## Overview

The Department of Mathematics is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the world. With approximately 55 regular faculty members representing most of the major fields of current research, along with 25 to 30 postdoctoral scholars, 180 graduate students, 475 undergraduate majors, one of the finest mathematics libraries in the nation, and a favorable climate in one of 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. In addition, the Noetherian Ring, an organization seeking to promote and support women in mathematics at Berkeley, is open to undergraduate students.

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. There are two NSF funded Research Training Groups: one in Representation Theory, Geometry and Combinatorics and one in Geometry, Topology and Operator Algebras. These groups run seminars, workshops, and other activities and support graduate student 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; and a student lecture series, Many Cheerful Facts.

### Facilities

The Mathematics Library on the first floor of Evans Hall, part of the system of 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: MA, PhD

## Courses

### Mathematics

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

**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.<BR/>

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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 [+]

**Rules & Requirements**

**Prerequisites:** 1A

**Credit Restrictions:** Students will receive no credit for Mathematics H1B after completing Mathematics 1B or N1B. <BR/>

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**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 N1A after completing MATH 1A, MATH 16B or MATH N16B. A deficient grade in MATH N1A may be removed by taking MATH 1A.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**Prerequisites:** 1A or N1A

**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.<BR/>

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Summer 2018 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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Spring 2019, Summer 2018 8 Week Session, Spring 2018

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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**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 Math N10A after completing Math 10A. A deficient grade in Math N10A may be removed by completing Math 10A.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: 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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

**Summer:** 8 weeks - 8 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

**Summer:** 8 weeks - 8 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

**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.

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**Prerequisites:** Three years of high school mathematics

**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<BR/>maybe removed by taking MATH N32.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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 [+]

**Rules & Requirements**

**Prerequisites:** Priority given to freshmen and sophomores

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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 [+]

**Rules & Requirements**

**Prerequisites:** Some units in a lower division Mathematics class

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2018, Spring 2017, Fall 2015

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 [+]

**Rules & Requirements**

**Prerequisites:** 1B

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

**Prerequisites:** Mathematics 1B or N1B

**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.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 8 Week Session, Summer 2018 8 Week Session, Summer 2017 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 [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Online:** This is an online course.

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

**Instructor:** Hutchings

Terms offered: Fall 2019, Spring 2019, Fall 2018

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, application to partial differential equations.

Linear Algebra and Differential Equations: Read More [+]

**Rules & Requirements**

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

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2017, Fall 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** 1B

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Summer 2019 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, application to partial differential equations.

Linear Algebra and Differential Equations: Read More [+]

**Rules & Requirements**

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

**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.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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

Discrete Mathematics: Read More [+]

**Rules & Requirements**

**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.

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 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 [+]

**Rules & Requirements**

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

**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.

**Hours & Format**

**Summer:** 8 weeks - 10 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2009, Fall 2008, Summer 2008 8 Week Session

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2016, Fall 2012, Spring 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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Summer:** 8 weeks - 6 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2017 8 Week Session, Summer 2015 10 Week Session, Summer 2014 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 [+]

**Rules & Requirements**

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Fall 2018, Spring 2018

Directed Group Study, topics vary with instructor.

Supervised Group Study: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Summer:** 8 weeks - 1.5-7.5 hours of directed group study per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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 [+]

**Rules & Requirements**

**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.

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2018, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** Math 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

**Formerly known as:** 103

**Also listed as:** ECON C103

Terms offered: Fall 2019, Summer 2019 8 Week Session, Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Summer:** 8 weeks - 8 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Summer 2019 8 Week Session, Spring 2019

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

Linear Algebra: Read More [+]

**Rules & Requirements**

**Prerequisites:** 54 or a course with equivalent linear algebra content

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 54 or a course with equivalent linear algebra content

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Summer 2019 8 Week Session, Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** 54 or a course with equivalent linear algebra content

**Hours & Format**

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

**Summer:** 8 weeks - 8 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 54 or a course with equivalent linear algebra content

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 110 and 113, or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Summer 2019 8 Week Session, Spring 2019, Summer 2018 8 Week Session

