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 postbaccalaureate 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:
 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.
 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.
 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)
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
 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.
 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.
 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
Code  Title  Units 

Lower Division  
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
MATH 55  Discrete Mathematics ^{1}  4 
Upper Divison  
MATH 104  Introduction to Analysis  4 
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
MATH 185  Introduction to Complex Analysis  4 
Two semielectives  
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. 
Code  Title  Units 

Lower division  
STAT 20  Introduction to Probability and Statistics  4 
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
MATH 55  Discrete Mathematics ^{1}  4 
Upper division  
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
Select two of the following:  
Numerical Analysis  
The Classical Geometries  
Introduction to the Theory of Sets  
MATH 151  Mathematics of the Secondary School Curriculum I  4 
MATH 152  Mathematics of the Secondary School Curriculum II  4 
MATH 153  Mathematics of the Secondary School Curriculum III  4 
MATH 160  History of Mathematics  4 
Recommended courses:  
Sudents are encouraged, though not required, to take, the following:  
MATH 104  Introduction to Analysis  4 
MATH 115  Introduction to Number Theory  4 
MATH 185  Introduction to Complex Analysis  4 
^{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
 All courses taken to fulfill the minor requirements below must be taken for graded credit.
 A minimum of three of the upper division courses taken to fulfill the minor requirements must be completed at UC Berkeley.
 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.
 Courses used to fulfill the minor requirements may be applied toward the SevenCourse Breadth requirement, for Letters & Science students.
 No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs.
 All minor requirements must be completed prior to the last day of finals during the semester in which the student plans to graduate.
 All minor requirements must be completed within the unit ceiling. (For further information regarding the unit ceiling, please see the College Requirements tab.)
Requirements
Code  Title  Units 

Lower Division  
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
Upper Division  
MATH 104  Introduction to Analysis  4 
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
MATH 185  Introduction to Complex Analysis  4 
One elective: select one additional upper division math course  4 
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 researchled, 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 firstlevel reading and composition course by the end of their second semester and a secondlevel 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 BerkeleyWashington 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 realworld problems. Their training in rigorous thought and creative problemsolving 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:
 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.
 Problemsolving and modeling skills (important for all, but especially for majors in Applied Mathematics)
 The ability to recognize which realworld 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.
 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 K12 mathematics in an accessible and mathematically correct manner.
 Reading and research skills
 Sufficient experience in mathematical language and foundational material to be wellprepared 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 graduatelevel 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 TeleBEARS period in which the change is to become effective.
Courses
Mathematics
MATH 1A Calculus 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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 onehalf years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A
Credit Restrictions: Students will receive no credit for 1A after taking 16B and 2 units after taking 16A.
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.
MATH 1B Calculus 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. Firstorder ordinary differential equations. Secondorder ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.
Calculus: Read More [+]
Rules & Requirements
Prerequisites: 1A
Credit Restrictions: Students will receive 2 units of credit for 1B after taking 16B.
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.
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. Firstorder ordinary differential equations. Secondorder 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 2 units of credit for H1B after taking 16B.
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.
MATH 10A Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units
Terms offered: Summer 2017 8 Week Session, Fall 2016, Summer 2016 8 Week Session
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 [+]
Rules & Requirements
Prerequisites: Three and onehalf years of high school math, including trigonometry and analytic geometry
Credit Restrictions: Students will receive 2 units for Mathematics 10A after completing Mathematics 1A.
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 3 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.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read Less []
MATH 10B Methods of Mathematics: Calculus, Statistics, and Combinatorics 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Summer 2016 8 Week Session
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 [+]
Rules & Requirements
Prerequisites: Continuation of 10A
Credit Restrictions: Students will receive 2 units of credit for Mathematics 10B after completing Mathematics 55.
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 3 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.
Methods of Mathematics: Calculus, Statistics, and Combinatorics: Read Less []
MATH 16A Analytic Geometry and Calculus 3 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details
Credit Restrictions: Students will receive no credit for 16A after taking 1A. Two units of 16A may be used to remove a deficient grade in 1A.
Hours & Format
Fall and/or spring: 15 weeks  2 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.
MATH 16B Analytic Geometry and Calculus 3 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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 16B after 1B, 2 units after 1A. Two units of 16B may be used to remove a deficient grade in 1A.
