berkeley math phd

Mathematics

The Department of Mathematics is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the world. With one of the finest mathematics libraries in the nation, and a favorable climate, it is America's most exciting and cosmopolitan centers for mathematics research and teaching. UC Berkeley has become a favorite location for the study of mathematics by students and faculty from all over the world.

UC Berkeley is increasingly interested in developing the talents of outstanding mathematics students and has a number of challenging honors-level courses. The department encourages all major students to participate in the annual  William Lowell Putnam Mathematical Competition . Additionally, the department sponsors undergraduate teams in the annual Mathematical Contest in Modeling, in which teams of three write mathematical solutions to real-life problems. An active  Mathematics Undergraduate Student Association (MUSA) , of which all departmental majors are automatically members, contributes to making Berkeley a stimulating and rewarding place to study mathematics. Moreover,  Women in Mathematics at Berkeley (WIM)  serves to foster a community and provide a network amongst the undergraduate women in mathematics at Cal. 

Berkeley's mathematics education program is greatly enriched by its large number of graduate students, postdoctoral faculty and fellows, and visiting teachers in residence each year. They come from all over the world to teach courses, participate in seminars, collaborate in research, give talks at the weekly Mathematics Colloquium, and be available as consultants.  An affiliated interdisciplinary group, with its own doctoral program, is the  Group in Logic and the Methodology of Science . We have an NSF-funded Research Training Groups in  Representation Theory, Geometry and Combinatorics , which  runs seminars, workshops, and other activities and supports graduate students and postdoctoral fellows in their areas of interest.

The Department has several  graduate student groups : the  Mathematics Graduate Student Association (MGSA) , comprising all graduate students, the  Noetherian Ring , a group of women in mathematics,  Unbounded Representation (Urep) , promoting dialogue on diversity in the math community, and a student lecture series, Many Cheerful Facts.

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

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

Undergraduate Programs

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

Graduate Programs

Applied Mathematics : PhD Mathematics : PhD

Visit Department Website

MATH 1 Foundations of Lower Division Mathematics 2 Units

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 [+]

Hours & Format

Fall and/or spring: 7.5 weeks - 3 hours of lecture and 3 hours of discussion per week

Summer: 3 weeks - 5 hours of lecture and 5 hours of discussion per week

Additional Format: Three hours of lecture and three hours of discussion per week for seven and one-half weeks. Five hours of lecture and five hours of discussion per week for three weeks.

Additional Details

Subject/Course Level: Mathematics/Undergraduate

Grading/Final exam status: Offered for pass/not pass grade only. Alternative to final exam.

Foundations of Lower Division Mathematics: Read Less [-]

MATH 1A Calculus 4 Units

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 [+]

Rules & Requirements

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

Credit Restrictions: Students will receive no credit for MATH 1A after completing MATH N1A , MATH 16B , Math N16B or XMATH 1A . A deficient grade in MATH 1A may be removed by taking MATH N1A .

Fall and/or spring: 15 weeks - 3 hours of lecture and 3 hours of discussion per week

Summer: 8 weeks - 6 hours of lecture and 2 hours of discussion per week

Additional Format: Three hours of lecture and three hours of discussion per week. Six hours of lecture and two hours of discussion per week for 8 weeks.

Grading/Final exam status: Letter grade. Final exam required.

Calculus: Read Less [-]

MATH 1B Calculus 4 Units

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 [+]

Prerequisites: 1A or N1A

Credit Restrictions: Students will receive no credit for Math 1B after completing Math N1B, H1B, Xmath 1B. A deficient grade in MATH 1B may be removed by taking MATH N1B or MATH H1B .

Fall and/or spring: 15 weeks - 3-3 hours of lecture and 2-3 hours of discussion per week

Additional Format: Three hours of lecture and two to three hours of discussion per week.

MATH H1B Honors Calculus 4 Units

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 [+]

Prerequisites: 1A

Credit Restrictions: Students will receive no credit for Mathematics H1B after completing Mathematics 1B or N1B.

Fall and/or spring: 15 weeks - 3 hours of lecture and 2 hours of discussion per week

Summer: 8 weeks - 5 hours of lecture and 5 hours of discussion per week

Additional Format: Three hours of lecture and two hours of discussion per week. Five hours of lecture and five hours of discussion per week for 8 weeks.

Honors Calculus: Read Less [-]

MATH N1A Calculus 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for MATH N1A after completing MATH 1A , MATH 16B or MATH N16B . A deficient grade in MATH N1A may be removed by taking MATH 1A .

Summer: 8 weeks - 10 hours of lecture per week

Additional Format: Ten hours of lecture per week for 8 weeks.

MATH N1B Calculus 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for Math N1B after completing Math 1B, H1B, or Xmath 1B. A deficient grade in N1B may be removed by completing Mathematics 1B or H1B.

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

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 [+]

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

Credit Restrictions: Students will receive no credit for Mathematics 10A after completing Mathematics N10A. A deficient grade in Math 10A may be removed by taking Math N10A.

Additional Format: Three hours of lecture and three hours of discussion per week.

Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read Less [-]

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

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 [+]

Prerequisites: Continuation of 10A

Credit Restrictions: Students will receive no credit for Mathematics 10B after completing Mathematics N10B. A deficient grade in Math 10B may be removed by taking Math N10B.

MATH N10A Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for Math N10A after completing Math 10A. A deficient grade in Math N10A may be removed by completing Math 10A.

MATH N10B Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units

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 [+]

Prerequisites: Math 10A or N10A

Credit Restrictions: Students will receive no credit for Math N10B after completing Math 10B. A deficient grade in Math N10B may be removed by completing Math 10B.

MATH 16A Analytic Geometry and Calculus 3 Units

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 [+]

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

Credit Restrictions: Students will receive no credit for 16A after taking N16A, 1A, or N1A. A deficient grade in Math 16A may be removed by taking Math N16A.

Fall and/or spring: 15 weeks - 3 hours of lecture and 1.5 hours of discussion per week

Additional Format: Three hours of lecture and one and one-half hours of discussion per week.

Analytic Geometry and Calculus: Read Less [-]

MATH 16B Analytic Geometry and Calculus 3 Units

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 [+]

Prerequisites: 16A

Credit Restrictions: Students will receive no credit for MATH 16B after completing MATH N16B , 1B , or N1B. A deficient grade in Math 16B may be removed by taking Math N16B.

MATH N16A Analytic Geometry and Calculus 3 Units

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 [+]

Prerequisites: Three years of high school math, including trigonometry

Credit Restrictions: Students will receive no credit for 16A after taking N16A, 1A or N1A. A deficient grade in N16A may be removed by completing 16A.

Summer: 8 weeks - 8 hours of lecture per week

Additional Format: Eight hours of lecture per week for 8 weeks.

MATH N16B Analytic Geometry and Calculus 3 Units

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 [+]

Prerequisites: Mathematics 16A or N16A

Credit Restrictions: Students will receive no credit for Math N16B after Math 16B, 1B or N1B. A deficient grade in N16B may be removed by completing 16B.

MATH 24 Freshman Seminars 1 Unit

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 [+]

Repeat rules: Course may be repeated for credit when topic changes.

Fall and/or spring: 15 weeks - 1 hour of seminar per week

Additional Format: One hour of Seminar per week for 15 weeks.

Grading/Final exam status: The grading option will be decided by the instructor when the class is offered. Final Exam To be decided by the instructor when the class is offered.

Freshman Seminars: Read Less [-]

MATH 32 Precalculus 4 Units

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 [+]

Prerequisites: Three years of high school mathematics

Credit Restrictions: Students will receive no credit for Math 32 after taking N32, 1A or N1A, 1B or N1B, 16A or N16A, 16B or N16B. A deficient grade in Math 32 may be removed by taking Math N32.

Summer: 6 weeks - 5 hours of lecture and 5 hours of discussion per week

Additional Format: Three hours of lecture and two hours of discussion per week. Five hours of lecture and five hours of discussion per week for 6 weeks.

Precalculus: Read Less [-]

MATH N32 Precalculus 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for MATH N32 after completing MATH 32 , 1A -1B (or N1A-N1B) or 16A-16B (or N16A-16B), or XMATH 32 . A deficient grade in MATH 32 or XMATH 32 maybe removed by taking MATH N32 .

