Mathematics (MATH) | Berkeley Academic Guide (2024)

Courses

Terms offered: Fall 2024, Summer 2024 3 Week Session, Fall 2023
This course aims to bring students with varying Math backgrounds up-to-speed with the expectations of UC Berkeley’s lower division mathematics courses. This course will support comprehension of the fundamental concepts necessary to excel in Math 16A/16B, 1A/1B, 10A/10B, and beyond. You can take this prep course concurrently with or prior to your Calculus classes. The course curriculum covers algebraic operations, laws of exponents and logarithms, inequalities and absolute values, single-variable function properties, polynomials, power and exponential functions, logarithmic functions, trigonometric functions, coordinate geometry in two and three dimensions, complex numbers, and functions of several variables.
Foundations of Lower Division Mathematics: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.
Calculus: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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.
Calculus: Read More [+]

Terms offered: Fall 2015, Fall 2014, Fall 2013
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.
Honors Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
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.
Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
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.
Calculus: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
The sequence Math 10A, Math 10B is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable, ordinary differential equations, and matrix algebra and systems of linear equations.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
The sequence Math 10A, Math 10B is intended for majors in the life sciences. Elementary combinatorics and discrete and continuous probability theory. Representation of data, statistical models and testing. Sequences and applications of linear algebra.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
The sequence Math 10A, Math 10B is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable, ordinary differential equations, and matrix algebra and systems of linear equations.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

Terms offered: Summer 2021 8 Week Session, Summer 2020 8 Week Session, Summer 2019 8 Week Session
The sequence Math 10A, Math 10B is intended for majors in the life sciences. Elementary combinatorics and discrete and continuous probability theory. Representation of data, statistical models and testing. Sequences and applications of linear algebra.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions. This course is intended for business and social science majors. (See also the Math 1 sequence.)
Analytic Geometry and Calculus: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.
Analytic Geometry and Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
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.
Analytic Geometry and Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.
Analytic Geometry and Calculus: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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.
Freshman Seminars: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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.
Precalculus: Read More [+]

Terms offered: Summer 2022 8 Week Session, Summer 2021 8 Week Session, Summer 2020 8 Week Session
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.
Precalculus: Read More [+]

Terms offered: Spring 2019, Spring 2018, Spring 2010
Freshman and sophom*ore 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.
Freshman/Sophom*ore Seminar: Read More [+]

Terms offered: Spring 2017, Spring 2016, Fall 2015
Students with partial credit in lower division mathematics courses may, with consent of instructor, complete the credit under this heading.
Supplementary Work in Lower Division Mathematics: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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.
Multivariable Calculus: Read More [+]

Terms offered: Spring 2023, Spring 2022, Spring 2021
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.
Honors Multivariable Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 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.
Multivariable Calculus: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 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.
Multivariable Calculus: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; orthogonality, symmetric matrices. Linear second-order differential equations; first-order systems with constant coefficients. Fourier series.
Linear Algebra and Differential Equations: Read More [+]

Terms offered: Fall 2022, Fall 2021, Fall 2020
Honors version of 54. Basic linear algebra: matrix arithmetic and determinants. Vectors spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. hom*ogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.
Honors Linear Algebra and Differential Equations: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; orthogonality, symmetric matrices. Linear second-order differential equations; first-order systems with constant coefficients. Fourier series.
Linear Algebra and Differential Equations: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; orthogonality, symmetric matrices. Linear second-order differential equations; first-order systems with constant coefficients. Fourier series.
Linear Algebra and Differential Equations: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.
Discrete Mathematics: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session
Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.
Discrete Mathematics: Read More [+]

Terms offered: Fall 2024, Fall 2023
This is a first course in Linear Algebra. Core topics include: algebra and geometry of vectors and matrices; systems of linear equations and Gaussian elimination; eigenvalues and eigenvectors; Gram-Schmidt and least squares; symmetric matrices and quadratic forms; singular value decomposition and other factorizations. Time permitting, additional topics may include: Markov chains and Perron-Frobenius, dimensionality reduction, or linear programming. This course differs from Math 54 in that it does not cover Differential Equations, but focuses on Linear Algebra motivated by first applications in Data Science and Statistics.
Linear Algebra: Read More [+]

