recommended: MATH 2A and MATH 2B and MATH 3A, or equivalent.  
MATH 227B.  Mathematical and Computational Biology.  4 Units.  
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Numerical simulations.
Prerequisite: MATH 227A with a minimum grade of B-.   
MATH 227C.  Mathematical and Computational Biology .  4 Units.  
Analytical and numerical methods for dynamical systems, temporal-spatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Probabilistic methods.
Prerequisite: MATH 227A with a minimum grade of B-.   
MATH 228.  Topics in Applied Math Careers.  2-4 Units.  
Prepares students for math careers in industry.
Prerequisite: A basic course in programming; familiarity with probability and differential equations at the upper undergraduate level.   
Repeatability: May be taken 1 time as topics vary  
MATH 230A.  Algebra.  4 Units.  
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
Prerequisite: Recommended: MATH 120A and MATH 121A and MATH 120B, or equivalent.  
MATH 230B.  Algebra.  4 Units.  
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
Prerequisite: MATH 230A with a minimum grade of B-.   
MATH 230C.  Algebra.  4 Units.  
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
Prerequisite: MATH 230B with a minimum grade of B-.   
MATH 232A.  Algebraic Number Theory.  4 Units.  
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 230C with a minimum grade of B-.   
MATH 232B.  Algebraic Number Theory.  4 Units.  
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 232A with a minimum grade of B-.   
MATH 232C.  Algebraic Number Theory.  4 Units.  
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, L-functions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 232B with a minimum grade of B-.   
MATH 233A.  Algebraic Geometry.  4 Units.  
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
Prerequisite: MATH 230C with a minimum grade of B-.   
MATH 233B.  Algebraic Geometry.  4 Units.  
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
Prerequisite: MATH 233A with a minimum grade of B-.   
MATH 233C.  Algebraic Geometry.  4 Units.  
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, Riemann-Roch theorem, Jacobians, classification of curves and surfaces.
Prerequisite: MATH 233B with a minimum grade of B-.   
MATH 234B.  Topics in Algebra.  4 Units.  
Group theory, homological algebra, and other selected topics.
Prerequisite: MATH 230C with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 234C.  Topics in Algebra.  4 Units.  
Group theory, homological algebra, and other selected topics.
Prerequisite: MATH 230C with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 240A.  Differential Geometry.  4 Units.  
Riemannian manifolds, connections, curvature, and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
Prerequisite: MATH 218A with a minimum grade of B-.   
MATH 240B.  Differential Geometry.  4 Units.  
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
Prerequisite: MATH 240A with a minimum grade of B-.   
MATH 240C.  Differential Geometry.  4 Units.  
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
Prerequisite: MATH 240B with a minimum grade of B-.   
MATH 245A.  Topics in Geometric Analysis.  4 Units.  
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 218A with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 245B.  Topics in Geometric Analysis.  4 Units.  
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 245A with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 245C.  Topics in Geometric Analysis.  4 Units.  
Studies in selected areas of differential geometry, a continuation of MATH 240A-MATH 240B-MATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 245B with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 249.  Topics in Differential Geometry.  4 Units.  
Studies in selected areas of differential geometry. Topics addressed vary each quarter.
Repeatability: May be taken unlimited times as topics vary  
MATH 250A.  Algebraic Topology.  4 Units.  
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: Recommended: MATH 120B and MATH 141, or equivalent.  
MATH 250B.  Algebraic Topology.  4 Units.  
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: MATH 250A with a minimum grade of B-.   
MATH 250C.  Algebraic Topology.  4 Units.  
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: MATH 250B with a minimum grade of B-.   
MATH 260A.  Functional Analysis.  4 Units.  
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
Prerequisite: MATH 210C with a minimum grade of B- and MATH 220C with a minimum grade of B-.   
MATH 260B.  Functional Analysis.  4 Units.  
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
Prerequisite: MATH 260A with a minimum grade of B-.   
MATH 260C.  Functional Analysis.  4 Units.  
Normed linear spaces, Hilbert spaces, Banach spaces, Stone-Weierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the Gelfand-Neumark Theorem for commutative C*-algebras, the spectral theorem for bounded self-adjoint operators, unbounded operators on Hilbert spaces.
Prerequisite: MATH 260B with a minimum grade of B-.   
MATH 268C.  Topics in Functional Analysis.  4 Units.  
Selected topics such as spectral theory, abstract harmonic analysis, Banach algebras, operator algebras, and other related topics.
Prerequisite: MATH 268B.   
Repeatability: May be taken unlimited times as topics vary  
MATH 270A.  Probability.  4 Units.  
Probability spaces, distribution, and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
Prerequisite: MATH 210C with a minimum grade of B-. Recommended: MATH 130C or equivalent.  
MATH 270B.  Probability.  4 Units.  
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
Prerequisite: MATH 270A with a minimum grade of B-.   
MATH 270C.  Probability.  4 Units.  
