Mathematics

University of California, Berkeley

Overview

The Department of Mathematics is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the world. With approximately 55 regular faculty members representing most of the major fields of current research, along with 25 to 30 postdoctoral scholars, 180 graduate students, 475 undergraduate majors, one of the finest mathematics libraries in the nation, and a favorable climate in one of America's most exciting and cosmopolitan centers for mathematics research and teaching, UC Berkeley has become a favorite location for the study of mathematics by students and faculty from all over the world.

Berkeley is increasingly interested in developing the talents of outstanding mathematics students and has a number of challenging honors-level courses. The department encourages all major students to participate in the annual William Lowell Putnam Mathematical Competition. Additionally, the department sponsors undergraduate teams in the annual Mathematical Contest in Modeling, in which teams of three write mathematical solutions to real-life problems. An active Mathematics Undergraduate Student Association (MUSA), of which all departmental majors are automatically members, contributes to making Berkeley a stimulating and rewarding place to study mathematics. In addition, the Noetherian Ring, an organization seeking to promote and support women in mathematics at Berkeley, is open to undergraduate students.

Berkeley's mathematics education program is greatly enriched by its large number of graduate students, postdoctoral faculty and fellows, and visiting teachers in residence each year. They come from all over the world to teach courses, participate in seminars, collaborate in research, give talks at the weekly Mathematics Colloquium, and be available as consultants. An affiliated interdisciplinary group, with its own doctoral program, is the Group in Logic and the Methodology of Science. There are two NSF funded Research Training Groups: one in Representation Theory, Geometry and Combinatorics and one in Geometry, Topology and Operator Algebras. These groups run seminars, workshops, and other activities and support graduate student and postdoctoral fellows in their areas of interest. The department has several graduate student groups: the Mathematics Graduate Student Association (MGSA), comprising all graduate students; the Noetherian Ring, a group of women in mathematics; and a student lecture series, Many Cheerful Facts.

Facilities

The Mathematics Library on the first floor of Evans Hall, part of the system of University of California Libraries, provides researchers and students with access to world-class collections.

The Mathematical Sciences Research Institute (MSRI) was founded by the National Science Foundation in 1981. In a beautifully designed building on the hills above the Berkeley campus and overlooking San Francisco Bay, about 1,700 mathematicians from around the world come each year to participate in research programs in a wide variety of mathematical topics. The combined and cooperative efforts of the department, the center, and the MSRI provide a program of mathematics courses, workshops, seminars, and colloquia of remarkable variety and exciting intensity.

Undergraduate Programs

Applied Mathematics: BA
Mathematics: BA (also available with a Teaching Concentration), Minor

Graduate Programs

Applied Mathematics: PhD
Mathematics: MA, PhD

Visit Department Website

Courses

Mathematics

MATH 1A Calculus 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

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MATH 1B Calculus 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

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MATH H1B Honors Calculus 4 Units

Terms offered: Spring 2017, Fall 2015, Fall 2014
Honors version of 1B. Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

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MATH 10A Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Fall 2016
This sequence is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable. Representation of data, elementary probability theory, statistical models, and testing.

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MATH 10B Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units

Terms offered: Summer 2017 8 Week Session, Spring 2017, Summer 2016 8 Week Session
Elementary combinatorics and discrete probability theory. Introduction to graphs, matrix algebra, linear equations, difference equations, and differential equations.

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MATH 16A Analytic Geometry and Calculus 3 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions.

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MATH 16B Analytic Geometry and Calculus 3 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.

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MATH 24 Freshman Seminars 1 Unit

Terms offered: Fall 2017, Spring 2017, Fall 2016
The Berkeley Seminar Program has been designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small-seminar setting. Berkeley Seminars are offered in all campus departments, and topics vary from department to department and semester to semester.

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MATH 32 Precalculus 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Polynomial and rational functions, exponential and logarithmic functions, trigonometry and trigonometric functions. Complex numbers, fundamental theorem of algebra, mathematical induction, binomial theorem, series, and sequences.

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MATH N32 Precalculus 4 Units

Terms offered: Prior to 2007
Polynomial and rational functions, exponential and logarithmic functions, trigonometry and trigonometric functions. Complex numbers, fundamental theorem of algebra, mathematical induction, binomial theorem, series, and sequences.

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MATH 39A Freshman/Sophomore Seminar 2 - 4 Units

Terms offered: Spring 2010, Spring 2009, Spring 2008
Freshman and sophomore seminars offer lower division students the opportunity to explore an intellectual topic with a faculty member and a group of peers in a small-seminar setting. These seminars are offered in all campus departments; topics vary from department to department and from semester to semester.

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MATH 49 Supplementary Work in Lower Division Mathematics 1 - 3 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Students with partial credit in lower division mathematics courses may, with consent of instructor, complete the credit under this heading.

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MATH 53 Multivariable Calculus 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

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MATH H53 Honors Multivariable Calculus 4 Units

Terms offered: Spring 2017, Fall 2015, Spring 2015
Honors version of 53. Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

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MATH W53 Multivariable Calculus 4 Units

Terms offered: Summer 2017 8 Week Session, Summer 2016 10 Week Session, Summer 2016 8 Week Session
Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

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MATH 54 Linear Algebra and Differential Equations 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.

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MATH H54 Honors Linear Algebra and Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Honors version of 54. Basic linear algebra: matrix arithmetic and determinants. Vectors spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.

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MATH 55 Discrete Mathematics 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.

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MATH 74 Transition to Upper Division Mathematics 3 Units

Terms offered: Summer 2009 8 Week Session, Spring 2009, Fall 2008
The course will focus on reading and understanding mathematical proofs. It will emphasize precise thinking and the presentation of mathematical results, both orally and in written form. The course is intended for students who are considering majoring in mathematics but wish additional training.

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MATH 91 Special Topics in Mathematics 4 Units

Terms offered: Spring 2016, Fall 2012, Spring 2012
Topics to be covered and the method of instruction to be used will be announced at the beginning of each semester that such courses are offered. See department bulletins.