Terms offered: Spring 2024, Fall 2022, Fall 2021
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.
Transition to Upper Division Mathematics: Read More [+]

Terms offered: Fall 2022, Spring 2016, Fall 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.
Special Topics in Mathematics: Read More [+]

Terms offered: Summer 2019 Second 6 Week Session, Summer 2017 8 Week Session, Summer 2015 10 Week Session
Elements of college algebra. Designed for students who do not meet the prerequisites for 32. Offered through the Student Learning Center.
College Algebra: Read More [+]

Terms offered: Fall 2023, Fall 2022, Fall 2021
Directed Group Study, topics vary with instructor.
Supervised Group Study: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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 [+]

Terms offered: Spring 2017, Spring 2016, Fall 2015
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.
Supervised Independent Study: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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.
Introduction to Mathematical Economics: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
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.
Introduction to Analysis: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
Honors section corresponding to 104. Recommended for students who enjoy mathematics and are good at it. Greater emphasis on theory and challenging problems.
Honors Introduction to Analysis: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Second Course in Analysis: Read More [+]

Terms offered: Spring 2023
A rigorous development of the basics of modern probability theory based on a self-contained treatment of measure theory. The topics covered include: probability spaces; random variables; expectation; convergence of random variables and expectations; laws of large numbers; zero-one laws; convergence in distribution and the central limit theorem; Markov chains; random walks; the Poisson process; and discrete-parameter martingales.

Mathematical Probability Theory: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.
Abstract Linear Algebra: Read More [+]

Terms offered: Fall 2022, Fall 2021, Fall 2020
Honors section corresponding to course 110 for exceptional students with strong mathematical inclination and motivation. Emphasis is on rigor, depth, and hard problems.
Honors Linear Algebra: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
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.
Introduction to Abstract Algebra: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2022
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.
Honors Introduction to Abstract Algebra: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Second Course in Abstract Algebra: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Fall 2023
Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.
Introduction to Number Theory: Read More [+]

Terms offered: Fall 2022, Fall 2021, Fall 2020
Construction and analysis of simple cryptosystems, public key cryptography, RSA, signature schemes, key distribution, hash functions, elliptic curves, and applications.
Cryptography: Read More [+]

Terms offered: Fall 2022, Spring 2022, Spring 2020
Introduction to signal processing including Fourier analysis and wavelets. Theory, algorithms, and applications to one-dimensional signals and multidimensional images.
Fourier Analysis, Wavelets, and Signal Processing: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Mathematical Tools for the Physical Sciences: Read More [+]

Terms offered: Spring 2024, Spring 2022, Spring 2021
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.
Mathematical Tools for the Physical Sciences: Read More [+]

Terms offered: Fall 2023, Fall 2022, Fall 2021
Existence and uniqueness of solutions, linear systems, regular singular points. Other topics selected from analytic systems, autonomous systems, Sturm-Liouville Theory.
Ordinary Differential Equations: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
An introduction to computer programming with a focus on the solution of mathematical and scientific problems. Basic programming concepts such as variables, statements, loops, branches, functions, data types, and object orientation. Mathematical/scientific tools such as arrays, floating point numbers, plotting, symbolic algebra, and various packages. Examples from a wide range of mathematical applications such as evaluation of complex algebraic expressions, number theory, combinatorics, statistical analysis, efficient algorithms, computational geometry, Fourier analysis, and optimization. Mainly based on the Julia programming language, but some examples will demonstrate other languages such as MATLAB, Python, C, and Mathematica.
Programming for Mathematical Applications: Read More [+]

Terms offered: Fall 2023, Fall 2022, Fall 2021
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.
Mathematical Logic: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
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.
Introduction to Partial Differential Equations: Read More [+]

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.
Mathematical and Computational Methods in Molecular Biology: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.
Numerical Analysis: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
Iterative solution of systems of nonlinear equations, evaluation of eigenvalues and eigenvectors of matrices, applications to simple partial differential equations. Practice on the computer.
Numerical Analysis: Read More [+]

Terms offered: Summer 2024 8 Week Session, Summer 2023 8 Week Session, Summer 2022 8 Week Session