Hours & Format
Fall and/or spring: 15 weeks  2 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.
MATH 24 Freshman Seminars 1 Unit
Terms offered: Spring 2017, Fall 2016, Spring 2016
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 smallseminar 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 as topic varies. 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 required.
MATH 32 Precalculus 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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, plus satisfactory score on one of the following: CEEB MAT test, math SAT, or UC/CSU diagnostic examination
Credit Restrictions: Students will receive no credit for 32 after taking 1A1B or 16A16B and will receive 3 units after taking 96.
Hours & Format
Fall and/or spring: 15 weeks  2 hours of lecture and 2 hours of discussion per week
Summer:
6 weeks  5 hours of lecture and 5 hours of discussion per week
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.
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 [+]
Rules & Requirements
Prerequisites: Three years of high school mathematics, plus satisfactory score on one of the following: CEEB MAT test, math SAT, or UC/CSU diagnostic examination
Credit Restrictions: Students will receive no credit for N32 after taking 1A1B or 16A16B and will receive 3 units after taking 96.
Hours & Format
Summer: 8 weeks  12.5 hours of lecture per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
Instructor: Gibson
MATH 39A Freshman/Sophomore Seminar 2  4 Units
Terms offered: Spring 2010, Spring 2009, Spring 2008
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 smallseminar 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
Hours & Format
Fall and/or spring: 15 weeks  24 hours of seminar per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
MATH 49 Supplementary Work in Lower Division Mathematics 1  3 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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.
Hours & Format
Fall and/or spring: 15 weeks  0 hours of independent study per week
Summer:
6 weeks  15 hours of independent study per week
8 weeks  14 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 []
MATH 53 Multivariable Calculus 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Parametric equations and polar coordinates. Vectors in 2 and 3dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
Multivariable Calculus: Read More [+]
Rules & Requirements
Prerequisites: Mathematics 1B
Credit Restrictions: Students will receive no credit for Mathematics 53 after completing Mathematics W53, 53M; 3 units for Mathematics 50A and 1 unit for Mathematics 50B. A deficient grade in 53 may be removed by completing Mathematics W53.
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 3 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.
MATH H53 Honors Multivariable Calculus 4 Units
Terms offered: Spring 2017, Fall 2015, Spring 2015
Honors version of 53. Parametric equations and polar coordinates. Vectors in 2 and 3dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
Honors Multivariable Calculus: Read More [+]
Rules & Requirements
Prerequisites: 1B
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.
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 3dimensional 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 taking Mathematics 53. A deficient grade in Mathematics W53 may be removed by completing Mathematics 53.<BR/>
Hours & Format
Summer: 8 weeks  5 hours of webbased lecture and 5 hours of webbased 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
MATH 54 Linear Algebra and Differential Equations 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; firstorder differential equations with constant coefficients. Fourier series and partial differential equations.
Linear Algebra and Differential Equations: Read More [+]
Rules & Requirements
Prerequisites: 1B
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 3 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.
MATH H54 Honors Linear Algebra and Differential Equations 4 Units
Terms offered: Fall 2016, Spring 2016, Fall 2014
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; firstorder differential equations with constant coefficients. Fourier series and partial differential equations.
Honors Linear Algebra and Differential Equations: Read More [+]
Rules & Requirements
Prerequisites: 1B
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 []
MATH 55 Discrete Mathematics 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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. 1A1B recommended
Credit Restrictions: Students will receive no credit for 55 after taking Computer Science 70.
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.
MATH 74 Transition to Upper Division Mathematics 3 Units
Terms offered: Summer 2009 8 Week Session, Spring 2009, Fall 2008
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 02 hours of discussion per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
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 [+]
Rules & Requirements
Repeat rules: Course may be repeated for credit.
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.
MATH 96 College Algebra 2 Units
Terms offered: Summer 2017 8 Week Session, Summer 2016 8 Week Session, Summer 2015 8 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: Students will receive no credit for 96 after taking P, PS, or 32.
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.
MATH 98 Supervised Group Study 1  4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Directed Group Study, topics vary with instructor.
Supervised Group Study: Read More [+]
Rules & Requirements
Repeat rules: Course may be repeated for a maximum of 4 units.
Hours & Format
Fall and/or spring: 15 weeks  14 hours of directed group study per week
Summer: 8 weeks  1.57.5 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.