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MATH 96 College Algebra 2 Units

Terms offered: Summer 2017 8 Week Session, Summer 2016 8 Week Session, Summer 2015 8 Week Session
Elements of college algebra. Designed for students who do not meet the prerequisites for 32. Offered through the Student Learning Center.

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MATH 98 Supervised Group Study 1 - 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Directed Group Study, topics vary with instructor.

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MATH 98BC Berkeley Connect 1 Unit

Terms offered: Fall 2017, Spring 2017, Fall 2016
Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department
faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.
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MATH 99 Supervised Independent Study 1 - 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Supervised independent study by academically superior, lower division students. 3.3 GPA required and prior consent of instructor who is to supervise the study. A written proposal must be submitted to the department chair for pre-approval.

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MATH C103 Introduction to Mathematical Economics 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Selected topics illustrating the application of mathematics to economic theory. This course is intended for upper-division students in Mathematics, Statistics, the Physical Sciences, and Engineering, and for economics majors with adequate mathematical preparation. No economic background is required.

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MATH 104 Introduction to Analysis 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

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MATH H104 Honors Introduction to Analysis 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Honors section corresponding to 104. Recommended for students who enjoy mathematics and are good at it. Greater emphasis on theory and challenging problems.

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MATH 105 Second Course in Analysis 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Differential calculus in Rn: the derivative as a linear map; the chain rule; inverse and implicit function theorems. Lebesgue integration on the line; comparison of Lebesgue and Riemann integrals. Convergence theorems. Fourier series, L2 theory. Fubini's theorem, change of variable.

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MATH 110 Linear Algebra 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.

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MATH H110 Honors Linear Algebra 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Honors section corresponding to course 110 for exceptional students with strong mathematical inclination and motivation. Emphasis is on rigor, depth, and hard problems.

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MATH 113 Introduction to Abstract Algebra 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

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MATH H113 Honors Introduction to Abstract Algebra 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Honors section corresponding to 113. Recommended for students who enjoy mathematics and are willing to work hard in order to understand the beauty of mathematics and its hidden patterns and structures. Greater emphasis on theory and challenging problems.

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MATH 114 Second Course in Abstract Algebra 4 Units

Terms offered: Spring 2017, Fall 2015, Spring 2015
Further topics on groups, rings, and fields not covered in Math 113. Possible topics include the Sylow Theorems and their applications to group theory; classical groups; abelian groups and modules over a principal ideal domain; algebraic field extensions; splitting fields and Galois theory; construction and classification of finite fields.

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MATH 115 Introduction to Number Theory 4 Units

Terms offered: Summer 2017 8 Week Session, Spring 2017, Summer 2016 8 Week Session
Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.

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MATH 116 Cryptography 4 Units

Terms offered: Fall 2015, Fall 2014, Fall 2013
Construction and analysis of simple cryptosystems, public key cryptography, RSA, signature schemes, key distribution, hash functions, elliptic curves, and applications.

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MATH 118 Fourier Analysis, Wavelets, and Signal Processing 4 Units

Terms offered: Fall 2017, Spring 2017, Spring 2016
Introduction to signal processing including Fourier analysis and wavelets. Theory, algorithms, and applications to one-dimensional signals and multidimensional images.

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MATH 121A Mathematical Tools for the Physical Sciences 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Rapid review of series and partial differentiation, complex variables and analytic functions, integral transforms, calculus of variations.

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MATH 121B Mathematical Tools for the Physical Sciences 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Special functions, series solutions of ordinary differential equations, partial differential equations arising in mathematical physics, probability theory.

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MATH 123 Ordinary Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Existence and uniqueness of solutions, linear systems, regular singular points. Other topics selected from analytic systems, autonomous systems, Sturm-Liouville Theory.

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MATH 125A Mathematical Logic 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Sentential and quantificational logic. Formal grammar, semantical interpretation, formal deduction, and their interrelation. Applications to formalized mathematical theories. Selected topics from model theory or proof theory.

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MATH 126 Introduction to Partial Differential Equations 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Waves and diffusion, initial value problems for hyperbolic and parabolic equations, boundary value problems for elliptic equations, Green's functions, maximum principles, a priori bounds, Fourier transform.

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MATH 127 Mathematical and Computational Methods in Molecular Biology 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Introduction to mathematical and computational problems arising in the context of molecular biology. Theory and applications of combinatorics, probability, statistics, geometry, and topology to problems ranging from sequence determination to structure analysis.

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MATH 128A Numerical Analysis 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.

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MATH 128B Numerical Analysis 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Iterative solution of systems of nonlinear equations, evaluation of eigenvalues and eigenvectors of matrices, applications to simple partial differential equations. Practice on the computer.

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MATH 130 The Classical Geometries 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
A critical examination of Euclid's Elements; ruler and compass constructions; connections with Galois theory; Hilbert's axioms for geometry, theory of areas, introduction of coordinates, non-Euclidean geometry, regular solids, projective geometry.

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MATH 135 Introduction to the Theory of Sets 4 Units

Terms offered: Fall 2017, Spring 2017, Spring 2016
Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences.

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MATH 136 Incompleteness and Undecidability 4 Units

Terms offered: Spring 2017, Fall 2015, Spring 2015
Functions computable by algorithm, Turing machines, Church's thesis. Unsolvability of the halting problem, Rice's theorem. Recursively enumerable sets, creative sets, many-one reductions. Self-referential programs. Godel's incompleteness theorems, undecidability of validity, decidable and undecidable theories.

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MATH 140 Metric Differential Geometry 4 Units

Terms offered: Spring 2017, Fall 2015, Spring 2015
Frenet formulas, isoperimetric inequality, local theory of surfaces in Euclidean space, first and second fundamental forms. Gaussian and mean curvature, isometries, geodesics, parallelism, the Gauss-Bonnet-Von Dyck Theorem.

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MATH 141 Elementary Differential Topology 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Manifolds in n-dimensional Euclidean space and smooth maps, Sard's Theorem, classification of compact one-manifolds, transversality and intersection modulo 2.