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
Prerequisite: MATH 270B with a minimum grade of B-.   
MATH 271A.  Stochastic Processes.  4 Units.  
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
Prerequisite: MATH 210C with a minimum grade of B-.   
Overlaps with STATS 270.  
MATH 271B.  Stochastic Processes.  4 Units.  
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
Prerequisite: MATH 271A with a minimum grade of B-.   
Overlaps with STATS 270.  
MATH 271C.  Stochastic Processes.  4 Units.  
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes
Prerequisite: MATH 271B with a minimum grade of B-.   
Overlaps with STATS 270.  
MATH 274.  Topics in Probability.  4 Units.  
Selected topics, such as theory of stochastic processes, martingale theory, stochastic integrals, stochastic differential equations.
Prerequisite: Recommended: MATH 270C.  
Repeatability: May be taken unlimited times as topics vary  
MATH 280A.  Mathematical Logic.  4 Units.  
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
Prerequisite: Recommended: MATH 150.  
MATH 280B.  Mathematical Logic.  4 Units.  
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
Prerequisite: MATH 280A with a minimum grade of B-.   
MATH 280C.  Mathematical Logic.  4 Units.  
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
Prerequisite: MATH 280B with a minimum grade of B-.   
MATH 281A.  Set Theory.  4 Units.  
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
MATH 281B.  Set Theory.  4 Units.  
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
Prerequisite: MATH 281A with a minimum grade of B-.   
MATH 281C.  Set Theory.  4 Units.  
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
Prerequisite: MATH 281B with a minimum grade of B-.   
MATH 282A.  Model Theory.  4 Units.  
Languages, structures, compactness, and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
MATH 282B.  Model Theory.  4 Units.  
Languages, structures, compactness and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
Prerequisite: MATH 282A with a minimum grade of B-.   
MATH 282C.  Model Theory.  4 Units.  
Languages, structures, compactness and completeness. Model-theoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. O-minimality. Applications to algebra.
Prerequisite: MATH 282B with a minimum grade of B-.   
MATH 290A.  Methods in Applied Mathematics.  4 Units.  
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
MATH 290B.  Methods in Applied Mathematics.  4 Units.  
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
Prerequisite: MATH 290A.   
MATH 290C.  Methods in Applied Mathematics.  4 Units.  
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, Euler-Lagrange equation. Second variation and Legendre condition.
Prerequisite: MATH 290B.   
MATH 295A.  Partial Differential Equations.  4 Units.  
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
Prerequisite: MATH 210C with a minimum grade of B-. Recommended: MATH 112B and MATH 112C or equivalent.  
MATH 295B.  Partial Differential Equations.  4 Units.  
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
Prerequisite: MATH 295A with a minimum grade of B-.   
MATH 295C.  Partial Differential Equations.  4 Units.  
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
Prerequisite: MATH 295B with a minimum grade of B-.   
MATH 296.  Topics in Partial Differential Equations.  4 Units.  
Studies in selected areas of partial differential equations, a continuation of MATH 295A-MATH 295B-MATH 295C. Topics addressed vary each quarter.
Prerequisite: MATH 295C with a minimum grade of B-.   
Repeatability: May be taken unlimited times as topics vary  
MATH 297.  Mathematics Colloquium.  1 Unit.  
Weekly colloquia on topics of current interest in mathematics.
Grading Option: Satisfactory/Unsatisfactory only  
Repeatability: May be taken unlimited times  
MATH 298A.  Seminar .  2 Units.  
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Grading Option: Satisfactory/Unsatisfactory only  
Repeatability: May be taken unlimited times as topics vary  
MATH 298B.  Seminar .  2 Units.  
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Prerequisite: MATH 298A with a minimum grade of B-.   
Grading Option: Satisfactory/Unsatisfactory only  
Repeatability: May be taken unlimited times as topics vary  
MATH 298C.  Seminar .  2 Units.  
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Prerequisite: MATH 298B with a minimum grade of B-.   
Grading Option: Satisfactory/Unsatisfactory only  
Repeatability: May be taken unlimited times as topics vary  
MATH 299A.  Supervised Reading and Research.  1-12 Units.  
Supervised reading and research with Mathematics faculty.
Repeatability: May be taken unlimited times  
MATH 299B.  Supervised Reading and Research.  1-12 Units.  
Supervised reading and research with Mathematics faculty.
Prerequisite: MATH 299A with a minimum grade of B-.   
Repeatability: May be taken unlimited times  
MATH 299C.  Supervised Reading and Research.  1-12 Units.  
Supervised reading and research with Mathematics faculty.
Prerequisite: MATH 299B with a minimum grade of B-.   
Repeatability: May be taken unlimited times  
MATH 399.  University Teaching.  1-4 Units.  
Limited to Teaching Assistants.
Grading Option: Satisfactory/Unsatisfactory only  
Repeatability: May be taken unlimited times