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2018, Fall 2015, Fall 2014

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

Cryptography: Read More [+]

**Rules & Requirements**

**Prerequisites:** 55

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Fall 2017, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** Math 53, 54, 55

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** Math 113 or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Summer 2019 8 Week Session, Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Summer:** 8 weeks - 6 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Introduction to Partial Differential Equations: Read Less [-]

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Fall 2019, Summer 2019 8 Week Session, Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 110 and 128A

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Fall 2017, Fall 2016

A critical examination of Euclid's Elements; ruler and compass constructions; connections with Galois theory; Hilbert's axioms for geometry, theory of areas, introduction of coordinates, non-Euclidean geometry, regular solids, projective geometry.

The Classical Geometries: Read More [+]

**Rules & Requirements**

**Prerequisites:** 110 and 113

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 113 and 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Spring 2018

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 [+]

**Rules & Requirements**

**Prerequisites:** 53, 54, and 55

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Fall 2017, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 104 or equivalent and linear algebra

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Spring 2018

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 [+]

**Rules & Requirements**

**Prerequisites:** 104 and 113

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2018, Spring 2018, Fall 2016

Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.

Elementary Algebraic Geometry: Read More [+]

**Rules & Requirements**

**Prerequisites:** 113

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Spring 2017

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Spring 2019, Fall 2017, Fall 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** 151; 54, 113, or equivalent

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Spring 2018, Spring 2017, Spring 2016

The real line and least upper bound, limit and decimal expansion of a number, differentiation and integration, Fundamental Theorem of Calculus, characterizations of sine, cosine, exp, and log.

Mathematics of the Secondary School Curriculum III: Read More [+]

**Rules & Requirements**

**Prerequisites:** 151, 152

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53, 54, and 113

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 53 and 54

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2018, Spring 2017, Spring 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** 55

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Summer 2019 8 Week Session, Summer 2019 First 6 Week Session

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Summer:** 8 weeks - 8 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2019, Spring 2018, Spring 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2015, Fall 2014, Fall 2013

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 [+]

**Rules & Requirements**

**Prerequisites:** 104, 110, 2 semesters lower division Physics

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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

Terms offered: Fall 2019, Summer 2019 First 6 Week Session, Spring 2019

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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2011, Spring 2004, Spring 2003

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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2017, Spring 2016, Spring 2015

Independent study of an advanced topic leading to an honors thesis.

Honors Thesis: Read More [+]

**Rules & Requirements**

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

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

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 [+]

**Rules & Requirements**

**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.

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

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Spring 2017, Fall 2016, Spring 2016

Topics will vary with instructor.

Directed Group Study: Read More [+]

**Rules & Requirements**

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

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

**Hours & Format**

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

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

Supervised Independent Study and Research: Read More [+]

**Rules & Requirements**

**Prerequisites:** The standard college regulations for all 199 courses

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Undergraduate

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 202A and 110

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2011, Spring 2011, Spring 2010

Asymptotic methods for differential equations, with emphasis upon many physical examples. Topics will include matched asymptotic expansions, Laplace's method, stationary phase, boundary layers, multiple scales, WKB approximations, asymptotic Lagrangians, bifurcation theory.

Asymptotic Analysis in Applied Mathematics: Read More [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2016, Spring 2016, Fall 2014

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 [+]

**Rules & Requirements**

**Prerequisites:** 104

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 185

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Fall 2016, Fall 2015

Banach algebras. Spectrum of a Banach algebra element. Gelfand theory of commutative Banach algebras. Analytic functional calculus. Hilbert space operators. C*-algebras of operators. Commutative C*-algebras. Spectral theorem for bounded self-adjoint and normal operators (both forms: the spectral integral and the "multiplication operator" formulation). Riesz theory of compact operators. Hilbert-Schmidt operators. Fredholm operators. The Fredholm index. Selected additional topics.