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MATH 142 Elementary Algebraic Topology 4 Units

Terms offered: Spring 2017, Fall 2015, Fall 2014
The topology of one and two dimensional spaces: manifolds and triangulation, classification of surfaces, Euler characteristic, fundamental groups, plus further topics at the discretion of the instructor.

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MATH 143 Elementary Algebraic Geometry 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.

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MATH 151 Mathematics of the Secondary School Curriculum I 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Theory of rational numbers based on the number line, the Euclidean algorithm and fractions in lowest terms. The concepts of congruence and similarity, equation of a line, functions, and quadratic functions.

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MATH 152 Mathematics of the Secondary School Curriculum II 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry.

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MATH 153 Mathematics of the Secondary School Curriculum III 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
The real line and least upper bound, limit and decimal expansion of a number, differentiation and integration, Fundamental Theorem of Calculus, characterizations of sine, cosine, exp, and log.

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MATH 160 History of Mathematics 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
History of algebra, geometry, analytic geometry, and calculus from ancient times through the seventeenth century and selected topics from more recent mathematical history.

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MATH 170 Mathematical Methods for Optimization 4 Units

Terms offered: Spring 2017, Fall 2015, Fall 2014
Linear programming and a selection of topics from among the following: matrix games, integer programming, semidefinite programming, nonlinear programming, convex analysis and geometry, polyhedral geometry, the calculus of variations, and control theory.

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MATH 172 Combinatorics 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Basic combinatorial principles, graphs, partially ordered sets, generating functions, asymptotic methods, combinatorics of permutations and partitions, designs and codes. Additional topics at the discretion of the instructor.

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MATH 185 Introduction to Complex Analysis 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

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MATH H185 Honors Introduction to Complex Analysis 4 Units

Terms offered: Spring 2016, Spring 2015, Spring 2014
Honors section corresponding to Math 185 for exceptional students with strong mathematical inclination and motivation. Emphasis is on rigor, depth, and hard problems.

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MATH 189 Mathematical Methods in Classical and Quantum Mechanics 4 Units

Terms offered: Fall 2015, Fall 2014, Fall 2013
Topics in mechanics presented from a mathematical viewpoint: e.g., hamiltonian mechanics and symplectic geometry, differential equations for fluids, spectral theory in quantum mechanics, probability theory and statistical mechanics. See department bulletins for specific topics each semester course is offered.

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MATH 191 Experimental Courses in Mathematics 1 - 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
The topics to be covered and the method of instruction to be used will be announced at the beginning of each semester that such courses are offered. See departmental bulletins.

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MATH 195 Special Topics in Mathematics 4 Units

Terms offered: Spring 2011, Spring 2004, Spring 2003
Lectures on special topics, which will be announced at the beginning of each semester that the course is offered.

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MATH 196 Honors Thesis 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Independent study of an advanced topic leading to an honors thesis.

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MATH 197 Field Study 1 - 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
For Math/Applied math majors. Supervised experience relevant to specific aspects of their mathematical emphasis of study in off-campus organizations. Regular individual meetings with faculty sponsor and written reports required. Units will be awarded on the basis of three hours/week/unit.

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MATH 198 Directed Group Study 1 - 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Topics will vary with instructor.

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MATH 198BC Berkeley Connect 1 Unit

Terms offered: Fall 2017, Spring 2017, Fall 2016
Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department
faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.
Berkeley Connect: Read More [+]

MATH 199 Supervised Independent Study and Research 1 - 4 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017

Supervised Independent Study and Research: Read More [+]

MATH 202A Introduction to Topology and Analysis 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Metric spaces and general topological spaces. Compactness and connectedness. Characterization of compact metric spaces. Theorems of Tychonoff, Urysohn, Tietze. Complete spaces and the Baire category theorem. Function spaces; Arzela-Ascoli and Stone-Weierstrass theorems. Partitions of unity. Locally compact spaces; one-point compactification. Introduction to measure and integration. Sigma algebras of sets. Measures and outer measures. Lebesgue measure
on the line and Rn. Construction of the integral. Dominated convergence theorem.
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MATH 202B Introduction to Topology and Analysis 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Measure and integration. Product measures and Fubini-type theorems. Signed measures; Hahn and Jordan decompositions. Radon-Nikodym theorem. Integration on the line and in Rn. Differentiation of the integral. Hausdorff measures. Fourier transform. Introduction to linear topological spaces, Banach spaces and Hilbert spaces. Banach-Steinhaus theorem; closed graph theorem. Hahn-Banach theorem. Duality; the dual of LP. Measures on locally compact
spaces; the dual of C(X). Weak and weak-* topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. Additional topics chosen may include compact operators, spectral theory of compact operators, and applications to integral equations.
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MATH 203 Asymptotic Analysis in Applied Mathematics 4 Units

Terms offered: Fall 2011, Spring 2011, Spring 2010
Asymptotic methods for differential equations, with emphasis upon many physical examples. Topics will include matched asymptotic expansions, Laplace's method, stationary phase, boundary layers, multiple scales, WKB approximations, asymptotic Lagrangians, bifurcation theory.

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MATH 204 Ordinary Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Rigorous theory of ordinary differential equations. Fundamental existence theorems for initial and boundary value problems, variational equilibria, periodic coefficients and Floquet Theory, Green's functions, eigenvalue problems, Sturm-Liouville theory, phase plane analysis, Poincare-Bendixon Theorem, bifurcation, chaos.

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MATH 205 Theory of Functions of a Complex Variable 4 Units

Terms offered: Spring 2017, Fall 2015, Spring 2015
Normal families. Riemann Mapping Theorem. Picard's theorem and related theorems. Multiple-valued analytic functions and Riemann surfaces. Further topics selected by the instructor may include: harmonic functions, elliptic and algebraic functions, boundary behavior of analytic functions and HP spaces, the Riemann zeta functions, prime number theorem.