Numerical Analysis: Read More [+]

Terms offered: Spring 2024, Spring 2022, Fall 2020
Isometries of Euclidean space. The Platonic solids and their symmetries. Crystallographic groups. Projective geometry. Hyperbolic geometry.
Groups and Geometries: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2022
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.
Introduction to the Theory of Sets: Read More [+]

Terms offered: Fall 2024, Fall 2023, Spring 2022
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.
Incompleteness and Undecidability: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2022
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.
Metric Differential Geometry: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2022
Manifolds in n-dimensional Euclidean space and smooth maps, Sard's Theorem, classification of compact one-manifolds, transversality and intersection modulo 2.
Elementary Differential Topology: Read More [+]

Terms offered: Fall 2023, Fall 2022, Fall 2021
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.
Elementary Algebraic Topology: Read More [+]

Terms offered: Fall 2023, Spring 2023, Spring 2022
Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.
Elementary Algebraic Geometry: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Mathematics of the Secondary School Curriculum I: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry.
Mathematics of the Secondary School Curriculum II: Read More [+]

Terms offered: Fall 2023
Introduction to applied linear algebra, numerical analysis and optimization with applications in data science and statistics.
Topics covered include:
• Floating-point arithmetic, condition number, perturbation theory, backward stability analysis
• Matrix decompositions (LU/QR/Cholesky/SVD), least squares problems, orthogonal matrices
• Eigenvalues, eigenvectors, Rayleigh quotients, generalized eigenvalues
• Principal components, low rank approximation, compressed sensing, matrix completion
• Convexity, Newton’s method, Levenberg-Marquardt method, quasi-Newton methods
• Randomized linear algebra, stochastic gradient descent
• Machine learning, neural networks (deep/convolution), adjoint methods, backpropagation
Numerical Analysis for Data Science and Statistics: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
History of algebra, geometry, analytic geometry, and calculus from ancient times through the seventeenth century and selected topics from more recent mathematical history.
History of Mathematics: Read More [+]

Terms offered: Fall 2024, Fall 2023, Spring 2023
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.
Mathematical Methods for Optimization: Read More [+]

Terms offered: Fall 2023, Fall 2022, Spring 2021
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.
Combinatorics: Read More [+]

Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024
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.
Introduction to Complex Analysis: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2021
Honors section corresponding to Math 185 for exceptional students with strong mathematical inclination and motivation. Emphasis is on rigor, depth, and hard problems.
Honors Introduction to Complex Analysis: Read More [+]

Terms offered: Fall 2020, Fall 2015, Fall 2014
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.
Mathematical Methods in Classical and Quantum Mechanics: Read More [+]

Terms offered: Fall 2024, Fall 2023, Spring 2023
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.
Experimental Courses in Mathematics: Read More [+]

Terms offered: Spring 2021, Spring 2011, Spring 2004
Lectures on special topics, which will be announced at the beginning of each semester that the course is offered.
Special Topics in Mathematics: Read More [+]

Terms offered: Fall 2023, Fall 2022, Spring 2017
Independent study of an advanced topic leading to an honors thesis.
Honors Thesis: Read More [+]

Terms offered: Spring 2016, Spring 2015, Spring 2014
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.
Field Study: Read More [+]

Terms offered: Fall 2021, Fall 2019, Spring 2017
Topics will vary with instructor.
Directed Group Study: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2023
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 [+]

Terms offered: Fall 2019, Fall 2018, Fall 2017

Supervised Independent Study and Research: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Introduction to Topology and Analysis: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Introduction to Topology and Analysis: Read More [+]

Terms offered: Fall 2022, 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.
Ordinary Differential Equations: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Theory of Functions of a Complex Variable: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
Spectrum of an operator. Analytic functional calculus. Compact operators. Hilbert-Schmidt operators. Spectral theorem for bounded self-adjoint and normal operators. Unbounded self-adjoint operators. Banach algebras. Commutative Gelfand-Naimark theorem. Selected additional topics such as Fredholm operators and Fredholm index, Calkin algebra, Toeplitz operators, semigroups of operators, interpolation spaces, group algebras.
Functional Analysis: Read More [+]