Banach Algebras and Spectral Theory: Read More [+]

**Rules & Requirements**

**Prerequisites:** 202A-202B

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Spring 2018, Spring 2015

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 [+]

**Rules & Requirements**

**Prerequisites:** 206

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2017, Spring 2014, Spring 2012

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 [+]

**Rules & Requirements**

**Prerequisites:** 206

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Spring 2016, Fall 2014

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Fall 2017, Spring 2017

Smooth manifolds and maps, tangent and normal bundles. Sard's theorem and transversality, Whitney embedding theorem. Morse functions, differential forms, Stokes' theorem, Frobenius theorem. Basic degree theory. Flows, Lie derivative, Lie groups and algebras. Additional topics selected by instructor.

Differentiable Manifolds: Read More [+]

**Rules & Requirements**

**Prerequisites:** 202A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructors:** 113C, 202A, and 214

Terms offered: Spring 2019, Spring 2016, Spring 2015

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructors:** 113C, 202A, and 214

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Also listed as:** STAT C205A

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Also listed as:** STAT C205B

Terms offered: Spring 2018, Fall 2016, Spring 2015

Diffeomorphisms and flows on manifolds. Ergodic theory. Stable manifolds, generic properties, structural stability. Additional topics selected by the instructor.

Dynamical Systems: Read More [+]

**Rules & Requirements**

**Prerequisites:** 214

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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 [+]

**Rules & Requirements**

**Prerequisites:** Some familiarity with differential equations and their applications

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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

Terms offered: Spring 2018, Fall 2016, Spring 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

**Hours & Format**

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

**Summer:** 8 weeks - 6 hours of lecture per week

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 105 or 202A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 105 or 202A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2016, Fall 2015, Fall 2014, Fall 2013

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 [+]

**Rules & Requirements**

**Prerequisites:** Statistics C205A-C205B or consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Also listed as:** STAT C206A

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

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Also listed as:** STAT C206B

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

Terms offered: Fall 2019, Fall 2016, Fall 2014

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 [+]

**Rules & Requirements**

**Prerequisites:** Graduate status or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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

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

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 [+]

**Rules & Requirements**

**Prerequisites:** Graduate status or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 125B and 135

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 125B and 135.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 125B and 135

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 125B and 135.

Terms offered: Fall 2015, Fall 2013, Spring 2012

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 [+]

**Rules & Requirements**

**Prerequisites:** Mathematics <BR/>225B

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 225C.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 128A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 128A-128B.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 128A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 128A-128B.

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 [+]

**Rules & Requirements**

**Prerequisites:** 225B

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Spring 2014, Fall 2011

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 [+]

**Rules & Requirements**

**Prerequisites:** 125A and 135

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 125A and 135.

Terms offered: Fall 2014, Fall 2010, Spring 2009

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 [+]

**Rules & Requirements**

**Prerequisites:** 225B and 235A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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 [+]

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Also listed as:** MCELLBI C244

Terms offered: Fall 2019, Fall 2018, Fall 2016

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 [+]

**Rules & Requirements**

**Prerequisites:** 214

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2017, Fall 2014, Spring 2013

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 [+]

**Rules & Requirements**

**Prerequisites:** 214 and 215A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2019, Fall 2017, Fall 2015

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 [+]

**Rules & Requirements**

**Prerequisites:** 214

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** Pachter

**Also listed as:** MCELLBI C243

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 [+]

**Rules & Requirements**

**Prerequisites:** Math 113

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Fall 2017, Fall 2016

(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 [+]

**Rules & Requirements**

**Prerequisites:** 250A or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 114 or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2019, Spring 2018, Spring 2017

Tensor algebras and exterior algebras, with application to linear transformations. Commutative ideal theory, localization. Elementary specialization and valuation theory. Related topics in algebra.

Multilinear Algebra and Further Topics: Read More [+]

**Rules & Requirements**

**Prerequisites:** 250A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2016, Spring 2013, Fall 2009

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

Ring Theory: Read More [+]

**Rules & Requirements**

**Prerequisites:** 250A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2015, Fall 2014, Fall 2013

Structure of finite dimensional algebras, applications to representations of finite groups, the classical linear groups.

Representation Theory: Read More [+]

**Rules & Requirements**

**Prerequisites:** 250A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2016, Fall 2014, Summer 2014 10 Week Session

Modules over a ring, homomorphisms and tensor products of modules, functors and derived functors, homological dimension of rings and modules.