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MATH 206 Banach Algebras and Spectral Theory 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Banach algebras. Spectrum of a Banach algebra element. Gelfand theory of commutative Banach algebras. Analytic functional calculus. Hilbert space operators. C*-algebras of operators. Commutative C*-algebras. Spectral theorem for bounded self-adjoint and normal operators (both forms: the spectral integral and the "multiplication operator" formulation). Riesz theory of compact operators. Hilbert-Schmidt operators. Fredholm operators. The
Fredholm index. Selected additional topics.
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MATH 208 C*-algebras 4 Units

Terms offered: Spring 2015, Spring 2013, Spring 2011
Basic theory of C*-algebras. Positivity, spectrum, GNS construction. Group C*-algebras and connection with group representations. Additional topics, for example, C*-dynamical systems, K-theory.

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MATH 209 Von Neumann Algebras 4 Units

Terms offered: Spring 2017, Spring 2014, Spring 2012
Basic theory of von Neumann algebras. Density theorems, topologies and normal maps, traces, comparison of projections, type classification, examples of factors. Additional topics, for example, Tomita Takasaki theory, subfactors, group actions, and noncommutative probability.

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MATH 212 Several Complex Variables 4 Units

Terms offered: Spring 2016, Fall 2014, Spring 2012
Power series developments, domains of holomorphy, Hartogs' phenomenon, pseudo convexity and plurisubharmonicity. The remainder of the course may treat either sheaf cohomology and Stein manifolds, or the theory of analytic subvarieties and spaces.

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MATH 214 Differentiable Manifolds 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2015
Smooth manifolds and maps, tangent and normal bundles. Sard's theorem and transversality, Whitney embedding theorem. Morse functions, differential forms, Stokes' theorem, Frobenius theorem. Basic degree theory. Flows, Lie derivative, Lie groups and algebras. Additional topics selected by instructor.

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MATH 215A Algebraic Topology 4 Units

Terms offered: Spring 2017, Fall 2015, Fall 2014
Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibrations, relations between homotopy and homology, obstruction theory, and topics from spectral sequences, cohomology operations, and characteristic classes. Sequence begins fall.

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MATH 215B Algebraic Topology 4 Units

Terms offered: Spring 2016, Spring 2015, Spring 2014
Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibrations, relations between homotopy and homology, obstruction theory, and topics from spectral sequences, cohomology operations, and characteristic classes. Sequence begins fall.

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MATH C218A Probability Theory 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
The course is designed as a sequence with Statistics C205B/Mathematics C218B with the following combined syllabus. Measure theory concepts needed for probability. Expection, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations, martingales and martingale convergence theorems. Markov chains. Stationary processes. Brownian motion.

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MATH C218B Probability Theory 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
The course is designed as a sequence with with Statistics C205A/Mathematics C218A with the following combined syllabus. Measure theory concepts needed for probability. Expection, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations, martingales and martingale convergence theorems. Markov chains. Stationary processes. Brownian motion.

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MATH 219 Dynamical Systems 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2015
Diffeomorphisms and flows on manifolds. Ergodic theory. Stable manifolds, generic properties, structural stability. Additional topics selected by the instructor.

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MATH 220 Introduction to Probabilistic Methods in Mathematics and the Sciences 4 Units

Terms offered: Spring 2012, Spring 2011, Spring 2010
Brownian motion, Langevin and Fokker-Planck equations, path integrals and Feynman diagrams, time series, an introduction to statistical mechanics, Monte Carlo methods, selected applications.

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MATH 221 Advanced Matrix Computations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
Direct solution of linear systems, including large sparse systems: error bounds, iteration methods, least square approximation, eigenvalues and eigenvectors of matrices, nonlinear equations, and minimization of functions.

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MATH 222A Partial Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Laplace's equation, heat equation, wave equation, nonlinear first-order equations, conservation laws, Hamilton-Jacobi equations, Fourier transform, Sobolev spaces.

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MATH 222B Partial Differential Equations 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Second-order elliptic equations, parabolic and hyperbolic equations, calculus of variations methods, additional topics selected by instructor.

Partial Differential Equations: Read More [+]

MATH C223A Advanced Topics in Probability and Stochastic Process 3 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
The topics of this course change each semester, and multiple sections may be offered. Advanced topics in probability offered according to students demand and faculty availability.

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MATH C223B Advanced Topics in Probability and Stochastic Processes 3 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
The topics of this course change each semester, and multiple sections may be offered. Advanced topics in probability offered according to students demand and faculty availability.

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MATH 224A Mathematical Methods for the Physical Sciences 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Introduction to the theory of distributions. Fourier and Laplace transforms. Partial differential equations. Green's function. Operator theory, with applications to eigenfunction expansions, perturbation theory and linear and non-linear waves. Sequence begins fall.

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MATH 224B Mathematical Methods for the Physical Sciences 4 Units

Terms offered: Spring 2015, Spring 2014, Spring 2013
Introduction to the theory of distributions. Fourier and Laplace transforms. Partial differential equations. Green's function. Operator theory, with applications to eigenfunction expansions, perturbation theory and linear and non-linear waves. Sequence begins fall.

Mathematical Methods for the Physical Sciences: Read More [+]

MATH 225A Metamathematics 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Metamathematics of predicate logic. Completeness and compactness theorems. Interpolation theorem, definability, theory of models. Metamathematics of number theory, recursive functions, applications to truth and provability. Undecidable theories. Sequence begins fall.

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MATH 225B Metamathematics 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Metamathematics of predicate logic. Completeness and compactness theorems. Interpolation theorem, definability, theory of models. Metamathematics of number theory, recursive functions, applications to truth and provability. Undecidable theories. Sequence begins fall.

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MATH 227A Theory of Recursive Functions 4 Units

Terms offered: Fall 2015, Fall 2013, Spring 2012
Recursive and recursively enumerable sets of natural numbers; characterizations, significance, and classification. Relativization, degrees of unsolvability. The recursion theorem. Constructive ordinals, the hyperarithmetical and analytical hierarchies. Recursive objects of higher type. Sequence begins fall.