MATH 39A Freshman/Sophomore Seminar 2 - 4 Units

Terms offered: Spring 2019, Spring 2018, Spring 2010 Freshman and sophomore seminars offer lower division students the opportunity to explore an intellectual topic with a faculty member and a group of peers in a small-seminar setting. These seminars are offered in all campus departments; topics vary from department to department and from semester to semester. Freshman/Sophomore Seminar: Read More [+]

Prerequisites: Priority given to freshmen and sophomores

Repeat rules: Course may be repeated for credit without restriction.

Fall and/or spring: 15 weeks - 2-4 hours of seminar per week

Additional Format: Seminar format.

Grading/Final exam status: Letter grade. Final Exam To be decided by the instructor when the class is offered.

Freshman/Sophomore Seminar: Read Less [-]

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

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 [+]

Prerequisites: Some units in a lower division Mathematics class

Fall and/or spring: 15 weeks - 0 hours of independent study per week

Summer: 6 weeks - 1-5 hours of independent study per week 8 weeks - 1-4 hours of independent study per week

Additional Format: Meetings to be arranged.

Grading/Final exam status: Letter grade. Final exam not required.

Supplementary Work in Lower Division Mathematics: Read Less [-]

MATH 53 Multivariable Calculus 4 Units

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 [+]

Prerequisites: Mathematics 1B or N1B

Credit Restrictions: Students will receive no credit for Mathematics 53 after completing Mathematics N53 or W53; A deficient grade in 53 may be removed by completing Mathematics N53 or W53.

Multivariable Calculus: Read Less [-]

MATH H53 Honors Multivariable Calculus 4 Units

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 [+]

Prerequisites: 1B

Credit Restrictions: Students will receive no credit for Mathematics H53 after completing Math 53, Math N53, or Math W53.

Honors Multivariable Calculus: Read Less [-]

MATH N53 Multivariable Calculus 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for Mathematics N53 after completing Mathematics 53, H53, or W53; A deficient grade in N53 may be removed by completing Mathematics 53, H53, or W53.

MATH W53 Multivariable Calculus 4 Units

Prerequisites: Mathematics 1B or equivalent

Credit Restrictions: Students will receive no credit for Mathematics W53 after completing Mathematics 53 or N53. A deficient grade in Mathematics W53 may be removed by completing Mathematics 53 or N53.

Summer: 8 weeks - 5 hours of web-based lecture and 5 hours of web-based discussion per week

Additional Format: Five hours of web-based lecture and five hours of web-based discussion per week for 8 weeks.

Online: This is an online course.

Instructor: Hutchings

MATH 54 Linear Algebra and Differential Equations 4 Units

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 [+]

Prerequisites: 1B, N1B, 10B, or N10B

Credit Restrictions: Students will receive no credit for MATH 54 after completing MATH H54 , MATH N54 , MATH W54 , or MATH 56 . A deficient grade in MATH 54 may be removed by taking MATH N54 , MATH W54 , or MATH 56 .

Linear Algebra and Differential Equations: Read Less [-]

MATH H54 Honors Linear Algebra and Differential Equations 4 Units

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. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Honors Linear Algebra and Differential Equations: Read More [+]

Credit Restrictions: Students will receive no credit for Math H54 after completion of Math 54 or N54.

Honors Linear Algebra and Differential Equations: Read Less [-]

MATH N54 Linear Algebra and Differential Equations 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for Math N54 after completing Math 54 or Math H54; A deficient grade in N54 may be removed by completing Mathematics 54 or H54.

MATH W54 Linear Algebra and Differential Equations 4 Units

Prerequisites: Math 1B, N1B, 10B, or N10B

Credit Restrictions: Students will receive no credit for MATH W54 after completing MATH 54 , or MATH N54 . A deficient grade in MATH W54 may be removed by taking MATH 54 , MATH N54 , MATH 54 , or MATH N54 .

Summer: 8 weeks - 5.5 hours of web-based lecture and 6 hours of web-based discussion per week

Additional Format: Six hours of web-based discussion and five and one-half hours of web-based lecture per week for 8 weeks.

Instructor: Nadler

MATH 55 Discrete Mathematics 4 Units

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 [+]

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

Credit Restrictions: Students will receive no credit for Math 55 after completion of Math N55 or Computer Science 70. A deficient grade in Math 55 may be removed by completing Math N55.

Additional Format: Three hours of lecture and two hours of discussion per week.

Discrete Mathematics: Read Less [-]

MATH N55 Discrete Mathematics 4 Units

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 [+]

Credit Restrictions: Students will receive no credit for 55 after taking N55 or Computer Science 70. A deficient grade in Math N55 may be removed by completing Math 55.

MATH 56 Linear Algebra 4 Units

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 [+]

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

Credit Restrictions: Students will receive no credit for MATH 56 after completing MATH 54 , MATH N54 , or MATH W54 . A deficient grade in MATH 56 may be removed by taking MATH 54 , MATH N54 , or MATH W54 .

Grading/Final exam status: Letter grade. Final exam required, with common exam group.

Linear Algebra: Read Less [-]

MATH 74 Transition to Upper Division Mathematics 3 Units

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 [+]

Prerequisites: 53 and 54

Summer: 8 weeks - 6 hours of lecture and 0-2 hours of discussion per week

Additional Format: Six hours of lecture and at the discretion of the instructor and additional two hours of discussion per week for eight weeks.

Transition to Upper Division Mathematics: Read Less [-]

MATH 91 Special Topics in Mathematics 4 Units

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 [+]

Fall and/or spring: 15 weeks - 3-3 hours of lecture and 0-3 hours of discussion per week

Additional Format: Three hours of lecture and zero to three hours of discussion per week.

Special Topics in Mathematics: Read Less [-]

MATH 96 College Algebra 2 Units

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 [+]

Fall and/or spring: 15 weeks - 4 hours of workshop per week

Summer: 6 weeks - 10 hours of workshop per week 8 weeks - 10 hours of workshop per week

Additional Format: Four hours of Workshop per week for 15 weeks. Ten hours of Workshop per week for 8 weeks. Ten hours of Workshop per week for 6 weeks.

College Algebra: Read Less [-]

MATH 98 Supervised Group Study 1 - 4 Units

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

Repeat rules: Course may be repeated for credit up to a total of 4 units.

Fall and/or spring: 15 weeks - 1-4 hours of directed group study per week

Summer: 3 weeks - 5-20 hours of directed group study per week 6 weeks - 1-10 hours of directed group study per week 8 weeks - 1.5-7.5 hours of directed group study per week

Additional Format: One to four hours of directed group study per week. One and one-half to seven and one-half hours of directed group study per week for 8 weeks. One to ten hours of directed group study per week for 6 weeks. Five to twenty hours of directed group study per week for three weeks.

Grading/Final exam status: Offered for pass/not pass grade only. Final exam not required.

Supervised Group Study: Read Less [-]

MATH 98BC Berkeley Connect 1 Unit

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 [+]

Fall and/or spring: 15 weeks - 1 hour of discussion per week

Additional Format: One hour of discussion per week.

Berkeley Connect: Read Less [-]

MATH 99 Supervised Independent Study 1 - 4 Units

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 [+]

Prerequisites: Restricted to freshmen and sophomores only. Consent of instructor

Credit Restrictions: Enrollment is restricted; see the Introduction to Courses and Curricula section of this catalog.

Fall and/or spring: 15 weeks - 1-4 hours of independent study per week

Summer: 8 weeks - 1-4 hours of independent study per week

Additional Format: Independent study, weekly meeting with faculty. Independent study, weekly meeting with faculty.

Supervised Independent Study: Read Less [-]

MATH C103 Introduction to Mathematical Economics 4 Units

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 [+]

Prerequisites: Math 53 and 54

Fall and/or spring: 15 weeks - 3 hours of lecture per week

Additional Format: Three hours of Lecture per week for 15 weeks.

Formerly known as: 103

Also listed as: ECON C103

Introduction to Mathematical Economics: Read Less [-]

MATH 104 Introduction to Analysis 4 Units

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 [+]

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

Additional Format: Three hours of lecture per week. Eight hours of lecture per week for 8 weeks.

Introduction to Analysis: Read Less [-]

MATH H104 Honors Introduction to Analysis 4 Units

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 [+]

Honors Introduction to Analysis: Read Less [-]

MATH 105 Second Course in Analysis 4 Units

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 [+]

Prerequisites: 104

Second Course in Analysis: Read Less [-]

MATH 106 Mathematical Probability Theory 4 Units

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 [+]

Prerequisites: Mathematics 104

Additional Format: Three hours of lecture per week.