Homological Algebra: Read More [+]

**Rules & Requirements**

**Prerequisites:** 250A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

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

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 250A.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 254A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 250A.

Terms offered: Spring 2019, Fall 2014, Fall 2011

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 [+]

**Rules & Requirements**

**Prerequisites:** 250A-250B or consent of instructor

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Fall 2017

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 250A.

Terms offered: Spring 2019, Spring 2018, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** 256A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 250A.

Terms offered: Spring 2018, Spring 2014, Fall 2011

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 [+]

**Rules & Requirements**

**Prerequisites:** 250A

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Fall 2016, Spring 2015

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Spring 2017, Fall 2015

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 [+]

**Rules & Requirements**

**Prerequisites:** 214

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 214.

Terms offered: Fall 2017, Spring 2016, Spring 2014

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 [+]

**Rules & Requirements**

**Prerequisites:** 214

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

**Instructor:** 214.

Terms offered: Spring 2011, Fall 2008, Fall 2004

Approximations, degrees of maps, vector bundles, tubular neighborhoods. Introduction to Morse theory, handlebodies, cobordism, surgery. Additional topics selected by instructor from: characteristic classes, classification of manifolds, immersions, embeddings, singularities of maps.

Differential Topology: Read More [+]

**Rules & Requirements**

**Prerequisites:** 214 plus 215A or some familiarity with algebraic topology

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2019, Spring 2018, Fall 2017

This course will give introductions to current research developments. Every semester we will pick a different topic and go through the relevant literature. Each student will be expected to give one presentation.

Hot Topics Course in Mathematics: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Offered for satisfactory/unsatisfactory grade only.

Terms offered: 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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: 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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Spring 2018, Spring 2017, Fall 2016

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

Topics in Algebra: Read More [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Spring 2017, Spring 2014

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

Topics in Applied Mathematics: Read More [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2017, Spring 2016, Spring 2015

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

Topics in Topology: Read More [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Spring 2018, Spring 2017

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

Topics in Differential Geometry: Read More [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2019, Fall 2018, Spring 2018

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

Topics in Analysis: Read More [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Fall 2018, Fall 2017, Spring 2017

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 [+]

**Rules & Requirements**

**Prerequisites:** Consent of instructor

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Letter grade.

Terms offered: Summer 2016 10 Week Session, Spring 2016, Fall 2015

Intended for candidates for the Ph.D. degree.

Individual Research: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

**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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

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

Terms offered: Summer 2006 10 Week Session, Summer 2002 10 Week Session, Summer 2001 10 Week Session

Intended for candidates for the Ph.D. degree.

Individual Research: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

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

Terms offered: Not yet offered

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 [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate

**Grading:** Offered for satisfactory/unsatisfactory grade only.

Terms offered: Fall 2019, Fall 2018, Fall 2017

Investigation of special problems under the direction of members of the department.

Reading Course for Graduate Students: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

**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 Details**

**Subject/Course Level:** Mathematics/Graduate

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

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 [+]

**Rules & Requirements**

**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

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

**Hours & Format**

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

**Additional Details**

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

**Grading:** Offered for pass/not pass grade only.

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 [+]

**Hours & Format**

**Summer:** 8 weeks - 1 hour of lecture per week

**Additional Details**

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

**Grading:** Offered for satisfactory/unsatisfactory grade only.

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 [+]

**Rules & Requirements**

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

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

**Hours & Format**

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

**Additional Details**

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

**Grading:** Offered for satisfactory/unsatisfactory grade only.

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

Terms offered: Fall 2019, Spring 2019, Fall 2018

Mandatory for all graduate student instructors teaching for the first time in the Mathematics Department. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis of videotapes, reciprocal classroom visitations, and an individual project.