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MATH 228A Numerical Solution of Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Ordinary differential equations: Runge-Kutta and predictor-corrector methods; stability theory, Richardson extrapolation, stiff equations, boundary value problems. Partial differential equations: stability, accuracy and convergence, Von Neumann and CFL conditions, finite difference solutions of hyperbolic and parabolic equations. Finite differences and finite element solution of elliptic equations.

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MATH 228B Numerical Solution of Differential Equations 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Ordinary differential equations: Runge-Kutta and predictor-corrector methods; stability theory, Richardson extrapolation, stiff equations, boundary value problems. Partial differential equations: stability, accuracy and convergence, Von Neumann and CFL conditions, finite difference solutions of hyperbolic and parabolic equations. Finite differences and finite element solution of elliptic equations.

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MATH 229 Theory of Models 4 Units

Terms offered: Spring 2015, Spring 2013, Spring 2012
Syntactical characterization of classes closed under algebraic operations. Ultraproducts and ultralimits, saturated models. Methods for establishing decidability and completeness. Model theory of various languages richer than first-order.

Theory of Models: Read More [+]

MATH 235A Theory of Sets 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2014
Axiomatic foundations. Operations on sets and relations. Images and set functions. Ordering, well-ordering, and well-founded relations; general principles of induction and recursion. Ranks of sets, ordinals and their arithmetic. Set-theoretical equivalence, similarity of relations; definitions by abstraction. Arithmetic of cardinals. Axiom of choice, equivalent forms, and consequences. Sequence begins fall.

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MATH 236 Metamathematics of Set Theory 4 Units

Terms offered: Fall 2014, Fall 2010, Spring 2009
Various set theories: comparison of strength, transitive, and natural models, finite axiomatizability. Independence and consistency of axiom of choice, continuum hypothesis, etc. The measure problem and axioms of strong infinity.

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MATH 239 Discrete Mathematics for the Life Sciences 4 Units

Terms offered: Spring 2011, Fall 2008, Spring 2008
Introduction to algebraic statistics and probability, optimization, phylogenetic combinatorics, graphs and networks, polyhedral and metric geometry.

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MATH C239 Discrete Mathematics for the Life Sciences 4 Units

Terms offered: Spring 2013
Introduction to algebraic statistics and probability, optimization, phylogenetic combinatorics, graphs and networks, polyhedral and metric geometry.

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MATH 240 Riemannian Geometry 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Riemannian metric and Levi-Civita connection, geodesics and completeness, curvature, first and second variations of arc length. Additional topics such as the theorems of Myers, Synge, and Cartan-Hadamard, the second fundamental form, convexity and rigidity of hypersurfaces in Euclidean space, homogeneous manifolds, the Gauss-Bonnet theorem, and characteristic classes.

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MATH 241 Complex Manifolds 4 Units

Terms offered: Fall 2017, Fall 2014, Spring 2013
Riemann surfaces, divisors and line bundles on Riemann surfaces, sheaves and the Dolbeault theorem on Riemann surfaces, the classical Riemann-Roch theorem, theorem of Abel-Jacobi. Complex manifolds, Kahler metrics. Summary of Hodge theory, groups of line bundles, additional topics such as Kodaira's vanishing theorem, Lefschetz hyperplane theorem.

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MATH 242 Symplectic Geometry 4 Units

Terms offered: Fall 2017, Fall 2015, Spring 2014
Basic topics: symplectic linear algebra, symplectic manifolds, Darboux theorem, cotangent bundles, variational problems and Legendre transform, hamiltonian systems, Lagrangian submanifolds, Poisson brackets, symmetry groups and momentum mappings, coadjoint orbits, Kahler manifolds.

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MATH C243 Seq: Methods and Applications 3 Units

Terms offered: Spring 2015, Spring 2014
A graduate seminar class in which a group of students will closely examine recent computational methods in high-throughput sequencing followed by directly examining interesting biological applications thereof.

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MATH 245A General Theory of Algebraic Structures 4 Units

Terms offered: Fall 2015, Spring 2014, Fall 2011
Structures defined by operations and/or relations, and their homomorphisms. Classes of structures determined by identities. Constructions such as free objects, objects presented by generators and relations, ultraproducts, direct limits. Applications of general results to groups, rings, lattices, etc. Course may emphasize study of congruence- and subalgebra-lattices, or category-theory and adjoint functors, or other aspects.

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MATH 249 Algebraic Combinatorics 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2015
(I) Enumeration, generating functions and exponential structures, (II) Posets and lattices, (III) Geometric combinatorics, (IV) Symmetric functions, Young tableaux, and connections with representation theory. Further study of applications of the core material and/or additional topics, chosen by instructor.

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MATH 250A Groups, Rings, and Fields 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Group theory, including the Jordan-Holder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree.

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MATH 250B Multilinear Algebra and Further Topics 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Tensor algebras and exterior algebras, with application to linear transformations. Commutative ideal theory, localization. Elementary specialization and valuation theory. Related topics in algebra.

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MATH 251 Ring Theory 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2013
Topics such as: Noetherian rings, rings with descending chain condition, theory of the radical, homological methods.

Ring Theory: Read More [+]

MATH 252 Representation Theory 4 Units

Terms offered: Fall 2015, Fall 2014, Fall 2013
Structure of finite dimensional algebras, applications to representations of finite groups, the classical linear groups.

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MATH 253 Homological Algebra 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2014
Modules over a ring, homomorphisms and tensor products of modules, functors and derived functors, homological dimension of rings and modules.

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MATH 254A Number Theory 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, P-adic analysis, and transcendental numbers. Sequence begins fall.

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MATH 254B Number Theory 4 Units

Terms offered: Spring 2017, Spring 2015, Spring 2014
Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, P-adic analysis, and transcendental numbers. Sequence begins fall.

