Fall 2021

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.

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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.

Note that there are several programs that use Math 98 courses.  For the SLC adjunct course, you enroll by attending during the first week of classes.  There is no pre-enrollment, so it is not possible for this course to be full before the semester even starts.  You can find the schedule and more information at the link below.

https://slc.berkeley.edu/programs/mathematics-and-statistics/courses-supported/math-10a

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.

Required Text: Biocalculus: Calculus, Probability, and Statistics for the Life Sciences, 1st edition, by Stewart and Day.  The UC custom version does not have any special features.

You do NOT need a WebAssign code.  We will not be using any of the Cengage online systems.

Evening Midterm: Wednesday, October 13, 2021, 8-10pm

See bCourses about a week before classes begin for additional course materials.

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

Description 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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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.

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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.

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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.

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Prerequisites 1B

Description 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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Prerequisites 53 and 54

Description 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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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.

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Grading 

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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.

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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.

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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.

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

Description 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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Course Webpage https://math.berkeley.edu/~giventh/11021.html

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.

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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 

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Grading 

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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 

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Required Text 

Recommended Reading 

Grading 

Homework 

Course Webpage 

Prerequisites 55

Description Construction and analysis of simple cryptosystems, public key cryptography, RSA, signature schemes, key distribution, hash functions, elliptic curves, and applications.

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Prerequisites 104

Description 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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Prerequisites 53 and 54

Description 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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Prerequisites Math 104 and 113 or consent of instructor

Description 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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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.

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Required Text  John Stillwell, Classical topology and combinatorial group theory

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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.

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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.

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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.

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Prerequisites Consent of instructor

Description This is the Putnam Workshop intended for students who plan to participate in the Putnam Mathematical Competition held on the first Saturday in December.  It is considered repeatable for credit and can be taken more than once in a student's undergraduate career.

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Required Text 

Recommended Reading 

Grading 

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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    See course webpage.

Recommended Reading    See course webpage.

Grading Letter grade.   See course webpage.

Homework    See course webpage.

Course Webpage    Link is at:    math.berkeley.edu/~rieffel

Prerequisites 185 and 202A-202B or their equivalents

Description Basic theory, power series developments, biholomorphic maps, Hartogs' phenomenon, plurisubharmonicity. The remainder of the course will treat the theory of holomorphic partial differential equations with applications to equations with real analytic coefficients. It will be independendent from 212 given in the Fall of 2019.

Office 801

Office Hours Th 2-3 PM

Grading Letter grade.

Homework Biweekly

Course Webpage https://math.berkeley.edu/~zworski/212_21.html

Prerequisites 105 or 202A

Description 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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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.

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Required Text 

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Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 225B and 235A

Description 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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Grading Letter grade.

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Course Webpage 

Prerequisites 214 (Differential manifolds, Lie groups and algebras, De Rham complex) 

Description Unlike Riemannian geometry, whose purpose is to classify Riemannian metrics (according to Felix Klein's "Erlangen program" of characterizing various geometries), symplectic geometry should not be viewed as yet another branch. It is rather a language, or a common landscape for classical mechanics, quantization, PDEs, representations of Lie groups, and probably much else. As any language, it is elegant and powerful but not particularly deep. In the contrary, symplectic topology is a deep theory studying intricate rigidity properties of phase spaces of hamiltonian mechanics. It is not our goal to sink into symplectic topology, but time permitting, we'll have an informal primer of it as well.

For the most of the course, we will loosely follow the article Symplectic Geometry by Vladimir Arnold and myself, found on pages 1--135 in the volume Dynamical Systems IV of Springer's Encyclopaedia of Mathematical Sciences. Officially it is a survey paper, and as such is not required to contain proofs. In reality the exposition of the most essential material was organized as if a detailed textbook was first written, and then all trivial proofs removed and left as exercises to the reader, while all non-trivial ones left as outlines. This makes the text suitable for a graduate-level course, and testing this conjecture is a part of the plan.

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Office Hours 

Required Text Symplectic Geometry and its Applications, V. Arnold and S. Novikov (eds.) (Encyclopaedia of Mathematical Science.  Dynamical Systems IV ) freely available in the electronic PDF format for patrons of the UC Berkeley library

Recommended Reading 

Grading Letter grade.

Homework weekly

Course Webpagehttps://math.berkeley.edu/~giventh/24221.html

Prerequisites 250A

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

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Grading Letter grade.

Homework 

Course Webpage 

Prerequisites 250A for 254A; 254A for 254B

Description 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.

Office 883 Evans

Office Hours MWF 12-1 and MWF 3-4

Required Text Neukirch, Algebraic number theory

Recommended Reading 

Grading Letter grade.

Homework Due weekly

Course Webpage https://math.berkeley.edu/~vojta/254a.html

Prerequisites 206 or a basic knowledge of real, complex, and linear analysis

Description 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.

Office 

Office Hours 

Required Text 

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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 

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 

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