Mathematics

University of California, Berkeley

About the Program

Bachelor of Arts (BA)

The Department of Mathematics offers an undergraduate major in Mathematics leading to the Bachelor of Arts (BA) degree. The program provides an excellent preparation for advanced degrees in math, physical sciences, economics, and industrial engineering as well as graduate study in business, education, law, and medicine. The program also prepares 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 advisor. 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 advisor.

Students interested in the honors program should consult with an advisor 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. Exceptions will be made for major courses taken in Spring 2020, Fall 2020, Spring 2021, and Summer 2021. Other exceptions to this requirement are noted as applicable.
  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
or MATH N1A Calculus
MATH 1BCalculus4
or MATH N1B Calculus
MATH 53Multivariable Calculus4
or MATH N53 Multivariable Calculus
Multivariable Calculus [4]
MATH 54Linear Algebra and Differential Equations 14
or MATH N54 Linear Algebra and Differential Equations
or MATH 56 Linear Algebra
Linear Algebra and Differential Equations [4]
MATH 55Discrete Mathematics 24
or MATH N55 Discrete Mathematics
Upper Division
MATH 104Introduction to Analysis4
MATH 110Abstract Linear 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
Programming for Mathematical Applications [4]
Numerical Analysis [4]
Numerical Analysis
Geometry
Groups and Geometries [4]
Metric Differential Geometry [4]
Elementary Differential Topology [4]
Elementary Algebraic Topology [4]
Elementary Algebraic Geometry [4]
Logic and Foundations
Mathematical Logic [4]
Introduction to the Theory of Sets [4]
Incompleteness and Undecidability [4]
Two electives, select at least two additional upper division or graduate mathematics courses must be taken 3
1

For students double-majoring in Physics, PHYSICS 89 may be substituted, provided that the grade is at least a C.

For students double-majoring in Computer Science or Electrical Engineering and Computer Sciences, EECS 16A plus EECS 16B  may be substituted, provided that the grades are at least a C.

2

For students double-majoring in Computer Science or Electrical Engineering and Computer Sciences, COMPSCI 70 may be substituted, provided that the grade is at least a C.

3

These two electives must receive the Faculty Advisor's written approval on the Course Approval Form which is then returned to an Undergraduate Advisor 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. 

4

Math 91 (Fall 2022 only) may be taken in lieu of Math 54. 

Major Requirements: Mathematics with a Teaching Concentration
Lower division
STAT 20Introduction to Probability and Statistics4
MATH 1ACalculus4
or MATH N1A Calculus
MATH 1BCalculus4
or MATH N1B Calculus
MATH 53Multivariable Calculus4
or MATH N53 Multivariable Calculus
MATH 54Linear Algebra and Differential Equations 14
or MATH N54 Linear Algebra and Differential Equations
MATH 55Discrete Mathematics 24
or MATH N55 Discrete Mathematics
Upper division
MATH 104Introduction to Analysis4
MATH 110Abstract Linear Algebra4
MATH 113Introduction to Abstract Algebra4
MATH 151Mathematics of the Secondary School Curriculum I4
MATH 152Mathematics of the Secondary School Curriculum II4
MATH 160History of Mathematics4
Select two of the following:
Introduction to Number Theory [4]
Ordinary Differential Equations [4]
Programming for Mathematical Applications [4]
Mathematical Logic [4]
Numerical Analysis [4]
Groups and Geometries [4]
Introduction to the Theory of Sets [4]
Incompleteness and Undecidability [4]
Mathematical Methods for Optimization [4]
Introduction to Complex Analysis [4]
1

For students double-majoring in Physics, PHYSICS 89 may be substituted, provided that the grade is at least a C.

For students double-majoring in Computer Science or Electrical Engineering and Computer Sciences, EECS 16A plus EECS 16B  may be substituted, provided that the grades are at least a C.

2

For students double-majoring in Computer Science or Electrical Engineering and Computer Sciences, COMPSCI 70 may be substituted, provided that the grade is at least a C.

3

Math 91 (Fall 2022 only) may be taken in lieu of Math 54. 