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MATH 255 Algebraic Curves 4 Units

Terms offered: Fall 2014, Fall 2011, Spring 2009
Elliptic curves. Algebraic curves, Riemann surfaces, and function fields. Singularities. Riemann-Roch theorem, Hurwitz's theorem, projective embeddings and the canonical curve. Zeta functions of curves over finite fields. Additional topics such as Jacobians or the Riemann hypothesis.

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MATH 256A Algebraic Geometry 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall.

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MATH 256B Algebraic Geometry 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall.

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MATH 257 Group Theory 4 Units

Terms offered: Spring 2014, Fall 2011, Fall 2010
Topics such as: generators and relations, infinite discrete groups, groups of Lie type, permutation groups, character theory, solvable groups, simple groups, transfer and cohomological methods.

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MATH 258 Harmonic Analysis 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2015
Basic properties of Fourier series, convergence and summability, conjugate functions, Hardy spaces, boundary behavior of analytic and harmonic functions. Additional topics at the discretion of the instructor.

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MATH 261A Lie Groups 4 Units

Terms offered: Spring 2017, Fall 2015, Fall 2013
Lie groups and Lie algebras, fundamental theorems of Lie, general structure theory; compact, nilpotent, solvable, semi-simple Lie groups; classification theory and representation theory of semi-simple Lie algebras and Lie groups, further topics such as symmetric spaces, Lie transformation groups, etc., if time permits. In view of its simplicity and its wide range of applications, it is preferable to cover compact Lie groups and their representations
in 261A. Sequence begins Fall.
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MATH 261B Lie Groups 4 Units

Terms offered: Fall 2017, Spring 2016, Spring 2014
Lie groups and Lie algebras, fundamental theorems of Lie, general structure theory; compact, nilpotent, solvable, semi-simple Lie groups; classification theory and representation theory of semi-simple Lie algebras and Lie groups, further topics such as symmetric spaces, Lie transformation groups, etc., if time permits. In view of its simplicity and its wide range of applications, it is preferable to cover compact Lie groups and their representations
in 261A. Sequence begins Fall.
Lie Groups: Read More [+]

MATH 265 Differential Topology 4 Units

Terms offered: Spring 2011, Fall 2008, Fall 2004
Approximations, degrees of maps, vector bundles, tubular neighborhoods. Introduction to Morse theory, handlebodies, cobordism, surgery. Additional topics selected by instructor from: characteristic classes, classification of manifolds, immersions, embeddings, singularities of maps.

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MATH 270 Hot Topics Course in Mathematics 2 Units

Terms offered: Spring 2017, Spring 2016, Fall 2015
This course will give introductions to current research developments. Every semester we will pick a different topic and go through the relevant literature. Each student will be expected to give one presentation.

Hot Topics Course in Mathematics: Read More [+]

MATH 273 Topics in Numerical Analysis 4 Units

Terms offered: Spring 2016, Spring 2014
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Numerical Analysis: Read More [+]

MATH 274 Topics in Algebra 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Algebra: Read More [+]

MATH 275 Topics in Applied Mathematics 4 Units

Terms offered: Spring 2017, Spring 2014, Fall 2013
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Applied Mathematics: Read More [+]

MATH 276 Topics in Topology 4 Units

Terms offered: Fall 2017, Spring 2016, Spring 2015
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Topology: Read More [+]

MATH 277 Topics in Differential Geometry 4 Units

Terms offered: Spring 2017, Spring 2016, Fall 2015
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Differential Geometry: Read More [+]

MATH 278 Topics in Analysis 4 Units

Terms offered: Fall 2015, Spring 2015, Fall 2014
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Analysis: Read More [+]

MATH 279 Topics in Partial Differential Equations 4 Units

Terms offered: Spring 2017, Spring 2016, Fall 2014
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Topics in Partial Differential Equations: Read More [+]

MATH 290 Seminars 1 - 6 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Topics in foundations of mathematics, theory of numbers, numerical calculations, analysis, geometry, topology, algebra, and their applications, by means of lectures and informal conferences; work based largely on original memoirs.

Seminars: Read More [+]

MATH 295 Individual Research 1 - 12 Units

Terms offered: Fall 2017, Summer 2017 3 Week Session, Summer 2017 8 Week Session
Intended for candidates for the Ph.D. degree.

Individual Research: Read More [+]

MATH 299 Reading Course for Graduate Students 1 - 6 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Investigation of special problems under the direction of members of the department.

Reading Course for Graduate Students: Read More [+]

MATH 301 Undergraduate Mathematics Instruction 1 - 2 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
May be taken for one unit by special permission of instructor. Tutoring at the Student Learning Center or for the Professional Development Program.

Undergraduate Mathematics Instruction: Read More [+]

MATH 302 Teaching Workshop 1 Unit

Terms offered: Summer 2002 10 Week Session, Summer 2001 10 Week Session
Mandatory for all graduate student instructors teaching summer course for the first time in the Department. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis, classroom visitations by senior faculty member.

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MATH 303 Professional Preparation: Supervised Teaching of Mathematics 2 - 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Meeting with supervising faculty and with discussion sections. Experience in teaching under the supervision of Mathematics faculty.

Professional Preparation: Supervised Teaching of Mathematics: Read More [+]

MATH 375 Teaching Workshop 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Mandatory for all graduate student instructors teaching for the first time in the Mathematics Department. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis of videotapes, reciprocal classroom visitations, and an individual project.

Teaching Workshop: Read More [+]

MATH 600 Individual Study for Master's Students 1 - 6 Units

Terms offered: Fall 2017, Summer 2017 8 Week Session, Spring 2017
Individual study for the comprehensive or language requirements in consultation with the field adviser.

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MATH 602 Individual Study for Doctoral Students 1 - 8 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Individual study in consultation with the major field adviser intended to provide an opportunity for qualified students to prepare themselves for the various examinations required for candidates for the Ph.D. Course does not satisfy unit or residence requirements for doctoral degree.

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Faculty and Instructors

+ Indicates this faculty member is the recipient of the Distinguished Teaching Award.