Teaching Workshop: Read More [+]

**Rules & Requirements**

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

**Hours & Format**

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

**Additional Details**

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

**Grading:** Offered for satisfactory/unsatisfactory grade only.

**Formerly known as:** Mathematics 300

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 [+]

**Rules & Requirements**

**Prerequisites:** For candidates for master's degree

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

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

**Hours & Format**

**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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate examination preparation

**Grading:** Offered for satisfactory/unsatisfactory grade only.

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 [+]

**Rules & Requirements**

**Prerequisites:** For qualified graduate students

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

**Hours & Format**

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

**Additional Details**

**Subject/Course Level:** Mathematics/Graduate examination preparation

**Grading:** Offered for satisfactory/unsatisfactory grade only.

## Faculty and Instructors

**+ **Indicates this faculty member is the recipient of the Distinguished Teaching Award.

#### Faculty

**Mina Aganagic, Professor. **Particle physics.

Research Profile

**Ian Agol, Professor. **Low-dimensional topology.

**David Aldous, Professor. **Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, complex networks, random networks, entropy, spatial networks.

Research Profile

**Denis Auroux, Professor. **Mirror symmetry, symplectic topology.

Research Profile

**Richard H. Bamler, Assistant Professor. **

**Richard E. Borcherds, Professor. **Mathematics, lie algebras, vertex algebras, automorphic forms.

Research Profile

**+ F. Michael Christ, Professor. **Mathematics, harmonic analysis, partial differential equations, complex analysis in several variables, spectral analysis of Schrodinger operators.

Research Profile

**James W. Demmel, Professor. **Computer science, scientific computing, numerical analysis, linear algebra.

Research Profile

**Semyon Dyatlov, Assistant Professor. **Microlocal analysis, scattering theory, quantum chaos, PDE.

Research Profile

**David Eisenbud, Professor. **Mathematics, algebraic geometry, commutative algebra, computation.

Research Profile

**Lawrence C. Evans, Professor. **Optimization theory, nonlinear partial differential equations, calculus of variations.

Research Profile

**Steven N. Evans, Professor. **Genetics, random matrices, superprocesses and other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.

Research Profile

**Edward Frenkel, Professor. **Mathematics, representation theory, integrable systems, mathematical physics.

Research Profile

**Alexander B. Givental, Professor. **Mathematics, mathematical physics, symplectic geometry, singularities, mirror symmetry.

Research Profile

**Ming Gu, Professor. **Mathematics, scientific computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations.

Research Profile

**Mark D. Haiman, Professor. **Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes.

Research Profile

**Alan Hammond, Associate Professor. **Statistical mechanics.

**Jenny Harrison, Professor. **Mathematics, geometric analysis.

Research Profile

**Olga V. Holtz, Professor. **Numerical analysis, matrix and operator theory, approximation theory, wavelets and splines, orthogonal polynomials and special functions, analysis of algorithms and computational complexity.

Research Profile

**Michael Hutchings, Professor. **Mathematics, low dimensional, symplectic topology, geometry.

Research Profile

**Michael J. Klass, Professor. **Statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums.

Research Profile

**Lin Lin, Assistant Professor. **Numerical analysis, computational quantum chemistry, computational materials science.

**John W. Lott, Professor. **Differential geometry.

**Antonio Montalban, Associate Professor. **Mathematical logic.

Research Profile

**David Nadler, Professor. **Geometric representation.

**Martin Olsson, Professor. **Algebraic geometry, arithmetic geometry.

Research Profile

**Per-Olof Persson, Associate Professor. **Applied mathematics, numerical methods, computational fluid and solid mechanics.

Research Profile

**James W. Pitman, Professor. **Fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence.

Research Profile

**Nicolai Reshetikhin, Professor. **Mathematics, representation theory, mathematical physics, low-dimensional topology.

Research Profile

**Fraydoun Rezakhanlou, Professor. **Mathematics, probability theory, partial differential equations.

Research Profile

**Kenneth A. Ribet, Professor. **Mathematics, algebraic geometry, algebraic number theory.

Research Profile

**Marc Rieffel, Professor. **Mathematics, operator algebras, non-commutative geometry, non-commutative harmonic analysis, quantum geometry.

Research Profile

**Thomas Scanlon, Professor. **Mathematics, model theory, applications to number theory.

Research Profile

**Vera Serganova, Professor. **Mathematics, Super-representation theory.

Research Profile

**James A. Sethian, Professor. **Mathematics, applied mathematics, partial differential equations, computational physics, level set Methods, computational fluid mechanics and materials sciences. fast marching methods.