 

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.

General Guidelines

  1. All minors must be declared no later than one semester before a student's Expected Graduation Term (EGT). If the semester before EGT is fall or spring, the deadline is the last day of RRR week. If the semester before EGT is summer, the deadline is the final Friday of Summer Sessions. To declare a minor, contact the department advisor for information on requirements, and the declaration process.
  2. All courses taken to fulfill the minor requirements below must be taken for graded credit.
  3. A minimum of three of the upper division courses taken to fulfill the minor requirements must be completed at UC Berkeley.
  4. 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.
  5. Courses used to fulfill the minor requirements may be applied toward the Seven-Course Breadth requirement, for Letters & Science students.
  6. No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs.
  7. All minor requirements must be completed prior to the last day of finals during the semester in which the student plans to graduate. 
  8. All minor requirements must be completed within the unit ceiling. (For further information regarding the unit ceiling, please see the College Requirements tab.)

For students double-majoring in Physics, PHYSICS 89 may be substituted for MATH 54, provided that the grade is at least a C.

For students double-majoring in Computer Science or Electrical Engineering and Computer Sciences, EECS 16A plus EECS 16B may be substituted for MATH 54provided that the grades are at least a C.

 Requirements

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

Math 91 (Fall 2022 only) may be taken in lieu of Math 54. 

College Requirements

Undergraduate students 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. For College advising appointments, please visit the L&S Advising Pages. 

University of California Requirements

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.

Berkeley Campus Requirement

American Cultures

All undergraduate students at Cal need to take and pass this course 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.

College of Letters & Science Essential Skills Requirements

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 parts A & B reading and composition courses in sequential order by the end of their fourth semester.

College of Letters & Science 7 Course Breadth Requirements

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

  • 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, or two years for transfer students. 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), Berkeley Summer Abroad, 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 UCEAP 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.

Major Map

Major Maps help undergraduate students discover academic, co-curricular, and discovery opportunities at UC Berkeley based on intended major or field of interest. Developed by the Division of Undergraduate Education in collaboration with academic departments, these experience maps will help you:

  • Explore your major and gain a better understanding of your field of study

  • Connect with people and programs that inspire and sustain your creativity, drive, curiosity and success

  • Discover opportunities for independent inquiry, enterprise, and creative expression

  • Engage locally and globally to broaden your perspectives and change the world

  • Reflect on your academic career and prepare for life after Berkeley

Use the major map below as a guide to planning your undergraduate journey and designing your own unique Berkeley experience.

View the Mathematics Major Map PDF.

Advising

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

Faculty advisors are also available to students. Faculty advisors approve major electives which are not already pre-approved and listed on our website and can also approve courses from study abroad or other 4 year institutions towards a student’s upper-division major requirements. 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 if you need to solicit help in how best to prepare.

We also encourage students to take advantage of the expertise of the Math Department’s Peer Advisors. They can provide a student perspective on courses, instructors, effective study habits, and enrichment opportunities. They hold office hours, host events, record a podcast, and post interesting information on the Ed Discussion forum. 

Information about all of the above Math Department advising resources can be found here.

Courses

Mathematics

Contact Information

Department of Mathematics

970 Evans Hall

Phone: 510-642-6550

Fax: 510-642-8204

Visit Department Website

Department Chair

Michael Hutchings

923 Evans Hall

Phone: 510-643-4329

chair@math.berkeley.edu

Vice-Chair for Undergraduate Affair

Per-Olof Persson

1081 Evans Hall

persson@berkeley.edu

Undergraduate Student Advisor

Thomas Brown

965 Evans Hall

Phone: 510-643-9292

brown@math.berkeley.edu

Undergraduate Student Advisor

Marsha Snow

964 Evans Hall

Phone: 510-643-4148

snow@math.berkeley.edu

Undergraduate Programs Manager & Advisor

Hanh Tran

962 Evans Hall

hanhmtran@berkeley.edu

Curriculum Analyst

Zhanara Gallegos

973 Evans Hall

Zhanara@berkeley.edu

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