Faculty

Mina Aganagic, Professor. Particle physics.
Research Profile

Ian Agol, Professor. Low-dimensional topology.

David Aldous, Professor. Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, complex networks, random networks, entropy, spatial networks.
Research Profile

Denis Auroux, Professor. Mirror symmetry, symplectic topology.
Research Profile

Richard H. Bamler, Assistant Professor.

Richard E. Borcherds, Professor. Mathematics, lie algebras, vertex algebras, automorphic forms.
Research Profile

+ F. Michael Christ, Professor. Mathematics, harmonic analysis, partial differential equations, complex analysis in several variables, spectral analysis of Schrodinger operators.
Research Profile

James W. Demmel, Professor. Computer science, scientific computing, numerical analysis, linear algebra.
Research Profile

David Eisenbud, Professor. Mathematics, algebraic geometry, commutative algebra, computation.
Research Profile

Lawrence C. Evans, Professor. Optimization theory, nonlinear partial differential equations, calculus of variations.
Research Profile

Steven N. Evans, Professor. Genetics, random matrices, superprocesses & other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics & historical linguistics.
Research Profile

Edward Frenkel, Professor. Mathematics, representation theory, integrable systems, mathematical physics.
Research Profile

Alexander B. Givental, Professor. Mathematics, mathematical physics, symplectic geometry, singularities, mirror symmetry.
Research Profile

Ming Gu, Professor. Mathematics, scientific computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations.
Research Profile

Mark D. Haiman, Professor. Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes.
Research Profile

+ Ole H. Hald, Professor. Mathematics, numerical analysis.
Research Profile

Alan Hammond, Associate Professor. Statistical mechanics.

Jenny Harrison, Professor. Mathematics, geometric analysis.
Research Profile

Olga V. Holtz, Professor. Numerical analysis, matrix and operator theory, approximation theory, wavelets and splines, orthogonal polynomials and special functions, analysis of algorithms and computational complexity.
Research Profile

Michael Hutchings, Professor. Mathematics, low dimensional, symplectic topology, geometry.
Research Profile

Michael J. Klass, Professor. Statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums.
Research Profile

Lin Lin, Assistant Professor. Numerical analysis, computational quantum chemistry, computational materials science.

John W. Lott, Professor. Differential geometry.

Antonio Montalban, Associate Professor. Mathematical logic.
Research Profile

David Nadler, Professor. Geometric representation.

Arthur E. Ogus, Professor. Mathematics, algebraic geometry, algebraic differential equations, log poles.
Research Profile

Martin Olsson, Professor. Algebraic geometry, arithmetic geometry.
Research Profile

Lior Pachter, Professor. Mathematics, applications of statistics, combinatorics to problems in biology.
Research Profile

Per-Olof Persson, Associate Professor. Applied mathematics, numerical methods, computational fluid and solid mechanics.
Research Profile

James W. Pitman, Professor. Fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence.
Research Profile

Nicolai Reshetikhin, Professor. Mathematics, representation theory, mathematical physics, low-dimensional topology.
Research Profile

Fraydoun Rezakhanlou, Professor. Mathematics, probability theory, partial differential equations.
Research Profile

Kenneth A. Ribet, Professor. Mathematics, algebraic geometry, algebraic number theory.
Research Profile

Marc Rieffel, Professor. Mathematics, operator algebras, non-commutative geometry, non-commutative harmonic analysis, quantum geometry.
Research Profile

Thomas Scanlon, Professor. Mathematics, model theory, applications to number theory.
Research Profile

Vera Serganova, Professor. Mathematics, Super-representation theory.
Research Profile

James A. Sethian, Professor. Mathematics, applied mathematics, partial differential equations, computational physics, level set Methods, computational fluid mechanics and materials sciences. fast marching methods.
Research Profile

Chris Shannon, Professor. Economics, mathematical economics, economic theory.
Research Profile

Vivek V. Shende, Assistant Professor. Geometry.

Sug Woo Shin, Associate Professor. Number theory, automorphic forms.

Theodore A. Slaman, Professor. Mathematics, recursion theory.
Research Profile

Nikhil Srivastava, Assistant Professor. Theoretical computer science, random matrices, geometry of polynomials.

John Steel, Professor. Mathematics, descriptive set theory, set theory, fine structure.
Research Profile

John Strain, Professor. Mathematics, numerical analysis, applied mathematics, fast algorithms, materials science.
Research Profile

Bernd Sturmfels, Professor. Mathematics, combinatorics, computational algebraic geometry.
Research Profile

Daniel Ioan Tataru, Professor. Mathematics, partial differential equations, nonlinear waves.
Research Profile

Peter Teichner, Professor. Topology, quantum field theory.
Research Profile

Constantin Teleman, Professor. Lie algebras, algebraic geometry, Lie groups, topology, topological quantum field theory.
Research Profile

Luca Trevisan, Professor. Computational complexity, spectral graph theory.

Dan Voiculescu, Professor. Random matrices, pperator algebras, free probability theory.
Research Profile

Paul A. Vojta, Professor. Mathematics, algebraic geometry, diophantine geometry, Nevanlinna theory, Arakelov theory.
Research Profile

Katrin Wehrheim, Associate Professor. Low-dimensional and symplectic topology.

Jon Wilkening, Associate Professor. Applied mathematics, numerical analysis, computational solid and fluid mechanics.
Research Profile

Lauren K. Williams, Associate Professor. Algebraic combinatorics.
Research Profile

Mariusz Wodzicki, Professor. Analysis, mathematics, Non-commutative and algebraic geometry, K-theory.
Research Profile

Xinyi Yuan, Assistant Professor. Number theory.
Research Profile

Maciej Zworski, Professor. Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.
Research Profile

Lecturers

Alexander Coward, Lecturer.

Alexander Paulin, Lecturer.

Kelli Talaska, Lecturer.

Visiting Faculty

Alexis Brice Emmanuel Bouthier, Visiting Assistant Professor.

Jeff Calder, Visiting Assistant Professor.

