Mathematics

University of California, Berkeley

This is an archived copy of the 2016-17 guide. To access the most recent version of the guide, please visit http://guide.berkeley.edu.

About the Program

Bachelor of Arts (BA)

The Department of Mathematics offers an undergraduate major program in mathematics, leading to the Bachelor of Arts (BA) degree. Major programs within the department provide excellent preparation for advanced degrees in math, physical sciences, economics, and industrial engineering as well as graduate study in business, education, law, and medicine. They also prepare students for post-baccalaureate positions in business, technology, industry, teaching, government, and finance.

Students majoring in Mathematics may choose to major with a teaching concentration. The teaching concentration is designed to increase the number and quality of math teachers.

Admission to the Major

Students should contact a mathematics undergraduate adviser. Contact information is available on the contact tab or  here.

Honors Program

In addition to completing the requirements for the major in mathematics, students in the honors program must:

  1. Earn a grade point average (GPA) of at least 3.5 in upper division and graduate courses in the major and at least 3.3 in all courses taken at the University.
  2. Complete either MATH 196, in which they will write a senior honors thesis, or pass two graduate mathematics courses with a grade of at least A-.
  3. Receive the recommendation of the head major adviser.

Students interested in the honors program should consult with an adviser early in their program, preferably by their junior year.

Minor Program

The department offers a minor in Mathematics.

Other Major Offered by the Department of Mathematics

Applied Mathematics  (Major only)

Visit Department Website

Major Requirements

In addition to the University, campus, and college requirements, listed on the College Requirements tab, students must fulfill the below requirements specific to their major program.

General Guidelines

  1. All courses taken to fulfill the major requirements below must be taken for graded credit, other than courses listed which are offered on a Pass/No Pass basis only. 
  2. No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs, with the exception of minors offered outside of the College of Letters & Science.
  3. A minimum grade point average (GPA) of 2.0 must be maintained in both upper and lower division courses used to fulfill the major requirements.

For information regarding residence requirements and unit requirements, please see the College Requirements tab.

Major Requirements: Mathematics

Lower Division
MATH 1ACalculus4
MATH 1BCalculus4
MATH 53Multivariable Calculus4
MATH 54Linear Algebra and Differential Equations4
MATH 55Discrete Mathematics 14
Upper Divison
MATH 104Introduction to Analysis4
MATH 110Linear Algebra4
MATH 113Introduction to Abstract Algebra4
MATH 185Introduction to Complex Analysis4
Two semi-electives
Select one course from two of the following three areas:
Computing
Numerical Analysis
Geometry
The Classical Geometries
Metric Differential Geometry
Elementary Differential Topology
Elementary Algebraic Topology
Elementary Algebraic Geometry
Logic and Foundations
Mathematical Logic
Introduction to the Theory of Sets
Incompleteness and Undecidability
Two electives, select at least two additional upper division or graduate mathematics courses must be taken 2
1

COMPSCI 70 can be substituted for MATH 55 for students with a double major in Computer Science or Electrical Engineering and Computer Science

2

These two electives must receive the Faculty Adviser's written approval on the Course Approval Form which is then returned to an Undergraduate Adviser in 964 or 965 Evans for the student's file. Courses in other departments may count toward this requirement provided they have substantial mathematical content and are offered for at least 3 units each. 

Major Requirements: Mathematics with a Teaching Concentration
Lower division
STAT 20Introduction to Probability and Statistics4
MATH 1ACalculus4
MATH 1BCalculus4
MATH 53Multivariable Calculus4
MATH 54Linear Algebra and Differential Equations4
MATH 55Discrete Mathematics 14
Upper division
MATH 110Linear Algebra4
MATH 113Introduction to Abstract Algebra4
Select two of the following:
Numerical Analysis
The Classical Geometries
Introduction to the Theory of Sets
MATH 151Mathematics of the Secondary School Curriculum I4
MATH 152Mathematics of the Secondary School Curriculum II4
MATH 153Mathematics of the Secondary School Curriculum III4
MATH 160History of Mathematics4
Recommended courses:
Sudents are encouraged, though not required, to take, the following:
MATH 104Introduction to Analysis4
MATH 115Introduction to Number Theory4
MATH 185Introduction to Complex Analysis4
1

COMPSCI 70 can be substituted for MATH 55 for students with a double major in Computer Science or Electrical Engineering and Computer Science.

