Fall 2023

Prerequisites 1A or N1A

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Three and one-half years of high school math, including trigonometry and analytic geometry. Students who have not had calculus in high school are strongly advised to take the Student Learning Center's Math 98 adjunct course for Math 10A; contact the SLC for more information

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Three years of high school math, including trigonometry. Consult the mathematics department for details

Description 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.)

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Mathematics 1B or N1B

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 1B, N1B, 10B, or N10B

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Mathematical maturity appropriate to a sophomore math class. 1A-1B recommended

Description Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 

Description Directed Group Study, topics vary with instructor.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Math 53 and 54

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 54 or a course with equivalent linear algebra content. 55 or an equivalent exposure to proofs is recommended

Description Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 54 or a course with equivalent linear algebra content. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 54 or a course with equivalent linear algebra content. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 54 or a course with equivalent linear algebra content. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 54 or a course with equivalent linear algebra content. 55 or an equivalent exposure to proofs

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites Math 104 and 113 or consent of instructor

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54

Description Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 104 and 113

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 1A-1B, 53, or equivalent

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 53 and 54

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 104

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 104

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 104

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 104

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 185 and 202A-202B or their equivalents; some background in geometry helpful but not strictly necessary

Description The course will cover the following topics:

1. Review of the theory of functions of one complex variables;
2. Holomorphy, power series in several complex variables, Hartogs property;
3. Domains of holomorphy, plurisubharmonic functions, pseudoconvex domains;
4. Entire functions, weighted L2 spaces, Bergman projectors for L2 spaces with quadratic plurisubharmonic weights;
5. Applications: Berezin-Toeplitz quantization, Catlin-D'Angelo-Quillen Theorem, analytic proof of the Nullstallensatz;
6. Solving the ∂ equation in L2 spaces with global plurisubharmonic weights;
7. Fefferman/Boutet de Monvel-Sjöstrand asymptotics for Bergman projectors for "nonlinear" weights;
8. Quick introduction to complex manifolds, complex line bundles and powers of line bundles;
9. Applications of Bergman kernel asymptotics: Kodaira's embedding theorem and the Catlin-Tian-Yau-Zelditch asymptotics.

Office Evans 801

Office Hours TBA

Required Text TBA

Recommended Reading 

Grading Letter grade.

Homework biweekly

Course Webpage https://math.berkeley.edu/~zworski/math212_2023.html

Prerequisites 

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites Consent of instructor

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 125A and (135 or 136)

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 214

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 250A

Description Topics such as: Noetherian rings, rings with descending chain condition, theory of the radical, homological methods.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 250A-250B for 256A; 256A for 256B

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 214

Description 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.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage 

Prerequisites Consent of instructor

Description Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Office 

Office Hours 

Required Text 

Recommended Reading 

Grading Letter grade.

Homework 

Course Webpage