MATH 98BC Berkeley Connect 1 Unit
Terms offered: Spring 2017, Fall 2016, Spring 2016
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 smallgroup discussions facilitated by a graduate student mentor (following a facultydirected curriculum), meet with their graduate student mentor for oneonone 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 [+]
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.
MATH 99 Supervised Independent Study 1  4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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 preapproval.
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.
Hours & Format
Fall and/or spring: 15 weeks  14 hours of independent study per week
Summer: 8 weeks  14 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.
MATH C103 Introduction to Mathematical Economics 4 Units
Terms offered: Spring 2017, Fall 2016, Fall 2015
Selected topics illustrating the application of mathematics to economic theory. This course is intended for upperdivision 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
MATH 104 Introduction to Analysis 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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.
MATH H104 Honors Introduction to Analysis 4 Units
Terms offered: Fall 2016, Fall 2015, Fall 2014
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.
MATH 105 Second Course in Analysis 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 110 Linear Algebra 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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.
MATH H110 Honors Linear Algebra 4 Units
Terms offered: Fall 2016, Fall 2015, Fall 2014
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.
MATH 113 Introduction to Abstract Algebra 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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.
MATH H113 Honors Introduction to Abstract Algebra 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 114 Second Course in Abstract Algebra 4 Units
Terms offered: Spring 2017, Fall 2015, Spring 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 [+]
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.
MATH 115 Introduction to Number Theory 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Summer 2016 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 02 hours of discussion per week
Summer: 8 weeks  6 hours of lecture and 04 hours of discussion per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
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 [+]
Rules & Requirements
Prerequisites: 55
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 02 hours of discussion per week
Summer: 8 weeks  6 hours of lecture and 04 hours of discussion per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
MATH 118 Fourier Analysis, Wavelets, and Signal Processing 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
Introduction to signal processing including Fourier analysis and wavelets. Theory, algorithms, and applications to onedimensional 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 []
MATH 121A Mathematical Tools for the Physical Sciences 4 Units
Terms offered: Fall 2016, Spring 2016, Fall 2015
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.
MATH 121B Mathematical Tools for the Physical Sciences 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 123 Ordinary Differential Equations 4 Units
Terms offered: Fall 2016, Spring 2016, Spring 2015
Existence and uniqueness of solutions, linear systems, regular singular points. Other topics selected from analytic systems, autonomous systems, SturmLiouville 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.
MATH 125A Mathematical Logic 4 Units
Terms offered: Fall 2016, Fall 2015, Fall 2014
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.
MATH 126 Introduction to Partial Differential Equations 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Summer 2016 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 [+]
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 []
MATH 127 Mathematical and Computational Methods in Molecular Biology 4 Units
Terms offered: Fall 2016, Spring 2016, Fall 2014
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 []
MATH 128A Numerical Analysis 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Programming for numerical calculations, roundoff 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
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
MATH 128B Numerical Analysis 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 130 The Classical Geometries 4 Units
Terms offered: Fall 2016, Fall 2015, Fall 2014
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, nonEuclidean 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.
MATH 135 Introduction to the Theory of Sets 4 Units
Terms offered: Spring 2017, Spring 2016, Fall 2014
Settheoretical paradoxes and means of avoiding them. Sets, relations, functions, order and wellorder. 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.
MATH 136 Incompleteness and Undecidability 4 Units
Terms offered: Spring 2017, Fall 2015, Spring 2015
Functions computable by algorithm, Turing machines, Church's thesis. Unsolvability of the halting problem, Rice's theorem. Recursively enumerable sets, creative sets, manyone reductions. Selfreferential 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.
MATH 140 Metric Differential Geometry 4 Units
Terms offered: Spring 2017, Fall 2015, Spring 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 GaussBonnetVon 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.
MATH 141 Elementary Differential Topology 4 Units
Terms offered: Fall 2016, Spring 2016, Fall 2014
Manifolds in ndimensional Euclidean space and smooth maps, Sard's Theorem, classification of compact onemanifolds, 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.
MATH 142 Elementary Algebraic Topology 4 Units
Terms offered: Spring 2017, Fall 2015, Fall 2014
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.
MATH 143 Elementary Algebraic Geometry 4 Units
Terms offered: Fall 2016, Fall 2015, Spring 2015
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.