 

Minor Requirements

Students who have a strong interest in an area of study outside their major often decide to complete a minor program. These programs have set requirements and are noted officially on the transcript in the memoranda section, but they are not noted on diplomas.

General Guidelines

  1. All courses taken to fulfill the minor requirements below must be taken for graded credit.
  2. A minimum of three of the upper division courses taken to fulfill the minor requirements must be completed at UC Berkeley.
  3. A minimum grade point average of 2.0 is required for the lower division minor requirements as well as for the five upper division courses used for the minor.
  4. Courses used to fulfill the minor requirements may be applied toward the Seven-Course Breadth requirement, for Letters & Science students.
  5. No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs.
  6. All minor requirements must be completed prior to the last day of finals during the semester in which the student plans to graduate. 
  7. All minor requirements must be completed within the unit ceiling. (For further information regarding the unit ceiling, please see the College Requirements tab.)

 Requirements

Lower Division
MATH 1ACalculus4
MATH 1BCalculus4
MATH 53Multivariable Calculus4
MATH 54Linear Algebra and Differential Equations4
Upper Division
MATH 104Introduction to Analysis4
MATH 110Linear Algebra4
MATH 113Introduction to Abstract Algebra4
MATH 185Introduction to Complex Analysis4
One elective: select one additional upper division math course4

College Requirements

Undergraduate students in the College of Letters & Science must fulfill the following requirements in addition to those required by their major program.

For detailed lists of courses that fulfill college requirements, please review the College of Letters & Sciences  page in this Guide.

Entry Level Writing

All students who will enter the University of California as freshmen must demonstrate their command of the English language by fulfilling the Entry Level Writing requirement. Fulfillment of this requirement is also a prerequisite to enrollment in all reading and composition courses at UC Berkeley. 

American History and American Institutions

The American History and Institutions requirements are based on the principle that a US resident graduated from an American university should have an understanding of the history and governmental institutions of the United States.

American Cultures

American Cultures is the one requirement that all undergraduate students at Cal need to take and pass in order to graduate. The requirement offers an exciting intellectual environment centered on the study of race, ethnicity and culture of the United States. AC courses offer students opportunities to be part of research-led, highly accomplished teaching environments, grappling with the complexity of American Culture.

Quantitative Reasoning

The Quantitative Reasoning requirement is designed to ensure that students graduate with basic understanding and competency in math, statistics, or computer science. The requirement may be satisfied by exam or by taking an approved course.

Foreign Language

The Foreign Language requirement may be satisfied by demonstrating proficiency in reading comprehension, writing, and conversation in a foreign language equivalent to the second semester college level, either by passing an exam or by completing approved course work.

Reading and Composition

In order to provide a solid foundation in reading, writing and critical thinking the College requires two semesters of lower division work in composition in sequence. Students must complete a first-level reading and composition course by the end of their second semester and a second-level course by the end of their fourth semester.

Breadth Requirements

The undergraduate breadth requirements provide Berkeley students with a rich and varied educational experience outside of their major program. As the foundation of a liberal arts education, breadth courses give students a view into the intellectual life of the University while introducing them to a multitude of perspectives and approaches to research and scholarship. Engaging students in new disciplines and with peers from other majors, the breadth experience strengthens interdisciplinary connections and context that prepares Berkeley graduates to understand and solve the complex issues of their day.