Terms offered: Spring 2023, Spring 2022, Spring 2021
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.
C*-algebras: Read More [+]

Terms offered: Spring 2024, Spring 2017, Spring 2014
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.
Von Neumann Algebras: Read More [+]

Terms offered: Fall 2023, Fall 2021, Fall 2019
Power series developments, domains of holomorphy, Hartogs' phenomenon, pseudo convexity and plurisubharmonicity. The remainder of the course may treat either sheaf cohom*ology and Stein manifolds, or the theory of analytic subvarieties and spaces.
Several Complex Variables: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2022
This is an introduction to abstract differential topology based on rigorous mathematical proofs. The topics include Smooth manifolds and maps, tangent and normal bundles. Sard's theorem and transversality, Whitney embedding theorem. differential forms, Stokes' theorem, Frobenius theorem. Basic degree theory. Flows, Lie derivative, Lie groups and algebras. Additional topics selected by instructor.
Differential Topology: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
Fundamental group and covering spaces, simplicial and singular hom*ology theory with applications, cohom*ology theory, duality theorem. hom*otopy theory, fibrations, relations between hom*otopy and hom*ology, obstruction theory, and topics from spectral sequences, cohom*ology operations, and characteristic classes. Sequence begins fall.
Algebraic Topology: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
Fundamental group and covering spaces, simplicial and singular hom*ology theory with applications, cohom*ology theory, duality theorem. hom*otopy theory, fibrations, relations between hom*otopy and hom*ology, obstruction theory, and topics from spectral sequences, cohom*ology operations, and characteristic classes. Sequence begins fall.
Algebraic Topology: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Probability Theory: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Probability Theory: Read More [+]

Terms offered: Fall 2024, Fall 2023, Spring 2022
Diffeomorphisms and flows on manifolds. Ergodic theory. Stable manifolds, generic properties, structural stability. Additional topics selected by the instructor.
Dynamical Systems: Read More [+]

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.
Introduction to Probabilistic Methods in Mathematics and the Sciences: Read More [+]

Terms offered: Fall 2024, Fall 2023, Spring 2022
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.
Advanced Matrix Computations: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Partial Differential Equations: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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 [+]

Terms offered: Fall 2024, Fall 2020, Fall 2016, Fall 2014
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.
Advanced Topics in Probability and Stochastic Process: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Advanced Topics in Probability and Stochastic Processes: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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 [+]

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 [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Metamathematics: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Metamathematics: Read More [+]

Terms offered: Spring 2021, Fall 2015, Fall 2013
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.
Theory of Recursive Functions: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Numerical Solution of Differential Equations: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Numerical Solution of Differential Equations: Read More [+]

Terms offered: Spring 2019, Spring 2015, Spring 2013
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 [+]

Terms offered: Fall 2024, Spring 2024, Fall 2018
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.
Theory of Sets: Read More [+]

Terms offered: Fall 2021, Fall 2014, Fall 2010
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.
Metamathematics of Set Theory: Read More [+]

Terms offered: Spring 2011, Fall 2008, Spring 2008
Introduction to algebraic statistics and probability, optimization, phylogenetic combinatorics, graphs and networks, polyhedral and metric geometry.
Discrete Mathematics for the Life Sciences: Read More [+]

Terms offered: Spring 2013
Introduction to algebraic statistics and probability, optimization, phylogenetic combinatorics, graphs and networks, polyhedral and metric geometry.
Discrete Mathematics for the Life Sciences: Read More [+]

Terms offered: Fall 2022, Fall 2021, Fall 2019
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, hom*ogeneous manifolds, the Gauss-Bonnet theorem, and characteristic classes.
Riemannian Geometry: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2021
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.
Complex Manifolds: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2021
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.
Symplectic Geometry: Read More [+]

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.
Seq: Methods and Applications: Read More [+]

Terms offered: Fall 2017, Fall 2015, Spring 2014
Structures defined by operations and/or relations, and their hom*omorphisms. 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.
General Theory of Algebraic Structures: Read More [+]

Terms offered: Fall 2024, Spring 2024, Spring 2023
(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.
Algebraic Combinatorics: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Groups, Rings, and Fields: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
Development of the main tools of commutative and hom*ological algebra applicable to algebraic geometry, number theory and combinatorics.