Research Profile

**Chris Shannon, Professor. **Economics, mathematical economics, economic theory.

Research Profile

**Vivek V. Shende, Assistant Professor. **Geometry.

**Sug Woo Shin, Associate Professor. **Number theory, automorphic forms.

**Pierre Simon, Assistant Professor. **Mathematical Logic, Model theory.

Research Profile

**Theodore A. Slaman, Professor. **Mathematics, recursion theory.

Research Profile

**Nikhil Srivastava, Assistant Professor. **Theoretical computer science, random matrices, geometry of polynomials.

**Zvezdelina Stankova, Teaching Professor. **Algebraic geometry, representation theory, combinatorics, Olympiad problem solving, Berkeley Math Circle.

Research Profile

**John Strain, Professor. **Mathematics, numerical analysis, applied mathematics, fast algorithms, materials science.

Research Profile

**Bernd Sturmfels, Professor. **Mathematics, combinatorics, computational algebraic geometry.

Research Profile

**Song Sun, Associate Professor. **Differential Geometry.

Research Profile

**Daniel Ioan Tataru, Professor. **Mathematics, partial differential equations, nonlinear waves.

Research Profile

**Constantin Teleman, Professor. **Lie algebras, algebraic geometry, Lie groups, topology, topological quantum field theory.

Research Profile

**Luca Trevisan, Professor. **Computational complexity, spectral graph theory.

**Dan Voiculescu, Professor. **Random matrices, pperator algebras, free probability theory.

Research Profile

**Paul A. Vojta, Professor. **Mathematics, algebraic geometry, diophantine geometry, Nevanlinna theory, Arakelov theory.

Research Profile

**Katrin Wehrheim, Associate Professor. **Low-dimensional and symplectic topology.

**Jon Wilkening, Professor. **Applied mathematics, numerical analysis, computational solid and fluid mechanics.

Research Profile

**Lauren K. Williams, Professor. **Algebraic combinatorics.

Research Profile

**Mariusz Wodzicki, Professor. **Analysis, mathematics, Non-commutative and algebraic geometry, K-theory.

Research Profile

**Xinyi Yuan, Assistant Professor. **Number theory.

Research Profile

**Maciej Zworski, Professor. **Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.

Research Profile

#### Lecturers

**Emiliano Gomez, Lecturer. **

**Alexander Paulin, Lecturer. **

**Kelli Talaska, Lecturer. **

#### Visiting Faculty

**Carolyn Abbott, Visiting Assistant Professor. **

**Semeon Artamonov, Visiting Assistant Professor. **

**Daniel Bragg, RTG Postdoc. **

**James Conway, Visiting Assistant Professor. **

**David Corwin, RTG Postdoc. **

**Wilfrid Gangbo, Chancellor's Professor. **

**Charles Hadfield, Visiting Assistant Professor. **

**Marina Iliopoulou, Visiting Assistant Professor. **

**Casey Jao, NSF Postdoc. **

**Tim Laux, Visiting Assistant Professor. **

**Koji Shimizu, Visiting Assistant Professor. **

**Slobodan Simic, Visiting Professor. **

**Dmitry Tonkonog, Visiting Assistant Professor. **

**Dimitry Vaintrob, Visiting Assistant Professor. **

**Xuwen Zhu, Visiting Assistant Professor. **

#### Emeritus Faculty

**John W. Addison, Professor Emeritus. **Mathematics, theory of definability, descriptive set theory, model theory, recursive function theory.

Research Profile

**Robert Anderson, Professor Emeritus. **Finance, probability theory, mathematical economics, nonstandard analysis.

Research Profile

**Grigory I. Barenblatt, Professor Emeritus. **Applied mathematics, Solid mechanics, Fluid mechanics, similarity methods asymptotics, mechanics of deformable solids.

Research Profile

**George Bergman, Professor Emeritus. **Mathematics, associative rings, universal algebra, category theory, counterexamples.

Research Profile

**Elwyn R. Berlekamp, Professor Emeritus. **Computer science, electrical engineering, mathematics, combinatorial game theory, algebraic coding theory.