Unit Requirements

  • 120 total units, including at least 60 L&S units

  • Of the 120 units, 36 must be upper division units

  • Of the 36 upper division units, 6 must be taken in courses offered outside your major department

Residence Requirements

For units to be considered in "residence," you must be registered in courses on the Berkeley campus as a student in the College of Letters & Science. Most students automatically fulfill the residence requirement by attending classes here for four years. In general, there is no need to be concerned about this requirement, unless you go abroad for a semester or year or want to take courses at another institution or through UC Extension during your senior year. In these cases, you should make an appointment to meet an adviser to determine how you can meet the Senior Residence Requirement.

Note: Courses taken through UC Extension do not count toward residence.

Senior Residence Requirement

After you become a senior (with 90 semester units earned toward your BA degree), you must complete at least 24 of the remaining 30 units in residence in at least two semesters. To count as residence, a semester must consist of at least 6 passed units. Intercampus Visitor, EAP, and UC Berkeley-Washington Program (UCDC) units are excluded.

You may use a Berkeley Summer Session to satisfy one semester of the Senior Residence requirement, provided that you successfully complete 6 units of course work in the Summer Session and that you have been enrolled previously in the college.

Modified Senior Residence Requirement

Participants in the UC Education Abroad Program (EAP) or the UC Berkeley Washington Program (UCDC) may meet a Modified Senior Residence requirement by completing 24 (excluding EAP) of their final 60 semester units in residence. At least 12 of these 24 units must be completed after you have completed 90 units.

Upper Division Residence Requirement

You must complete in residence a minimum of 18 units of upper division courses (excluding EAP units), 12 of which must satisfy the requirements for your major.

Student Learning Goals

Learning Goals for the Major

Mathematics is the language of science. In Galileo’s words:

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is impossible to understand a single word of it. Without those, one is wandering in a dark labyrinth.

Mathematics majors learn the internal workings of this language, its central concepts and their interconnections. These involve structures going far beyond the geometric figures to which Galileo refers. Majors also learn to use mathematical concepts to formulate, analyze, and solve real-world problems. Their training in rigorous thought and creative problem-solving is valuable not just in science, but in all walks of life.

Skills

By the time of graduation, majors should have acquired the following knowledge and skills:

  1. Analytical skills
    • An understanding of the basic rules of logic.
    • The ability to distinguish a coherent argument from a fallacious one, both in mathematical reasoning and in everyday life.
    • An understanding of the role of axioms or assumptions.
    • The ability to abstract general principles from examples.
  2. Problem-solving and modeling skills (important for all, but especially for majors in Applied Mathematics)
    • The ability to recognize which real-world problems are subject to mathematical reasoning.
    • The ability to make vague ideas precise by representing them in mathematical notation, when appropriate.
    • Techniques for solving problems expressed in mathematical notation.
  3. Communication skills
    • The ability to formulate a mathematical statement precisely.
    • The ability to write a coherent proof.
    • The ability to present a mathematical argument verbally.
    • Majors in Mathematics with a Teaching Concentration should acquire familiarity with techniques for explaining K-12 mathematics in an accessible and mathematically correct manner.
  4. Reading and research skills
    • Sufficient experience in mathematical language and foundational material to be well-prepared to extend one’s mathematical knowledge further through independent reading.
    • Exposure to and successful experience in solving mathematical problems presenting substantial intellectual challenge.

Advising

The Math Department has a small team of undergraduate advisers that information on requirements, policies, procedures, resources, opportunities, untying bureaucratic knots, developing study plans, attending commencement, certifying degrees and minors. Students are strongly encouraged to see an undergraduate adviser at least twice a year.

The individually assigned faculty adviser counsels students on the academic content of their mathematics major. The faculty adviser's signature is required on program forms (a) when a student first declares the major; and (b) confirming approval of courses that are not already preapproved to be used for the major electives. Appropriate questions for the faculty adviser include selection of electives and preparation for graduate-level courses in a specific mathematical area to be used for honors in the major. Be sure and let him/her know if you are considering graduate work in or related to mathematics, and solicit help in how best to prepare.

Occasionally, the student's adviser goes on sabbatical or is taken off the major advising list and a new official adviser will be appointed by the head major adviser. Requests to change advisers will be accommodated to the extent possible on an individual basis. Please make requests well in advance of the Tele-BEARS period in which the change is to become effective.