Commutative Algebra: Read More [+]

Terms offered: Fall 2021, Fall 2016, Spring 2013
Topics such as: Noetherian rings, rings with descending chain condition, theory of the radical, hom*ological methods.
Ring Theory: Read More [+]

Terms offered: Fall 2021, Fall 2020, Fall 2015
Structure of finite dimensional algebras, applications to representations of finite groups, the classical linear groups.
Representation Theory: Read More [+]

Terms offered: Spring 2023, Fall 2016, Fall 2014
Modules over a ring, hom*omorphisms and tensor products of modules, functors and derived functors, hom*ological dimension of rings and modules.
hom*ological Algebra: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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.
Number Theory: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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.
Number Theory: Read More [+]

Terms offered: Fall 2022, Spring 2019, Fall 2014
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.
Algebraic Curves: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohom*ology. Riemann-Roch theorem and selected applications. Sequence begins fall.
Algebraic Geometry: Read More [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohom*ology. Riemann-Roch theorem and selected applications. Sequence begins fall.
Algebraic Geometry: Read More [+]

Terms offered: Spring 2021, Spring 2018, Spring 2014
Topics such as: generators and relations, infinite discrete groups, groups of Lie type, permutation groups, character theory, solvable groups, simple groups, transfer and cohom*ological methods.
Group Theory: Read More [+]

Terms offered: Fall 2023, Fall 2021, Fall 2020
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.
Harmonic Analysis: Read More [+]

Terms offered: Fall 2024, Fall 2023, Fall 2022
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 [+]

Terms offered: Spring 2024, Spring 2023, Spring 2022
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 [+]

Terms offered: Spring 2024, Fall 2023, Spring 2023
This course will give introductions to research-related topics in mathematics. The topics will vary from semester to semester.
Advanced Topics Course in Mathematics: Read More [+]

Terms offered: Fall 2023, Spring 2019
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Interdisciplinary Topics in Mathematics: Read More [+]

Terms offered: Spring 2022, 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 [+]

Terms offered: Fall 2024, Fall 2023, Spring 2023
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Topics in Algebra: Read More [+]

Terms offered: Spring 2024, Spring 2023, Fall 2021
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Topics in Applied Mathematics: Read More [+]

Terms offered: Spring 2021, Fall 2017, Spring 2016
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Topics in Topology: Read More [+]

Terms offered: Spring 2023, Fall 2022, Fall 2021
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Topics in Differential Geometry: Read More [+]

Terms offered: Fall 2024, Spring 2024, Fall 2021
Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.
Topics in Analysis: Read More [+]

Terms offered: Fall 2023, Spring 2023, Fall 2022
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 [+]

Terms offered: Spring 2017, Spring 2015, Fall 2014
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 [+]

Terms offered: Summer 2016 10 Week Session, Spring 2016, Fall 2015
Intended for candidates for the Ph.D. degree.
Individual Research: Read More [+]

Terms offered: Summer 2022 8 Week Session, Summer 2021 8 Week Session, Summer 2006 10 Week Session
Intended for candidates for the Ph.D. degree.
Individual Research: Read More [+]

Terms offered: Prior to 2007
This is an independent study course designed to provide structure for graduate students engaging in summer internship opportunities. Requires a paper exploring how the theoretical constructs learned in academic courses were applied during the internship.
General Academic Internship: Read More [+]

Terms offered: Fall 2018, Fall 2017, Fall 2016
Investigation of special problems under the direction of members of the department.
Reading Course for Graduate Students: Read More [+]

Terms offered: Fall 2018, Spring 2018, Fall 2017
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 [+]

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.
Teaching Workshop: Read More [+]

Terms offered: Spring 2017, Spring 2016, Fall 2015
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 [+]

Terms offered: Summer 2006 10 Week Session, Fall 2005, Spring 2005
Individual study for the comprehensive or language requirements in consultation with the field adviser.
Individual Study for Master's Students: Read More [+]

Terms offered: Fall 2019, Fall 2018, 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.
Individual Study for Doctoral Students: Read More [+]

Mathematics (MATH) | Berkeley Academic Guide (2024)
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