Mathematical Probability Theory: Read Less [-]

MATH 110 Abstract Linear Algebra 4 Units

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 [+]

Prerequisites: 54, or 56, or a course with equivalent linear algebra content. 55, or 74, or an equivalent exposure to proofs is recommended

Fall and/or spring: 15 weeks - 3 hours of lecture and 1 hour of discussion per week

Summer: 8 weeks - 8 hours of lecture and 0 hours of discussion per week

Additional Format: Three hours of lecture and one hour of discussion per week. Eight hours of lecture and zero hour of discussion per week for 8 weeks.

Abstract Linear Algebra: Read Less [-]

MATH H110 Honors Linear Algebra 4 Units

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 [+]

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

Honors Linear Algebra: Read Less [-]

MATH 113 Introduction to Abstract Algebra 4 Units

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 [+]

Introduction to Abstract Algebra: Read Less [-]

MATH H113 Honors Introduction to Abstract Algebra 4 Units

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 [+]

Honors Introduction to Abstract Algebra: Read Less [-]

MATH 114 Second Course in Abstract Algebra 4 Units

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 [+]

Prerequisites: 110 and 113, or consent of instructor

Second Course in Abstract Algebra: Read Less [-]

MATH 115 Introduction to Number Theory 4 Units

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 [+]

Prerequisites: Math 55 is recommended

Introduction to Number Theory: Read Less [-]

MATH 116 Cryptography 4 Units

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 [+]

Prerequisites: 55

Fall and/or spring: 15 weeks - 3 hours of lecture and 0-2 hours of discussion per week

Summer: 8 weeks - 6 hours of lecture and 0-4 hours of discussion per week

Additional Format: Three hours of lecture per week, and at the discretion of the instructor, an additional two hours of discussion per week. Six hours of lecture per week, and at the discretion of the instructor, an additional four hours of discussion per week.

Cryptography: Read Less [-]

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

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 [+]

Fourier Analysis, Wavelets, and Signal Processing: Read Less [-]

MATH 121A Mathematical Tools for the Physical Sciences 4 Units

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 [+]

Mathematical Tools for the Physical Sciences: Read Less [-]

MATH 121B Mathematical Tools for the Physical Sciences 4 Units

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 [+]

MATH 123 Ordinary Differential Equations 4 Units

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 [+]

Ordinary Differential Equations: Read Less [-]

MATH 124 Programming for Mathematical Applications 4 Units

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 [+]

Prerequisites: Math 53, 54, 55

Additional Format: Three hours of lecture and one hour of discussion per week.

Programming for Mathematical Applications: Read Less [-]

MATH 125A Mathematical Logic 4 Units

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 [+]

Prerequisites: Math 104 and 113 or consent of instructor

Mathematical Logic: Read Less [-]

MATH 126 Introduction to Partial Differential Equations 4 Units

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 [+]

Summer: 8 weeks - 6 hours of lecture per week

Additional Format: Three hours of lecture per week. Six hours of lecture per week for 8 weeks.

Introduction to Partial Differential Equations: Read Less [-]

MATH 127 Mathematical and Computational Methods in Molecular Biology 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016 Introduction to mathematical and computational problems arising in the context of molecular biology. Theory and applications of combinatorics, probability, statistics, geometry, and topology to problems ranging from sequence determination to structure analysis. Mathematical and Computational Methods in Molecular Biology: Read More [+]

Prerequisites: 53, 54, and 55; Statistics 20 recommended

Mathematical and Computational Methods in Molecular Biology: Read Less [-]

MATH 128A Numerical Analysis 4 Units

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 [+]

Summer: 8 weeks - 4 hours of lecture and 4 hours of discussion per week

Additional Format: Three hours of lecture and one hour of discussion per week. Four hours of lecture and four hours of discussion per week for 8 weeks.

Numerical Analysis: Read Less [-]

MATH 128B Numerical Analysis 4 Units

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 [+]

Prerequisites: 110 and 128A

Summer: 8 weeks - 6 hours of lecture and 1.5 hours of discussion per week

Additional Format: Three hours of lecture and one hour of discussion per week. At the discretion of the instructor, an additional hour of discussion/computer laboratory per week.

MATH W128A Numerical Analysis 4 Units

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

Prerequisites: MATH 53 , MATH 54

Credit Restrictions: Students will receive no credit for MATH W128A after completing MATH 128A . A deficient grade in MATH W128A may be removed by taking MATH 128A , or MATH 128A .

Summer: 8 weeks - 4 hours of web-based lecture and 4 hours of web-based discussion per week

Additional Format: Four hours of web-based discussion and four hours of web-based lecture per week for 8 weeks.

Instructor: Persson

MATH 130 Groups and Geometries 4 Units

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 [+]

Prerequisites: 110 and 113

Groups and Geometries: Read Less [-]

MATH 135 Introduction to the Theory of Sets 4 Units

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 [+]

Introduction to the Theory of Sets: Read Less [-]

MATH 136 Incompleteness and Undecidability 4 Units

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 [+]

Incompleteness and Undecidability: Read Less [-]

MATH 140 Metric Differential Geometry 4 Units

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 [+]

Metric Differential Geometry: Read Less [-]

MATH 141 Elementary Differential Topology 4 Units

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 [+]

Prerequisites: 104 or equivalent and linear algebra

Elementary Differential Topology: Read Less [-]

MATH 142 Elementary Algebraic Topology 4 Units

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 [+]

Prerequisites: 104 and 113

Elementary Algebraic Topology: Read Less [-]

MATH 143 Elementary Algebraic Geometry 4 Units

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 [+]

Prerequisites: 113

Elementary Algebraic Geometry: Read Less [-]

MATH 151 Mathematics of the Secondary School Curriculum I 4 Units

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 [+]

Prerequisites: 1A-1B, 53, or equivalent

Fall and/or spring: 15 weeks - 3 hours of lecture and 0-1 hours of discussion per week

Additional Format: Three hours of lecture and zero to one hour of discussion per week.

Mathematics of the Secondary School Curriculum I: Read Less [-]

MATH 152 Mathematics of the Secondary School Curriculum II 4 Units

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 [+]

Prerequisites: 151; 54, 113, or equivalent

Mathematics of the Secondary School Curriculum II: Read Less [-]

MATH 156 Numerical Analysis for Data Science and Statistics 4 Units

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 [+]

Prerequisites: Math 53 and 54 or 56 or equivalent (e.g., Math 91 from Fall 2022 can replace Math 54)

Numerical Analysis for Data Science and Statistics: Read Less [-]

MATH 160 History of Mathematics 4 Units

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 [+]

Prerequisites: 53, 54, and 113

History of Mathematics: Read Less [-]

MATH 170 Mathematical Methods for Optimization 4 Units

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 [+]

Mathematical Methods for Optimization: Read Less [-]

MATH 172 Combinatorics 4 Units

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 [+]

Combinatorics: Read Less [-]

MATH 185 Introduction to Complex Analysis 4 Units

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 [+]

Fall and/or spring: 15 weeks - 3-3 hours of lecture and 0-2 hours of discussion per week

Additional Format: Three hours of lecture and zero to two hours of discussion per week. Eight hours of lecture and zero hour of discussion per week for 8 weeks.

Introduction to Complex Analysis: Read Less [-]

MATH H185 Honors Introduction to Complex Analysis 4 Units

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 [+]

Honors Introduction to Complex Analysis: Read Less [-]

MATH 189 Mathematical Methods in Classical and Quantum Mechanics 4 Units

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 [+]

Prerequisites: 104, 110, 2 semesters lower division Physics

Mathematical Methods in Classical and Quantum Mechanics: Read Less [-]

MATH 191 Experimental Courses in Mathematics 1 - 4 Units

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 [+]

Prerequisites: Consent of instructor

Fall and/or spring: 15 weeks - 1-4 hours of seminar per week

Summer: 6 weeks - 2.5-10 hours of seminar per week 8 weeks - 1.5-7.5 hours of seminar per week

Additional Format: Hours to be arranged. Hours to be arranged.

Experimental Courses in Mathematics: Read Less [-]

MATH 195 Special Topics in Mathematics 4 Units

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 [+]

Fall and/or spring: 15 weeks - 0 hours of lecture per week

Additional Format: Hours to be arranged.