Courses

Mathematics

MATH 1A Calculus 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH 1B Calculus 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH H1B Honors Calculus 4 Units

Terms offered: Fall 2015, Fall 2014, Fall 2013
Honors version of 1B. Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.
Honors Calculus: Read More [+]

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

Terms offered: Fall 2017, Summer 2017 8 Week Session, Fall 2016
This sequence is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable. Representation of data, elementary probability theory, statistical models, and testing.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

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

Terms offered: Spring 2018, Summer 2017 8 Week Session, Spring 2017
Elementary combinatorics and discrete probability theory. Introduction to graphs, matrix algebra, linear equations, difference equations, and differential equations.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read More [+]

MATH 16A Analytic Geometry and Calculus 3 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH 16B Analytic Geometry and Calculus 3 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH 24 Freshman Seminars 1 Unit

Terms offered: Spring 2018, Fall 2017, Spring 2017
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 [+]

MATH 32 Precalculus 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH N32 Precalculus 4 Units

Terms offered: Prior to 2007
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 [+]

MATH 39A Freshman/Sophomore Seminar 2 - 4 Units

Terms offered: Spring 2018, Spring 2010, Spring 2009
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 [+]

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

Terms offered: Spring 2017, Spring 2016, Fall 2015
Students with partial credit in lower division mathematics courses may, with consent of instructor, complete the credit under this heading.
Supplementary Work in Lower Division Mathematics: Read More [+]

MATH 53 Multivariable Calculus 4 Units

Terms offered: Spring 2018, Fall 2017, 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 [+]

MATH H53 Honors Multivariable Calculus 4 Units

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 [+]

MATH W53 Multivariable Calculus 4 Units

Terms offered: Summer 2017 8 Week Session, Summer 2016 10 Week Session, Summer 2016 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 [+]

MATH 54 Linear Algebra and Differential Equations 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 8 Week Session
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.
Linear Algebra and Differential Equations: Read More [+]

MATH H54 Honors Linear Algebra and Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 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 [+]

MATH 55 Discrete Mathematics 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 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 [+]

MATH 74 Transition to Upper Division Mathematics 3 Units

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 [+]

MATH 91 Special Topics in Mathematics 4 Units

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 [+]

MATH 96 College Algebra 2 Units

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 [+]

MATH 98 Supervised Group Study 1 - 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016
Directed Group Study, topics vary with instructor.
Supervised Group Study: Read More [+]

MATH 98BC Berkeley Connect 1 Unit

Terms offered: Spring 2018, Fall 2017, Spring 2017
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 [+]

MATH 99 Supervised Independent Study 1 - 4 Units

Terms offered: Spring 2017, Spring 2016, Fall 2015
Supervised independent study by academically superior, lower division students. 3.3 GPA required and prior consent of instructor who is to supervise the study. A written proposal must be submitted to the department chair for pre-approval.
Supervised Independent Study: Read More [+]

MATH C103 Introduction to Mathematical Economics 4 Units

Terms offered: Spring 2018, Spring 2017, Fall 2016
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 [+]

MATH 104 Introduction to Analysis 4 Units

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

MATH H104 Honors Introduction to Analysis 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
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 [+]

MATH 105 Second Course in Analysis 4 Units

Terms offered: Spring 2018, Spring 2017, Spring 2016
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 [+]

MATH 110 Linear Algebra 4 Units

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

MATH H110 Honors Linear Algebra 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
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 [+]

MATH 113 Introduction to Abstract Algebra 4 Units

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

MATH H113 Honors Introduction to Abstract Algebra 4 Units

Terms offered: Spring 2018, Spring 2017, Spring 2016
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 [+]

MATH 114 Second Course in Abstract Algebra 4 Units

Terms offered: Spring 2018, Spring 2017, Fall 2015
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 [+]