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 [+]
Rules & Requirements
Prerequisites: 1A1B, 53, or equivalent
Hours & Format
Fall and/or spring: 15 weeks  3 hours of lecture and 01 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 []
MATH 152 Mathematics of the Secondary School Curriculum II 4 Units
Terms offered: Fall 2016, Fall 2015, Fall 2014
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 01 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 []
MATH 153 Mathematics of the Secondary School Curriculum III 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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 01 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 []
MATH 160 History of Mathematics 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 170 Mathematical Methods for Optimization 4 Units
Terms offered: Spring 2017, Fall 2015, Fall 2014
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.
MATH 172 Combinatorics 4 Units
Terms offered: Spring 2017, Spring 2016, Spring 2015
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.
MATH 185 Introduction to Complex Analysis 4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
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.
MATH H185 Honors Introduction to Complex Analysis 4 Units
Terms offered: Spring 2016, Spring 2015, Spring 2014
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.
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 [+]
Rules & Requirements
Prerequisites: 104, 110, 2 semesters lower division Physics
Repeat rules: Course may be repeated for credit.
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 []
MATH 191 Experimental Courses in Mathematics 1  4 Units
Terms offered: Spring 2017, Fall 2016, Spring 2016
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.
Hours & Format
Fall and/or spring: 15 weeks  14 hours of seminar per week
Summer:
6 weeks  2.510 hours of seminar per week
8 weeks  1.57.5 hours of seminar per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam required.
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 [+]
Rules & Requirements
Prerequisites: Consent of instructor
Repeat rules: Course may be repeated for credit.
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.
MATH 196 Honors Thesis 4 Units
Terms offered: Spring 2017, Fall 2016, Spring 2016
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.
Hours & Format
Fall and/or spring: 15 weeks  0 hours of independent study per week
Summer:
6 weeks  15 hours of independent study per week
8 weeks  14 hours of independent study per week
Additional Details
Subject/Course Level: Mathematics/Undergraduate
Grading/Final exam status: Letter grade. Final exam not required.
MATH 197 Field Study 1  4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
For Math/Applied math majors. Supervised experience relevant to specific aspects of their mathematical emphasis of study in offcampus 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.
Hours & Format
Fall and/or spring: 15 weeks  33 hours of fieldwork per week
Summer: 8 weeks  33 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.
MATH 198 Directed Group Study 1  4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Topics will vary with instructor.
Directed Group Study: Read More [+]
Rules & Requirements
Prerequisites: Must have completed 60 units and be in good standing
Hours & Format
Fall and/or spring: 15 weeks  14 hours of directed group study per week
Summer: 8 weeks  14 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.
MATH 198BC Berkeley Connect 1 Unit
Terms offered: Spring 2017, Fall 2016, Spring 2016
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 smallgroup discussions facilitated by a graduate student mentor (following a facultydirected curriculum), meet with their graduate student mentor for oneonone 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 [+]
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.
MATH 199 Supervised Independent Study and Research 1  4 Units
Terms offered: Summer 2017 8 Week Session, Spring 2017, Fall 2016
Supervised Independent Study and Research: Read More [+]
Rules & Requirements
Prerequisites: The standard college regulations for all 199 courses
Hours & Format
Fall and/or spring: 15 weeks  0 hours of independent study per week
Summer:
6 weeks  15 hours of independent study per week
8 weeks  14 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.
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. Lowdimensional 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 measurevalued 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
PerOlof 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, lowdimensional 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, noncommutative geometry, noncommutative harmonic analysis, quantum geometry.
Research Profile
Thomas Scanlon, Professor. Mathematics, model theory, applications to number theory.
Research Profile
Vera Serganova, Professor. Mathematics, Superrepresentation 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.
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John Strain, Professor. Mathematics, numerical analysis, applied mathematics, fast algorithms, materials science.
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Bernd Sturmfels, Professor. Mathematics, combinatorics, computational algebraic geometry.
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Daniel Ioan Tataru, Professor. Mathematics, partial differential equations, nonlinear waves.
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Peter Teichner, Professor. Topology, quantum field theory.
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Constantin Teleman, Professor. Lie algebras, algebraic geometry, Lie groups, topology, topological quantum field theory.
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Luca Trevisan, Professor. Computational complexity, spectral graph theory.
Dan Voiculescu, Professor. Random matrices, pperator algebras, free probability theory.