MATH 196 Honors Thesis 4 Units

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

Prerequisites: Admission to the Honors Program; an overall GPA of 3.3 and a GPA of 3.5 in the major

Honors Thesis: Read Less [-]

MATH 197 Field Study 1 - 4 Units

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 [+]

Prerequisites: Upper division standing. Written proposal signed by faculty sponsor and approved by department chair

Credit Restrictions: Enrollment is restricted; see the Course Number Guide in the Bulletin.

Fall and/or spring: 15 weeks - 3-3 hours of fieldwork per week

Summer: 8 weeks - 3-3 hours of fieldwork per week

Additional Format: Five and one-half hours of work per week per unit. Three hours of work per week per unit.

Field Study: Read Less [-]

MATH 198 Directed Group Study 1 - 4 Units

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

Prerequisites: Must have completed 60 units and be in good standing

Summer: 8 weeks - 1-4 hours of directed group study per week

Additional Format: Group study. Group study.

Directed Group Study: Read Less [-]

MATH 198BC Berkeley Connect 1 Unit

Math 199 supervised independent study and research 1 - 4 units.

Terms offered: Fall 2019, Fall 2018, Fall 2017 Supervised Independent Study and Research: Read More [+]

Prerequisites: The standard college regulations for all 199 courses

Supervised Independent Study and Research: Read Less [-]

MATH 202A Introduction to Topology and Analysis 4 Units

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 [+]

Subject/Course Level: Mathematics/Graduate

Grading: Letter grade.

Introduction to Topology and Analysis: Read Less [-]

MATH 202B Introduction to Topology and Analysis 4 Units

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 [+]

Prerequisites: 202A and 110

MATH 204 Ordinary Differential Equations 4 Units

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 [+]

MATH 205 Theory of Functions of a Complex Variable 4 Units

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 [+]

Prerequisites: 185

Theory of Functions of a Complex Variable: Read Less [-]

MATH 206 Functional Analysis 4 Units

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 [+]

Prerequisites: 202A-202B

Functional Analysis: Read Less [-]

MATH 208 C*-algebras 4 Units

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 [+]

Prerequisites: 206

C*-algebras: Read Less [-]

MATH 209 Von Neumann Algebras 4 Units

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 [+]

Von Neumann Algebras: Read Less [-]

MATH 212 Several Complex Variables 4 Units

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 cohomology and Stein manifolds, or the theory of analytic subvarieties and spaces. Several Complex Variables: Read More [+]

Prerequisites: 185 and 202A-202B or their equivalents

Several Complex Variables: Read Less [-]

MATH 214 Differential Topology 4 Units

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 [+]

Prerequisites: 202A

Differential Topology: Read Less [-]

MATH 215A Algebraic Topology 4 Units

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

Prerequisites: 113 and point-set topology (e.g. 202A)

Instructors: 113C, 202A, and 214

Algebraic Topology: Read Less [-]

MATH 215B Algebraic Topology 4 Units

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

Prerequisites: 215A, 214 recommended (can be taken concurrently)

MATH C218A Probability Theory 4 Units

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 [+]

Also listed as: STAT C205A

Probability Theory: Read Less [-]

MATH C218B Probability Theory 4 Units

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 [+]

Also listed as: STAT C205B

MATH 219 Dynamical Systems 4 Units

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 [+]

Prerequisites: 214

Dynamical Systems: Read Less [-]

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

Terms offered: Spring 2012, Spring 2011, Spring 2010 Brownian motion, Langevin and Fokker-Planck equations, path integrals and Feynman diagrams, time series, an introduction to statistical mechanics, Monte Carlo methods, selected applications. Introduction to Probabilistic Methods in Mathematics and the Sciences: Read More [+]

Prerequisites: Some familiarity with differential equations and their applications

Introduction to Probabilistic Methods in Mathematics and the Sciences: Read Less [-]

MATH 221 Advanced Matrix Computations 4 Units

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 [+]

Additional Format: Three hours of Lecture per week for 15 weeks. Six hours of Lecture per week for 8 weeks.

Advanced Matrix Computations: Read Less [-]

MATH 222A Partial Differential Equations 4 Units

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 [+]

Prerequisites: 105 or 202A

Partial Differential Equations: Read Less [-]

MATH 222B Partial Differential Equations 4 Units

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 [+]

MATH C223A Advanced Topics in Probability and Stochastic Process 3 Units

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 [+]

Prerequisites: Statistics C205A-C205B or consent of instructor

Repeat rules: Course may be repeated for credit with instructor consent.

Also listed as: STAT C206A

Advanced Topics in Probability and Stochastic Process: Read Less [-]

MATH C223B Advanced Topics in Probability and Stochastic Processes 3 Units

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 [+]

Also listed as: STAT C206B

Advanced Topics in Probability and Stochastic Processes: Read Less [-]

MATH 224A Mathematical Methods for the Physical Sciences 4 Units

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 [+]

Prerequisites: Graduate status or consent of instructor

Instructors: 112 or 113C; 104A and 185, or 121A-121B-121C, or 120A-120B-120C.

Mathematical Methods for the Physical Sciences: Read Less [-]

MATH 224B Mathematical Methods for the Physical Sciences 4 Units

Terms offered: Spring 2015, Spring 2014, Spring 2013 Introduction to the theory of distributions. Fourier and Laplace transforms. Partial differential equations. Green's function. Operator theory, with applications to eigenfunction expansions, perturbation theory and linear and non-linear waves. Sequence begins fall. Mathematical Methods for the Physical Sciences: Read More [+]

MATH 225A Metamathematics 4 Units

Terms offered: Fall 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 [+]

Prerequisites: 125A and (135 or 136)

Metamathematics: Read Less [-]

MATH 225B Metamathematics 4 Units

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 [+]

MATH 227A Theory of Recursive Functions 4 Units

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 [+]

Prerequisites: Mathematics 225B

Instructor: 225C.

Theory of Recursive Functions: Read Less [-]

MATH 228A Numerical Solution of Differential Equations 4 Units

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 [+]

Prerequisites: 128A

Instructor: 128A-128B.

Numerical Solution of Differential Equations: Read Less [-]

MATH 228B Numerical Solution of Differential Equations 4 Units

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 [+]

MATH 229 Theory of Models 4 Units

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 [+]

Prerequisites: 225B

Theory of Models: Read Less [-]

MATH 235A Theory of Sets 4 Units

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 [+]

Prerequisites: 125A and 135

Instructor: 125A and 135.

Theory of Sets: Read Less [-]

MATH 236 Metamathematics of Set Theory 4 Units

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 [+]

Prerequisites: 225B and 235A

Metamathematics of Set Theory: Read Less [-]

MATH 239 Discrete Mathematics for the Life Sciences 4 Units

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

Prerequisites: Statistics 134 or equivalent introductory probability theory course, or consent of instructor

Discrete Mathematics for the Life Sciences: Read Less [-]

MATH C239 Discrete Mathematics for the Life Sciences 4 Units

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

Also listed as: MCELLBI C244

MATH 240 Riemannian Geometry 4 Units

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, homogeneous manifolds, the Gauss-Bonnet theorem, and characteristic classes. Riemannian Geometry: Read More [+]

Riemannian Geometry: Read Less [-]

MATH 241 Complex Manifolds 4 Units

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 [+]

Prerequisites: 214 and 215A

Complex Manifolds: Read Less [-]

MATH 242 Symplectic Geometry 4 Units

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 [+]

Symplectic Geometry: Read Less [-]

MATH C243 Seq: Methods and Applications 3 Units

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

Prerequisites: Graduate standing in Math, MCB, and Computational Biology; or consent of the instructor

Additional Format: <br/>

Instructor: Pachter

Also listed as: MCELLBI C243

Seq: Methods and Applications: Read Less [-]

MATH 245A General Theory of Algebraic Structures 4 Units

Terms offered: Fall 2017, Fall 2015, Spring 2014 Structures defined by operations and/or relations, and their homomorphisms. Classes of structures determined by identities. Constructions such as free objects, objects presented by generators and relations, ultraproducts, direct limits. Applications of general results to groups, rings, lattices, etc. Course may emphasize study of congruence- and subalgebra-lattices, or category-theory and adjoint functors, or other aspects. General Theory of Algebraic Structures: Read More [+]

Prerequisites: Math 113

General Theory of Algebraic Structures: Read Less [-]

MATH 249 Algebraic Combinatorics 4 Units

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 [+]

Prerequisites: 250A or consent of instructor

Algebraic Combinatorics: Read Less [-]

MATH 250A Groups, Rings, and Fields 4 Units

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 [+]

Prerequisites: 114 or consent of instructor

Groups, Rings, and Fields: Read Less [-]

MATH 250B Commutative Algebra 4 Units

Terms offered: Spring 2024, Spring 2023, Spring 2022 Development of the main tools of commutative and homological algebra applicable to algebraic geometry, number theory and combinatorics. Commutative Algebra: Read More [+]

Prerequisites: 250A

Commutative Algebra: Read Less [-]

MATH 251 Ring Theory 4 Units

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

Ring Theory: Read Less [-]

MATH 252 Representation Theory 4 Units

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 [+]

Representation Theory: Read Less [-]

MATH 253 Homological Algebra 4 Units

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

Homological Algebra: Read Less [-]

MATH 254A Number Theory 4 Units

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 [+]

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

Instructor: 250A.