MATH 115 Introduction to Number Theory 4 Units

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

MATH 116 Cryptography 4 Units

Terms offered: Fall 2015, Fall 2014, Fall 2013
Construction and analysis of simple cryptosystems, public key cryptography, RSA, signature schemes, key distribution, hash functions, elliptic curves, and applications.
Cryptography: Read More [+]

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

Terms offered: Fall 2017, Spring 2017, Spring 2016
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 [+]

MATH 121A Mathematical Tools for the Physical Sciences 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
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 [+]

MATH 121B Mathematical Tools for the Physical Sciences 4 Units

Terms offered: Spring 2018, Spring 2017, Spring 2016
Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Special functions, series solutions of ordinary differential equations, partial differential equations arising in mathematical physics, probability theory.
Mathematical Tools for the Physical Sciences: Read More [+]

MATH 123 Ordinary Differential Equations 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
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 [+]

MATH 125A Mathematical Logic 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
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 [+]

MATH 126 Introduction to Partial Differential Equations 4 Units

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

MATH 127 Mathematical and Computational Methods in Molecular Biology 4 Units

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

MATH 128A Numerical Analysis 4 Units

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

MATH 128B Numerical Analysis 4 Units

Terms offered: Spring 2018, Spring 2017, Spring 2016
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 [+]

MATH 130 The Classical Geometries 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
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 [+]

MATH 135 Introduction to the Theory of Sets 4 Units

Terms offered: Fall 2017, Spring 2017, Spring 2016
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 [+]

MATH 136 Incompleteness and Undecidability 4 Units

Terms offered: Spring 2018, Spring 2017, Fall 2015
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 [+]

MATH 140 Metric Differential Geometry 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2015
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 [+]

MATH 141 Elementary Differential Topology 4 Units

Terms offered: Fall 2017, Fall 2016, Spring 2016
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 [+]

MATH 142 Elementary Algebraic Topology 4 Units

Terms offered: Spring 2018, Spring 2017, Fall 2015
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 [+]

MATH 143 Elementary Algebraic Geometry 4 Units

Terms offered: Spring 2018, Fall 2016, Fall 2015
Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.
Elementary Algebraic Geometry: Read More [+]

MATH 151 Mathematics of the Secondary School Curriculum I 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
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 [+]

MATH 152 Mathematics of the Secondary School Curriculum II 4 Units

Terms offered: Fall 2017, Fall 2016, Fall 2015
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 [+]

MATH 153 Mathematics of the Secondary School Curriculum III 4 Units

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 [+]

MATH 160 History of Mathematics 4 Units

Terms offered: Spring 2018, Spring 2017, Spring 2016
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 [+]

MATH 170 Mathematical Methods for Optimization 4 Units

Terms offered: Spring 2018, Spring 2017, Fall 2015
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 [+]

MATH 172 Combinatorics 4 Units

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 [+]

MATH 185 Introduction to Complex Analysis 4 Units

Terms offered: Spring 2018, Fall 2017, Summer 2017 8 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 [+]

MATH H185 Honors Introduction to Complex Analysis 4 Units

Terms offered: Spring 2018, Spring 2016, Spring 2015
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 [+]

MATH 189 Mathematical Methods in Classical and Quantum Mechanics 4 Units

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 [+]

MATH 191 Experimental Courses in Mathematics 1 - 4 Units

Terms offered: Spring 2018, Fall 2017, Spring 2017
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 [+]

MATH 195 Special Topics in Mathematics 4 Units

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 [+]

MATH 196 Honors Thesis 4 Units

Terms offered: Spring 2017, Spring 2016, Spring 2015
Independent study of an advanced topic leading to an honors thesis.
Honors Thesis: Read More [+]

MATH 197 Field Study 1 - 4 Units

Terms offered: Spring 2016, Spring 2015, Spring 2014
For Math/Applied math majors. Supervised experience relevant to specific aspects of their mathematical emphasis of study in off-campus organizations. Regular individual meetings with faculty sponsor and written reports required. Units will be awarded on the basis of three hours/week/unit.
Field Study: Read More [+]

