Fall 2023

Prerequisites 

Description This 7.5-week 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.

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Prerequisites Three and one-half years of high school math, including trigonometry and analytic geometry. Students with high school exam credits (such as AP credit) should consider choosing a course more advanced than 1A

Description 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.

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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 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.)

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Prerequisites 16A

Description Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.

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Prerequisites Three years of high school mathematics

Course Description: Math 32 covers the core topics which need to be mastered before progressing to introductory calculus classes (Math 1A/16A/10A). This course covers the necessary foundational knowledge for calculus, including real numbers and operations, functions and graphs, equations and inequalities, linear, quadratic, polynomial, and rational functions, exponential and logarithmic functions, trigonometric and inverse trigonometric functions, trigonometric algebra, sequences and series, and complex numbers.

Who the Class is For: This class is aimed at students who intend to major in STEM or related fields but have limited exposure to rigorous mathematics.  In particular, it’s specifically for those students who intend to go through parts of our main lower division mathematics sequence (1A, 1B, 53,...) but require substantial preparation.  

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Course Webpage https://bcourses.berkeley.edu/courses/1528754

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 Prerequisites are 1B, N1B, 10B, or N10B. [N is the summer version]

Description 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.

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Prerequisites 

Description Directed Group Study, topics vary with instructor.

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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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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.

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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 

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Recommended Reading 

Grading 

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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 

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Recommended Reading 

Grading 

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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.

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Recommended Reading 

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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 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.

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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.

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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.

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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.

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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.

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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.

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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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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.

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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 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 

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 

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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.

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Grading Letter grade.

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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

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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.

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Grading Letter grade.

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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.

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Grading Letter grade.

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Prerequisites Graduate status or consent of instructor

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

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Grading Letter grade.

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Prerequisites 128A

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

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Grading Letter grade.

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Prerequisites 114 or consent of instructor

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

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Grading Letter grade.

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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.

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Grading Letter grade.

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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.

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Prerequisites Consent of instructor

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

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Grading Letter grade.

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