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Paul A. Vojta, Professor. Mathematics, algebraic geometry, diophantine geometry, Nevanlinna theory, Arakelov theory.
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Katrin Wehrheim, Associate Professor. Lowdimensional and symplectic topology.
Jon Wilkening, Associate Professor. Applied mathematics, numerical analysis, computational solid and fluid mechanics.
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Lauren K. Williams, Associate Professor. Algebraic combinatorics.
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Mariusz Wodzicki, Professor. Analysis, mathematics, Noncommutative and algebraic geometry, Ktheory.
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Xinyi Yuan, Assistant Professor. Number theory.
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Maciej Zworski, Professor. Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.
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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 LiBland, Visiting Assistant Professor.
Gang Liu, Visiting Assistant Professor.
Kathryn Mann, Visiting Assistant Professor.
Khoa L. Nguyen, Visiting Assistant Professor.
SungJin 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.
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Robert Anderson, Professor Emeritus. Finance, probability theory, mathematical economics, nonstandard analysis.
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George Bergman, Professor Emeritus. Mathematics, associative rings, universal algebra, category theory, counterexamples.
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Elwyn R. Berlekamp, Professor Emeritus. Computer science, electrical engineering, mathematics, combinatorial game theory, algebraic coding theory.
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Robert Bryant, Professor Emeritus. Symplectic geometry, differential geometry, Lie groups, geometric partial differential equations.
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Paul R. Chernoff, Professor Emeritus.
Alexandre J. Chorin, Professor Emeritus. Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods.
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Paul Concus, Professor Emeritus. Fluid mechanics, numerical analysis, applied mathematics, capillarity.
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Heinz O. Cordes, Professor Emeritus. Mathematics, classical analysis.
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Stephen P. L. Diliberto, Professor Emeritus. Mathematics, ordinary differential equations, celestial mechanics.
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Jacob Feldman, Professor Emeritus. Mathematics, stochastic processes, ergodic theory.
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F. Alberto Grunbaum, Professor Emeritus. Medical imaging, xray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birthanddeath processes.
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Leo A. Harrington, Professor Emeritus. Mathematics, model theory, recursion theory, set theory.
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Robert C. Hartshorne, Professor Emeritus. Mathematics, algebraic geometry.
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Morris W. Hirsch, Professor Emeritus. Game theory, dynamical systems, topology, biological models.
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WuYi Hsiang, Professor Emeritus. Mathematics, transformation groups, differential geometry.
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Vaughan F. R. Jones, Professor Emeritus. Mathematics, Von Neumann algebras.
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Robion C. Kirby, Professor Emeritus. Mathematics, topology of manifolds.
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TsitYuen 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.
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Keith Miller, Professor Emeritus. Mathematics, partial differential equations, numerical methods for PDE's.
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Calvin C. Moore, Professor Emeritus. Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K theory.
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John Neu, Professor Emeritus.
Andrew Ogg, Professor Emeritus.
Charles C. Pugh, Professor Emeritus. Mathematics, global theory of differential equations.
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Marina Ratner, Professor Emeritus.
John L. Rhodes, Professor Emeritus. Mathematics, algebra, semigroups, automata.
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Donald E. Sarason, Professor Emeritus. Mathematics, complex function theory, operator theory.
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Jack H. Silver, Professor Emeritus.
Isadore M. Singer, Professor Emeritus. Mathematics, physics, partial differential equations, geometry.
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Stephen Smale, Professor Emeritus. Algorithms, mathematics, numerical analysis, global analysis.
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Robert M. Solovay, Professor Emeritus.
John B. Wagoner, Professor Emeritus. Mathematics, dynamical systems, differential topology, algebraic Ktheory.
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Alan Weinstein, Professor Emeritus. Mathematics, mathematical physics, symplectic geometry.
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Joseph A. Wolf, Professor Emeritus. Harmonic analysis, differential geometry, Lie groups.
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W. Hugh Woodin, Professor Emeritus. Mathematics, set theory, large cardinals.
Research Profile
HungHsi Wu, Professor Emeritus. Real and complex geometry, school mathematics education.
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Contact Information
ViceChair for Undergraduate Affair
Fraydoun Rezahkanlou, PhD
803 Evans Hall
Phone: 5106422838
Interim Undergraduate Student Adviser
Ana Renteria
964 Evans Hall
Phone: 5106434148