MATH 198 Directed Group Study 1 - 4 Units

Terms offered: Spring 2017, Fall 2016, Spring 2016
Topics will vary with instructor.
Directed Group Study: Read More [+]

MATH 198BC Berkeley Connect 1 Unit

Terms offered: Spring 2018, Fall 2017, Spring 2017
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 [+]

MATH 199 Supervised Independent Study and Research 1 - 4 Units

Terms offered: Fall 2017, Spring 2017, Fall 2016

Supervised Independent Study and Research: Read More [+]

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

David Eisenbud, Professor. Mathematics, algebraic geometry, commutative algebra, computation.
Research Profile

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

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

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

Arthur E. Ogus, Professor. Mathematics, algebraic geometry, algebraic differential equations, log poles.
Research Profile

Martin Olsson, Professor. Algebraic geometry, arithmetic geometry.
Research Profile

Lior Pachter, Professor. Mathematics, applications of statistics, combinatorics to problems in biology.
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.

Theodore A. Slaman, Professor. Mathematics, recursion theory.
Research Profile

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

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

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

Peter Teichner, Professor. Topology, quantum field theory.
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, Associate Professor. Applied mathematics, numerical analysis, computational solid and fluid mechanics.
Research Profile

Lauren K. Williams, Associate 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

Alexander Coward, Lecturer.

Alexander Paulin, Lecturer.

Kelli Talaska, Lecturer.

Visiting Faculty

Alexis Brice Emmanuel Bouthier, Visiting Assistant Professor.

Jeff Calder, Visiting Assistant Professor.

Ivan Guillermo Contreras Palacios, Visiting Assistant Professor.

Tim Cramer, Visiting Assistant Professor.

Ved Datar, Visiting Assistant Professor.

David Dynerman, Visiting Assistant Professor.

Kenji Kozai, Visiting Assistant Professor.

Andrew Lawrie, Visiting Assistant Professor.

David Li-Bland, Visiting Assistant Professor.

Gang Liu, Visiting Assistant Professor.

Kathryn Mann, Visiting Assistant Professor.

Khoa L. Nguyen, Visiting Assistant Professor.

Sung-Jin Oh, Visiting Assistant Professor.

Mohammad Reza Pakzad, Visiting Professor.

Pierre Raphael, Visiting Professor.

Silvain Rideau, Visiting Assistant Professor.

Zvezdelina Stankova, Visiting Professor.

Hongbin Sun, Visiting Assistant Professor.

Adam Topaz, Visiting Assistant Professor.

Yan Zhang, 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

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

Paul R. Chernoff, Professor Emeritus.

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

Stephen P. L. Diliberto, Professor Emeritus. Mathematics, ordinary differential equations, celestial mechanics.
Research Profile

Jacob Feldman, Professor Emeritus. Mathematics, stochastic processes, ergodic theory.
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

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

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.

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

Marina Ratner, Professor Emeritus.

John L. Rhodes, Professor Emeritus. Mathematics, algebra, semigroups, automata.
Research Profile

Donald E. Sarason, Professor Emeritus. Mathematics, complex function theory, operator theory.
Research Profile

Jack H. Silver, Professor Emeritus.

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 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

Department of Mathematics

970 Evans Hall

Phone: 510-642-6550

Fax: 510-642-8204

Visit Department Website

Department Chair

Lawrence Craig Evans, PhD

949 Evans Hall

Phone: 510-642-8065

evans@math.berkeley.edu

Vice-Chair for Undergraduate Affair

Fraydoun Rezahkanlou, PhD

803 Evans Hall

Phone: 510-642-2838

rezakhan@berkeley.edu

Student Services Supervisor

Jennifer Pinney

967 Evans Hall

Phone: 510-642-2479

jensixt@berkeley.edu

Undergraduate Student Adviser

Thomas Brown

965 Evans Hall

Phone: 510-643-9292

brown@math.berkeley.edu

Interim Undergraduate Student Adviser

Ana Renteria

964 Evans Hall

Phone: 510-643-4148

ana.renteria26@berkeley.edu

Back to Top