Number Theory: Read Less [-]

MATH 254B Number Theory 4 Units

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 [+]

Prerequisites: 254A

MATH 255 Algebraic Curves 4 Units

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 [+]

Prerequisites: 250A-250B or consent of instructor

Algebraic Curves: Read Less [-]

MATH 256A Algebraic Geometry 4 Units

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 cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall. Algebraic Geometry: Read More [+]

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

Algebraic Geometry: Read Less [-]

MATH 256B Algebraic Geometry 4 Units

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 cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall. Algebraic Geometry: Read More [+]

Prerequisites: 256A

MATH 257 Group Theory 4 Units

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 cohomological methods. Group Theory: Read More [+]

Group Theory: Read Less [-]

MATH 258 Harmonic Analysis 4 Units

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 [+]

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

Harmonic Analysis: Read Less [-]

MATH 261A Lie Groups 4 Units

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 [+]

Instructor: 214.

Lie Groups: Read Less [-]

MATH 261B Lie Groups 4 Units

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 [+]

MATH 270 Advanced Topics Course in Mathematics 2 Units

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 [+]

Fall and/or spring: 15 weeks - 1.5 hours of lecture per week

Additional Format: One and one-half hours of lecture per week.

Grading: Offered for satisfactory/unsatisfactory grade only.

Advanced Topics Course in Mathematics: Read Less [-]

MATH 272 Interdisciplinary Topics in Mathematics 1 - 4 Units

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 [+]

Fall and/or spring: 15 weeks - 3-3 hours of lecture per week

Interdisciplinary Topics in Mathematics: Read Less [-]

MATH 273 Topics in Numerical Analysis 4 Units

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 [+]

Topics in Numerical Analysis: Read Less [-]

MATH 274 Topics in Algebra 4 Units

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 [+]

Topics in Algebra: Read Less [-]

MATH 275 Topics in Applied Mathematics 4 Units

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 [+]

Topics in Applied Mathematics: Read Less [-]

MATH 276 Topics in Topology 4 Units

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 [+]

Topics in Topology: Read Less [-]

MATH 277 Topics in Differential Geometry 4 Units

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 [+]

Topics in Differential Geometry: Read Less [-]

MATH 278 Topics in Analysis 4 Units

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 [+]

Topics in Analysis: Read Less [-]

MATH 279 Topics in Partial Differential Equations 4 Units

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 [+]

Topics in Partial Differential Equations: Read Less [-]

MATH 290 Seminars 1 - 6 Units

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 [+]

Fall and/or spring: 15 weeks - 0 hours of seminar per week

Seminars: Read Less [-]

MATH 295 Individual Research 1 - 12 Units

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

Fall and/or spring: 15 weeks - 1-12 hours of independent study per week

Summer: 3 weeks - 5 hours of independent study per week 6 weeks - 2.5-30 hours of independent study per week 8 weeks - 1.5-60 hours of independent study per week

Grading: The grading option will be decided by the instructor when the class is offered.

Individual Research: Read Less [-]

MATH N295 Individual Research 0.5 - 5 Units

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 [+]

Summer: 8 weeks - 1-5 hours of independent study per week

MATH N297 General Academic Internship 0.5 Units

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 [+]

Summer: 8 weeks - 2.5 hours of independent study per week

Additional Format: Two and one-half hours of independent study per week for 8 weeks.

General Academic Internship: Read Less [-]

MATH 299 Reading Course for Graduate Students 1 - 6 Units

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 [+]

Reading Course for Graduate Students: Read Less [-]

MATH 301 Undergraduate Mathematics Instruction 1 - 2 Units

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 [+]

Prerequisites: Permission of SLC instructor, as well as sophomore standing and at least a B average in two semesters of calculus. Apply at Student Learning Center

Fall and/or spring: 15 weeks - 3 hours of seminar and 4 hours of tutorial per week

Additional Format: Three hours of Seminar and Four hours of Tutorial per week for 15 weeks.

Subject/Course Level: Mathematics/Professional course for teachers or prospective teachers

Grading: Offered for pass/not pass grade only.

Undergraduate Mathematics Instruction: Read Less [-]

MATH 302 Teaching Workshop 1 Unit

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

Summer: 8 weeks - 1 hour of lecture per week

Additional Format: One hour of Lecture per week for 8 weeks.

Teaching Workshop: Read Less [-]

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

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 [+]

Prerequisites: 300, graduate standing and appointment as a Graduate Student Instructor

Fall and/or spring: 15 weeks - 2-4 hours of independent study per week

Additional Format: No formal meetings.

Professional Preparation: Supervised Teaching of Mathematics: Read Less [-]

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

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 [+]

Prerequisites: For candidates for master's degree

Credit Restrictions: Course does not satisfy unit or residence requirements for master's degree.

Fall and/or spring: 15 weeks - 1-6 hours of independent study per week

Summer: 8 weeks - 1.5-10 hours of independent study per week

Subject/Course Level: Mathematics/Graduate examination preparation

Individual Study for Master's Students: Read Less [-]

MATH 602 Individual Study for Doctoral Students 1 - 8 Units

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 [+]

Prerequisites: For qualified graduate students

Fall and/or spring: 15 weeks - 1-8 hours of independent study per week

Additional Format: One to Eight hour of Independent study per week for 15 weeks.

Individual Study for Doctoral Students: Read Less [-]

Contact Information

Department of mathematics.

970 Evans Hall

Phone: 510-642-6650

Department Chair

Martin Olsson

953 Evans Hall

Phone: 510-642-4129

[email protected]

Vice-Chair for Undergraduate Affairs

Richard Bamler

705 Evans Hall

[email protected]

Vice-Chair for Graduate Affairs

Thomas Scanlon

723 Evans Hall

[email protected]

Graduate Student Affairs Officer - Academic Advising

Clay Calder

910 Evans Hall

[email protected]

Undergraduate Student Advisor

Thomas Brown

965 Evans Hall

Phone: 510-643-9292

[email protected]

Marsha Snow

964 Evans Hall

Phone: 510-642-6550

[email protected]

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PhD-year-2020

Random matrix theory in numerical linear algebra.

• Read more about Random Matrix Theory in Numerical Linear Algebra

The Geometry of Divisors on Matroids

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The Local Langlands Correspondence, Rapoport-Zink Spaces, and Shimura Varieties

• Read more about The Local Langlands Correspondence, Rapoport-Zink Spaces, and Shimura Varieties

Singular stochastic differential equations with elliptic and hypoelliptic diffusions

• Read more about Singular stochastic differential equations with elliptic and hypoelliptic diffusions

Coisotropic Branes on Tori and Homological Mirror Symmetry

• Read more about Coisotropic Branes on Tori and Homological Mirror Symmetry

A Boundary Integral Method for Modeling Axisymmetric Flow Around a Rising Bubble in a Vertical Tube and Accurate Numerical Evaluation of Orthogonal Polynomials

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Spherical and Symmetric Supervarieties

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Duality for boolean algebra expansions and its applications

• Read more about Duality for boolean algebra expansions and its applications

Reflection Principles and Ordinal Analysis

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Numerics and stability for orbifolds with applications to symplectic embeddings

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Graduate Group in Science and Mathematics Education (SESAME)

The Graduate Group in Science and Mathematics Education (informally known as SESAME) is an interdisciplinary graduate program leading to a doctoral degree in science, mathematics, or engineering education. The program is designed to give graduates advanced expertise in a scientific discipline as well as in educational theory and research methodologies.

This Graduate Group was established so individuals with training or experience in a mathematical, scientific, or technical discipline can pursue advanced studies focused on educational issues in these disciplines. SESAME produces scholars who can communicate effectively with scientists and engineers as well as with educational researchers and practitioners. SESAME students are expected to obtain at least masters-level competency in their mathematical or scientific discipline.