Research Profile

**Robert Bryant, Professor Emeritus. **Symplectic geometry, differential geometry, Lie groups, geometric partial differential equations.

Research Profile

**Alexandre J. Chorin, Professor Emeritus. **Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods.

Research Profile

**Paul Concus, Professor Emeritus. **Fluid mechanics, numerical analysis, applied mathematics, capillarity.

Research Profile

**Heinz O. Cordes, Professor Emeritus. **Mathematics, classical analysis.

Research Profile

**F. Alberto Grunbaum, Professor Emeritus. **Medical imaging, x-ray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birth-and-death processes.

Research Profile

**+ Ole H. Hald, Professor Emeritus. **Mathematics, numerical analysis.

Research Profile

**Leo A. Harrington, Professor Emeritus. **Mathematics, model theory, recursion theory, set theory.

Research Profile

**Robert C. Hartshorne, Professor Emeritus. **Mathematics, algebraic geometry.

Research Profile

**Morris W. Hirsch, Professor Emeritus. **Game theory, dynamical systems, topology, biological models.

Research Profile

**Wu-Yi Hsiang, Professor Emeritus. **Mathematics, transformation groups, differential geometry.

Research Profile

**Vaughan F. R. Jones, Professor Emeritus. **Mathematics, Von Neumann algebras.

Research Profile

**William M. Kahan, Professor Emeritus. **Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems.

Research Profile

**Robion C. Kirby, Professor Emeritus. **Mathematics, topology of manifolds.

Research Profile

**Tsit-Yuen Lam, Professor Emeritus. **

**R. Sherman Lehman, Professor Emeritus. **

**H. W. Lenstra, Professor Emeritus. **

**Ralph N. McKenzie, Professor Emeritus. **Mathematics, logic, universal algebra, general algebra, lattice theory.

Research Profile

**Keith Miller, Professor Emeritus. **Mathematics, partial differential equations, numerical methods for PDE's.

Research Profile

**Calvin C. Moore, Professor Emeritus. **Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K- theory.

Research Profile

**John Neu, Professor Emeritus. **

**Andrew Ogg, Professor Emeritus. **

**Arthur E. Ogus, Professor Emeritus. **Mathematics, algebraic geometry, algebraic differential equations, log poles.

Research Profile

**Beresford N. Parlett, Professor Emeritus. **Numerical analysis, scientific computation.

**Charles C. Pugh, Professor Emeritus. **Mathematics, global theory of differential equations.

Research Profile

**John L. Rhodes, Professor Emeritus. **Mathematics, algebra, semigroups, automata.

Research Profile

**Rainer K. Sachs, Professor Emeritus. **Mathematical biology.

Research Profile

**Isadore M. Singer, Professor Emeritus. **Mathematics, physics, partial differential equations, geometry.

Research Profile

**Stephen Smale, Professor Emeritus. **Algorithms, mathematics, numerical analysis, global analysis.

Research Profile

**Robert M. Solovay, Professor Emeritus. **

**John Steel, Professor Emeritus. **Mathematics, descriptive set theory, set theory, fine structure.

Research Profile

**Peter Teichner, Professor Emeritus. **Topology, quantum field theory.

Research Profile

**John B. Wagoner, Professor Emeritus. **Mathematics, dynamical systems, differential topology, algebraic K-theory.

Research Profile

**Alan Weinstein, Professor Emeritus. **Mathematics, mathematical physics, symplectic geometry.

Research Profile

**Joseph A. Wolf, Professor Emeritus. **Harmonic analysis, differential geometry, Lie groups.

Research Profile

**W. Hugh Woodin, Professor Emeritus. **Mathematics, set theory, large cardinals.

Research Profile

**Hung-Hsi Wu, Professor Emeritus. **Real and complex geometry, school mathematics education.

Research Profile

## Contact Information

#### Vice-Chair for Undergraduate Affairs

Olga Holtz

821 Evans Hall

Phone: 510-642-2122

#### Vice-Chair for Graduate Affairs

Jon Wilkening

1051 Evans Hall

Phone: 510-643-7990