Ivan Guillermo Contreras Palacios, Visiting Assistant Professor.

Tim Cramer, Visiting Assistant Professor.

Ved Datar, Visiting Assistant Professor.

David Dynerman, Visiting Assistant Professor.

Kenji Kozai, Visiting Assistant Professor.

Andrew Lawrie, Visiting Assistant Professor.

David Li-Bland, Visiting Assistant Professor.

Gang Liu, Visiting Assistant Professor.

Kathryn Mann, Visiting Assistant Professor.

Khoa L. Nguyen, Visiting Assistant Professor.

Sung-Jin Oh, Visiting Assistant Professor.

Mohammad Reza Pakzad, Visiting Professor.

Pierre Raphael, Visiting Professor.

Silvain Rideau, Visiting Assistant Professor.

Zvezdelina Stankova, Visiting Professor.

Hongbin Sun, Visiting Assistant Professor.

Adam Topaz, Visiting Assistant Professor.

Yan Zhang, Visiting Assistant Professor.

Emeritus Faculty

John W. Addison, Professor Emeritus. Mathematics, theory of definability, descriptive set theory, model theory, recursive function theory.
Research Profile

Robert Anderson, Professor Emeritus. Finance, probability theory, mathematical economics, nonstandard analysis.
Research Profile

George Bergman, Professor Emeritus. Mathematics, associative rings, universal algebra, category theory, counterexamples.
Research Profile

Elwyn R. Berlekamp, Professor Emeritus. Computer science, electrical engineering, mathematics, combinatorial game theory, algebraic coding theory.
Research Profile

Robert Bryant, Professor Emeritus. Symplectic geometry, differential geometry, Lie groups, geometric partial differential equations.
Research Profile

Paul R. Chernoff, Professor Emeritus.

Alexandre J. Chorin, Professor Emeritus. Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods.
Research Profile

Paul Concus, Professor Emeritus. Fluid mechanics, numerical analysis, applied mathematics, capillarity.
Research Profile

Heinz O. Cordes, Professor Emeritus. Mathematics, classical analysis.
Research Profile

Stephen P. L. Diliberto, Professor Emeritus. Mathematics, ordinary differential equations, celestial mechanics.
Research Profile

Jacob Feldman, Professor Emeritus. Mathematics, stochastic processes, ergodic theory.
Research Profile

F. Alberto Grunbaum, Professor Emeritus. Medical imaging, x-ray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birth-and-death processes.
Research Profile

Leo A. Harrington, Professor Emeritus. Mathematics, model theory, recursion theory, set theory.
Research Profile

Robert C. Hartshorne, Professor Emeritus. Mathematics, algebraic geometry.
Research Profile

Morris W. Hirsch, Professor Emeritus. Game theory, dynamical systems, topology, biological models.
Research Profile

Wu-Yi Hsiang, Professor Emeritus. Mathematics, transformation groups, differential geometry.
Research Profile

Vaughan F. R. Jones, Professor Emeritus. Mathematics, Von Neumann algebras.
Research Profile

Robion C. Kirby, Professor Emeritus. Mathematics, topology of manifolds.
Research Profile

Tsit-Yuen Lam, Professor Emeritus.

R. Sherman Lehman, Professor Emeritus.

H. W. Lenstra, Professor Emeritus.

Ralph N. McKenzie, Professor Emeritus. Mathematics, logic, universal algebra, general algebra, lattice theory.
Research Profile

Keith Miller, Professor Emeritus. Mathematics, partial differential equations, numerical methods for PDE's.
Research Profile

Calvin C. Moore, Professor Emeritus. Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K- theory.
Research Profile

John Neu, Professor Emeritus.

Andrew Ogg, Professor Emeritus.

Charles C. Pugh, Professor Emeritus. Mathematics, global theory of differential equations.
Research Profile

Marina Ratner, Professor Emeritus.

John L. Rhodes, Professor Emeritus. Mathematics, algebra, semigroups, automata.
Research Profile

Donald E. Sarason, Professor Emeritus. Mathematics, complex function theory, operator theory.
Research Profile

Jack H. Silver, Professor Emeritus.

Isadore M. Singer, Professor Emeritus. Mathematics, physics, partial differential equations, geometry.
Research Profile

Stephen Smale, Professor Emeritus. Algorithms, mathematics, numerical analysis, global analysis.
Research Profile

Robert M. Solovay, Professor Emeritus.

John B. Wagoner, Professor Emeritus. Mathematics, dynamical systems, differential topology, algebraic K-theory.
Research Profile

Alan Weinstein, Professor Emeritus. Mathematics, mathematical physics, symplectic geometry.
Research Profile

Joseph A. Wolf, Professor Emeritus. Harmonic analysis, differential geometry, Lie groups.
Research Profile

W. Hugh Woodin, Professor Emeritus. Mathematics, set theory, large cardinals.
Research Profile

Hung-Hsi Wu, Professor Emeritus. Real and complex geometry, school mathematics education.
Research Profile

Contact Information

Department of Mathematics

970 Evans Hall

Phone: 510-642-6650

Fax: 510-642-8204

Visit Department Website

Department Chair

Lawrence Craig Evans, PhD

949 Evans Hall

Phone: 510-642-8065

evans@math.berkeley.edu

Vice-Chair for Undergraduate Affairs

Fraydoun Rezahkanlou, PhD

803 Evans Hall

Phone: 510-642-2838

rezakhan@berkeley.edu

Vice-Chair for Graduate Affairs

Jon Wilkening

914 Evans Hall

Phone: 510-643-7670

wilken@math.berkeley.edu

Director of Student Services

Jennifer Pinney

967 Evans Hall

Phone: 510-642-2479

jensixt@berkeley.edu

Undergraduate Student Affairs Officer

Thomas Brown

965 Evans Hall

Phone: 510-643-9292

brown@math.berkeley.edu

Graduate Adviser

Barbara Waller

910 Evans Hall

Phone: 510-642-0665

barb@math.berkeley.edu

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