See the  Online Graduate Application  to apply to the Interdisciplinary PhD in Science and Mathematics Education. We encourage you to read our Admissions Instructions thoroughly and begin your application early.

SESAME also offers a Learning Sciences Certificate in Instructional Design, Learning Technologies, and Education Research.

SESAME Faculty

The SESAME faculty consists of professors from UC Berkeley's School of Education and a variety of Berkeley’s science and engineering departments.

Core faculty

Affiliated faculty.

Lloyd Goldwasser (link is external) , Lecturer, School of Education

Emeritus faculty

Focus of study.

SESAME students work with faculty to gain a better understanding of learning; to design more effective teaching approaches; and to create experiences that enhance the scientific and mathematical literacy of the general public. A major aim of the Group is to identify general theoretical principles that can guide the design of effective instruction.

Many student projects are concerned with college-level teaching in their disciplines. Others are concerned with:

• K-12 curriculum development 
• research into cognitive processes underlying good performance in scientific domains
• investigations of principles for the design of computer-based educational software; or
• studies of informal learning in science museums and other places open to the public.

Program Structure

SESAME includes advanced courses in the student's discipline, science and mathematics education, and psychology; teaching experience; research seminars; colloquia presented by outside speakers; and research into an educational problem connected with engineering, science, mathematics, or computer-science education. 

While SESAME emphasizes research in the processes of learning and teaching, it is not a teacher training unit. Students interested in careers in college-level math/science teaching (along with educational research), science museum program development, or research in the learning and teaching of science are likely to find SESAME suitable. 

The faculty consists of professors from several of Berkeley’s science and engineering departments and the Graduate School of Education, and instructors associated with other campus units such as the Lawrence Hall of Science.

Entrance Requirements

To enter the program, a student must have an excellent academic record with a bachelor's or, preferably, a master's degree in a natural science, mathematics, or engineering/computer science.  Experience teaching, developing instructional materials, or doing educational or psychological research in these areas will also be favorably considered.  Knowledge of psychology, cognitive science, education, or statistics is helpful but not required. See  SESAME Admissions  for more information.

Type of Program (MA/PhD)

This program offers a PhD and students who enter without a master’s degree in their discipline are expected to obtain at least Master's-level competency in their mathematical or scientific discipline.  

The program typically takes 10 to 12 semesters to complete, depending upon whether students are also working toward their master’s degree. Full time enrollment is expected. 

SESAME graduates take leadership roles in promoting educational innovations in academic, industrial, and museum settings including the  Exploratorium  and the  Lawrence Hall of Science . Others teach in two- or four-year colleges or universities, or are directing educational programs of science museums or similar institutions that offer programs for the general public. Still others are active in educational research and curricular development, in industrial training programs, or in their own consulting businesses.

Transfer from within Berkeley 

Application for admission into SEASAME by students already enrolled in a graduate degree program of the Berkeley campus is formally accomplished by submitting a Graduate Petition for Change of Major or Degree Goal .

These petitions are considered along with other applications for admission to the doctoral program. A petition for Change of Degree Goal should be accompanied in all cases by a statement describing the reasons for the proposed change and the nature of the program of studies contemplated. Any applicants previously admitted by the Graduate Division must still submit the standard application form and required letters of recommendation. We may also request a copy of your file from your current department.

Admissions Instructions and FAQ

Lloyd Goldwasser, SESAME Lecturer 2121 Berkeley Way, Room 4321 [email protected]

PhD Program information

The Statistics PhD program is rigorous, yet welcoming to students with interdisciplinary interests and different levels of preparation. Students in the PhD program take core courses on the theory and application of probability and statistics during their first year. The second year typically includes additional course work and a transition to research leading to a dissertation. PhD thesis topics are diverse and varied, reflecting the scope of faculty research interests. Many students are involved in interdisciplinary research. Students may also have the option to pursue a designated emphasis (DE) which is an interdisciplinary specialization:  Designated Emphasis in Computational and Genomic Biology ,  Designated Emphasis in Computational Precision Health ,  Designated Emphasis in Computational and Data Science and Engineering . The program requires four semesters of residence.

Normal progress entails:

Year 1 . Perform satisfactorily in preliminary coursework. In the summer, students are required to embark on a short-term research project, internship, graduate student instructorship, reading course, or on another research activity. Years 2-3 . Continue coursework. Find a thesis advisor and an area for the oral qualifying exam. Formally choose a chair for qualifying exam committee, who will also serve as faculty mentor separate from the thesis advisor.  Pass the oral qualifying exam and advance to candidacy by the end of Year 3. Present research at BSTARS each year. Years 4-5 . Finish the thesis and give a lecture based on it in a department seminar.

Program Requirements

• Qualifying Exam

Course work and evaluation

Preliminary stage: the first year.

Effective Fall 2019, students are expected to take four semester-long courses for a letter grade during their first year which should be selected from the core first-year PhD courses offered in the department: Probability (204/205A, 205B,), Theoretical Statistics (210A, 210B), and Applied Statistics (215A, 215B). These requirements can be altered by a member of the PhD Program Committee (in consultation with the faculty mentor and by submitting a graduate student petition ) in the following cases:

• Students primarily focused on probability will be allowed to substitute one semester of the four required semester-long courses with an appropriate course from outside the department.
• Students may request to postpone one semester of the core PhD courses and complete it in the second year, in which case they must take a relevant graduate course in their first year in its place. In all cases, students must complete the first year requirements in their second year as well as maintain the overall expectations of second year coursework, described below. Some examples in which such a request might be approved are described in the course guidance below.
• Students arriving with advanced standing, having completed equivalent coursework at another institution prior to joining the program, may be allowed to take other relevant graduate courses at UC Berkeley to satisfy some or all of the first year requirements

Requirements on course work beyond the first year

Students entering the program before 2022 are required to take five additional graduate courses beyond the four required in the first year, resulting in a total of nine graduate courses required for completion of their PhD. In their second year, students are required to take three graduate courses, at least two of them from the department offerings, and in their third year, they are required to take at least two graduate courses. Students are allowed to change the timing of these five courses with approval of their faculty mentor. Of the nine required graduate courses, students are required to take for credit a total of 24 semester hours of courses offered by the Statistics department numbered 204-272 inclusive. The Head Graduate Advisor (in consultation with the faculty mentor and after submission of a graduate student petition) may consent to substitute courses at a comparable level in other disciplines for some of these departmental graduate courses. In addition, the HGA may waive part of this unit requirement.

Starting with the cohort entering in the 2022-23 academic year , students are required to take at least three additional graduate courses beyond the four required in the first year, resulting in a total of seven graduate courses required for completion of their PhD. Of the seven required graduate courses, five of these courses must be from courses offered by the Statistics department and numbered 204-272, inclusive. With these reduced requirements, there is an expectation of very few waivers from the HGA. We emphasize that these are minimum requirements, and we expect that students will take additional classes of interest, for example on a S/U basis, to further their breadth of knowledge. 

For courses to count toward the coursework requirements students must receive at least a B+ in the course (courses taken S/U do not count, except for STAT 272 which is only offered S/U).  Courses that are research credits, directed study, reading groups, or departmental seminars do not satisfy coursework requirements (for courses offered by the Statistics department the course should be numbered 204-272 to satisfy the requirements). Upper-division undergraduate courses in other departments can be counted toward course requirements with the permission of the Head Graduate Advisor. This will normally only be approved if the courses provide necessary breadth in an application area relevant to the student’s thesis research.

First year course work: For the purposes of satisfactory progression in the first year, grades in the core PhD courses are evaluated as: A+: Excellent performance in PhD program A: Good performance in PhD program A-: Satisfactory performance B+: Performance marginal, needs improvement B: Unsatisfactory performance First year and beyond: At the end of each year, students must meet with his or her faculty mentor to review their progress and assess whether the student is meeting expected milestones. The result of this meeting should be the completion of the student’s annual review form, signed by the mentor ( available here ). If the student has a thesis advisor, the thesis advisor must also sign the annual review form.

Guidance on choosing course work

Choice of courses in the first year: Students enrolling in the fall of 2019 or later are required to take four semesters of the core PhD courses, at least three of which must be taken in their first year. Students have two options for how to schedule their four core courses:

• Option 1 -- Complete Four Core Courses in 1st year: In this option, students would take four core courses in the first year, usually finishing the complete sequence of two of the three sequences.  Students following this option who are primarily interested in statistics would normally take the 210A,B sequence (Theoretical Statistics) and then one of the 205A,B sequence (Probability) or the 215A,B sequence (Applied Statistics), based on their interests, though students are allowed to mix and match, where feasible. Students who opt for taking the full 210AB sequence in the first year should be aware that 210B requires some graduate-level probability concepts that are normally introduced in 205A (or 204).
• Option 2 -- Postponement of one semester of a core course to the second year: In this option, students would take three of the core courses in the first year plus another graduate course, and take the remaining core course in their second year. An example would be a student who wanted to take courses in each of the three sequences. Such a student could take the full year of one sequence and the first semester of another sequence in the first year, and the first semester of the last sequence in the second year (e.g. 210A, 215AB in the first year, and then 204 or 205A in the second year). This would also be a good option for students who would prefer to take 210A and 215A in their first semester but are concerned about their preparation for 210B in the spring semester.  Similarly, a student with strong interests in another discipline, might postpone one of the spring core PhD courses to the second year in order to take a course in that discipline in the first year.  Students who are less mathematically prepared might also be allowed to take the upper division (under-graduate) courses Math 104 and/or 105 in their first year in preparation for 205A and/or 210B in their second year. Students who wish to take this option should consult with their faculty mentor, and then must submit a graduate student petition to the PhD Committee to request permission for  postponement. Such postponement requests will be generally approved for only one course. At all times, students must take four approved graduate courses for a letter grade in their first year.

After the first year: Students with interests primarily in statistics are expected to take at least one semester of each of the core PhD sequences during their studies. Therefore at least one semester (if not both semesters) of the remaining core sequence would normally be completed during the second year. The remaining curriculum for the second and third years would be filled out with further graduate courses in Statistics and with courses from other departments. Students are expected to acquire some experience and proficiency in computing. Students are also expected to attend at least one departmental seminar per week. The precise program of study will be decided in consultation with the student’s faculty mentor.

Remark. Stat 204 is a graduate level probability course that is an alternative to 205AB series that covers probability concepts most commonly found in the applications of probability. It is not taught all years, but does fulfill the requirements of the first year core PhD courses. Students taking Stat 204, who wish to continue in Stat 205B, can do so (after obtaining the approval of the 205B instructor), by taking an intensive one month reading course over winter break.

Designated Emphasis: Students with a Designated Emphasis in Computational and Genomic Biology or Designated Emphasis in Computational and Data Science and Engineering should, like other statistics students, acquire a firm foundation in statistics and probability, with a program of study similar to those above. These programs have additional requirements as well. Interested students should consult with the graduate advisor of these programs. 

Starting in the Fall of 2019, PhD students are required in their first year to take four semesters of the core PhD courses. Students intending to specialize in Probability, however, have the option to substitute an advanced mathematics class for one of these four courses. Such students will thus be required to take Stat 205A/B in the first year,  at least one of Stat 210A/B or Stat 215A/B in the first year, in addition to an advanced mathematics course. This substitute course will be selected in consultation with their faculty mentor, with some possible courses suggested below. Students arriving with advanced coursework equivalent to that of 205AB can obtain permission to substitute in other advanced probability and mathematics coursework during their first year, and should consult with the PhD committee for such a waiver.

During their second and third years, students with a probability focus are expected to take advanced probability courses (e.g., Stat 206 and Stat 260) to fulfill the coursework requirements that follow the first year. Students are also expected to attend at least one departmental seminar per week, usually the probability seminar. If they are not sufficiently familiar with measure theory and functional analysis, then they should take one or both of Math 202A and Math 202B. Other recommended courses from the department of Mathematics or EECS include:

Math 204, 222 (ODE, PDE) Math 205 (Complex Analysis) Math 258 (Classical harmonic analysis) EE 229 (Information Theory and Coding) CS 271 (Randomness and computation)

The Qualifying Examination 

The oral qualifying examination is meant to determine whether the student is ready to enter the research phase of graduate studies. It consists of a 50-minute lecture by the student on a topic selected jointly by the student and the thesis advisor. The examination committee consists of at least four faculty members to be approved by the department.  At least two members of the committee must consist of faculty from the Statistics and must be members of the Academic Senate. The chair must be a member of the student’s degree-granting program.

Qualifying Exam Chair. For qualifying exam committees formed in the Fall of 2019 or later, the qualifying exam chair will also serve as the student’s departmental mentor, unless a student already has two thesis advisors. The student must select a qualifying exam chair and obtain their agreement to serve as their qualifying exam chair and faculty mentor. The student's prospective thesis advisor cannot chair the examination committee. Selection of the chair can be done well in advance of the qualifying exam and the rest of the qualifying committee, and because the qualifying exam chair also serves as the student’s departmental mentor (unless the student has co-advisors), the chair is expected to be selected by the beginning of the third year or at the beginning of the semester of the qualifying exam, whichever comes earlier. For more details regarding the selection of the Qualifying Exam Chair, see the "Mentoring" tab.  

Paperwork and Application. Students at the point of taking a qualifying exam are assumed to have already found a thesis advisor and to should have already submitted the internal departmental form to the Graduate Student Services Advisor ( found here ).  Selection of a qualifying exam chair requires that the faculty member formally agree by signing the internal department form ( found here ) and the student must submit this form to the Graduate Student Services Advisor.  In order to apply to take the exam, the student must submit the Application for the Qualifying Exam via CalCentral at least three weeks prior to the exam. If the student passes the exam, they can then officially advance to candidacy for the Ph.D. If the student fails the exam, the committee may vote to allow a second attempt. Regulations of the Graduate Division permit at most two attempts to pass the oral qualifying exam. After passing the exam, the student must submit the Application for Candidacy via CalCentral .

The Doctoral Thesis

The Ph.D. degree is granted upon completion of an original thesis acceptable to a committee of at least three faculty members. The majority or at least half of the committee must consist of faculty from Statistics and must be members of the Academic Senate. The thesis should be presented at an appropriate seminar in the department prior to filing with the Dean of the Graduate Division. See Alumni if you would like to view thesis titles of former PhD Students.

Graduate Division offers various resources, including a workshop, on how to write a thesis, from beginning to end. Requirements for the format of the thesis are rather strict. For workshop dates and guidelines for submitting a dissertation, visit the Graduate Division website.

Students who have advanced from candidacy (i.e. have taken their qualifying exam and submitted the advancement to candidacy application) must have a joint meeting with their QE chair and their PhD advisor to discuss their thesis progression; if students are co-advised, this should be a joint meeting with their co-advisors. This annual review is required by Graduate Division.  For more information regarding this requirement, please see  https://grad.berkeley.edu/ policy/degrees-policy/#f35- annual-review-of-doctoral- candidates .

Teaching Requirement

For students enrolled in the graduate program before Fall 2016, students are required to serve as a Graduate Student Instructor (GSI) for a minimum of 20 hours (equivalent to a 50% GSI appointment) during a regular academic semester by the end of their third year in the program.

Effective with the Fall 2016 entering class, students are required to serve as a GSI for a minimum of two 50% GSI appointment during the regular academic semesters prior to graduation (20 hours a week is equivalent to a 50% GSI appointment for a semester) for Statistics courses numbered 150 and above. Exceptions to this policy are routinely made by the department.

Each spring, the department hosts an annual conference called BSTARS . Both students and industry alliance partners present research in the form of posters and lightning talks. All students in their second year and beyond are required to present a poster at BSTARS each year. This requirement is intended to acclimate students to presenting their research and allow the department generally to see the fruits of their research. It is also an opportunity for less advanced students to see examples of research of more senior students. However, any students who do not yet have research to present can be exempted at the request of their thesis advisor (or their faculty mentors if an advisor has not yet been determined).

Mentoring for PhD Students

Initial Mentoring: PhD students will be assigned a faculty mentor in the summer before their first year. This faculty mentor at this stage is not expected to be the student’s PhD advisor nor even have research interests that closely align with the student. The job of this faculty mentor is primarily to advise the student on how to find a thesis advisor and in selecting appropriate courses, as well as other degree-related topics such as applying for fellowships.  Students should meet with their faculty mentors twice a semester. This faculty member will be the designated faculty mentor for the student during roughly their first two years, at which point students will find a qualifying exam chair who will take over the role of mentoring the student.

Research-focused mentoring : Once students have found a thesis advisor, that person will naturally be the faculty member most directly overseeing the student’s progression. However, students will also choose an additional faculty member to serve as a the chair of their qualifying exam and who will also serve as a faculty mentor for the student and as a member of his/her thesis committee. (For students who have two thesis advisors, however, there is not an additional faculty mentor, and the quals chair does NOT serve as the faculty mentor).

The student will be responsible for identifying and asking a faculty member to be the chair of his/her quals committee. Students should determine their qualifying exam chair either at the beginning of the semester of the qualifying exam or in the fall semester of the third year, whichever is earlier. Students are expected to have narrowed in on a thesis advisor and research topic by the fall semester of their third year (and may have already taken qualifying exams), but in the case where this has not happened, such students should find a quals chair as soon as feasible afterward to serve as faculty mentor.

Students are required to meet with their QE chair once a semester during the academic year. In the fall, this meeting will generally be just a meeting with the student and the QE chair, but in the spring it must be a joint meeting with the student, the QE chair, and the PhD advisor. If students are co-advised, this should be a joint meeting with their co-advisors.

If there is a need for a substitute faculty mentor (e.g. existing faculty mentor is on sabbatical or there has been a significant shift in research direction), the student should bring this to the attention of the PhD Committee for assistance.

PhD Student Forms:

Important milestones: .

Each of these milestones is not complete until you have filled out the requisite form and submitted it to the GSAO. If you are not meeting these milestones by the below deadline, you need to meet with the Head Graduate Advisor to ask for an extension. Otherwise, you will be in danger of not being in good academic standing and being ineligible for continued funding (including GSI or GSR appointments, and many fellowships). 

†Students who are considering a co-advisor, should have at least one advisor formally identified by the end of the second year; the co-advisor should be identified by the end of the fall semester of the 3rd year in lieu of finding a Research Mentor/QE Chair.

Expected Progress Reviews: 

* These meetings do not need to be held in the semester that you take your Qualifying Exam, since the relevant people should be members of your exam committee and will discuss your research progress during your qualifying exam

** If you are being co-advised by someone who is not your primary advisor because your primary advisor cannot be your sole advisor, you should be meeting with that person like a research mentor, if not more frequently, to keep them apprised of your progress. However, if both of your co-advisors are leading your research (perhaps independently) and meeting with you frequently throughout the semester, you do not need to give a fall research progress report.

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The Man Who Couldn’t Stop Going to College

Benjamin B. Bolger has spent his whole life amassing academic degrees. What can we learn from him?

Bolger has spent the last 30-odd years attending top universities. Credit...

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By Joseph Bernstein

• Published June 3, 2024 Updated June 5, 2024

Benjamin B. Bolger has been to Harvard and Stanford and Yale. He has been to Columbia and Dartmouth and Oxford, and Cambridge, Brandeis and Brown. Over all, Bolger has 14 advanced degrees, plus an associate’s and a bachelor’s. Some of Bolger’s degrees took many years to complete, such as a doctorate from the Harvard Graduate School of Design. Others have required rather less commitment: low-residency M.F.A.s from Ashland University and the University of Tampa, for example.

Listen to this article, read by Robert Petkoff

Some produced microscopically specific research, like Bolger’s Harvard dissertation, “Deliberative Democratic Design: Participants’ Perception of Strategy Used for Deliberative Public Participation and the Types of Participant Satisfaction Generated From Deliberative Public Participation in the Design Process.” Others have been more of a grab bag, such as a 2004 master’s from Dartmouth, for which Bolger studied Iranian sociology and the poetry of Robert Frost.

He has degrees in international development, creative nonfiction and education. He has studied “conflict and coexistence” under Mari Fitzduff, the Irish policymaker who mediated during the Troubles, and American architecture under the eminent historian Gwendolyn Wright. He is currently working, remotely, toward a master’s in writing for performance from Cambridge.

Bolger is a broad man, with lank, whitish, chin-length hair and a dignified profile, like a figure from an antique coin. One of his favorite places is Walden Pond — he met his wife there, on one of his early-morning constitutionals — and as he expounds upon learning and nature, it is easy to imagine him back in Thoreau’s time, with all the other polymathic gentlemen, perhaps by lamplight, stroking their old-timey facial hair, considering propositions about a wide range of topics, advancing theories of the life well lived.

And there’s something almost anachronistically earnest, even romantic, about the reason he gives for spending the past 30-odd years pursuing college degrees. “I love learning,” he told me over lunch last year, without even a touch of irony. I had been pestering him for the better part of two days, from every angle I could imagine, to offer some deeper explanation for his life as a perpetual student. Every time I tried, and failed, I felt irredeemably 21st-century, like an extra in a historical production who has forgotten to remove his Apple Watch.

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Appiah, Carter and Dunkley elected to Royal Society

Three members of the Princeton University faculty —  Emily Carter, Jo Dunkley and Kwame Anthony Appiah  — and graduate alumna Erin Schuman are among the 94 scientists and scholars who have become fellows or foreign members of the Royal Society in 2024. To receive this honor, nominees must have made "a substantial contribution to the improvement of natural knowledge, including mathematics, engineering science and medical science ."

Kwame Anthony Appiah

Appiah , who is Princeton's Laurance S. Rockefeller University Professor of Philosophy and the University Center for Human Values, Emeritus, is widely known as the  Ethicist at the New York Times. He is now an honorary member of the Royal Society, a recent designation intended to honor scholars who do not have the body of scientific publications that most members do. The Royal Society honored his work in "many areas of philosophy and literary and cultural studies, beginning with doctoral work in the theory of meaning, ... the intellectual history of modern African ideas about race, culture and identity, [and] questions about global ethics, defending a 'rooted cosmopolitanism.'"

Since retiring from Princeton, Appiah has taken a position as the Silver Professor of Philosophy and Law at New York University. He has also taught at Cornell, Duke, Harvard and Yale. His previous honors include an honorary fellowship at Clare College, Cambridge; the presidency of the American Academy of Arts and Letters; a National Humanities Medal presented by President Obama in 2012; and in May 2023, he delivered Princeton's Baccalaureate address . He has a B.A. and Ph.D. from the University of Cambridge, both in philosophy.

Emily Carter

Carter, now a foreign member of the Royal Society, is the Gerhard R. Andlinger Professor in Energy and the Environment at Princeton University, and the senior strategic advisor and associate laboratory director at the U.S. Department of Energy's Princeton Plasma Physics Laboratory (PPPL). She has held many roles at Princeton, including serving as the founding director of the Andlinger Center for Energy and the Environment and the dean of the School of Engineering and Applied Science. 

The Royal Society honored "her pioneering development and application of quantum-mechanics-based atomic- and multi-scale simulation tools that have produced deep insights into materials science, sustainable energy and carbon mitigation." Her previous awards include election to the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, the U.S. National Academy of Inventors, the U.S. National Academy of Engineering, and the European Academy of Sciences.

Carter earned her bachelor’s degree in chemistry from the University of California-Berkeley and her doctoral degree in chemistry at Caltech. 

Dunkley, Princeton's Joseph Henry Professor of Physics and Astrophysical Sciences, is named a fellow of the Royal Society for her work in "cosmology, studying the origins and evolution of the universe. She plays leading roles in the international Atacama Cosmology Telescope and Simons Observatory projects, which measure the earliest accessible image of the universe." She has played significant roles in the European Space Agency’s Planck satellite project and NASA's Wilkinson Microwave Anisotropy Probe (WMAP), for which she and the other members of the WMAP science team shared the 2017 Breakthrough Prize and the Gruber Cosmology Prize.

Her other major honors include the Order of the British Empire, the Maxwell Medal, the Rosalind Franklin award and the New Horizons prize. She received her undergraduate and master's degrees from the University of Cambridge in physics, and her Ph.D. from the University of Oxford in astrophysics. She pursued postdoctoral studies at Princeton, then taught at Oxford until she joined the Princeton faculty in 2016.

Erin Schuman, a 1990 Ph.D. graduate of Princeton in philosophy and a new foreign member of the Royal Society, is the founding director of the Max Planck Institute for Brain Research. Her other honors include membership in the German Academy of Sciences Leopoldina, the American Academy of Arts and Sciences, and the U.S. National Academy of Sciences. 

Read the full announcement at the Royal Society website.

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From Voronoi Cells to Algebraic Statistics

Author:  Yulia Alexandr Bernd Sturmfels Publication date:  December 15, 2023 Publication type:  PhD Thesis (Author field refers to student + advisor)