420 Rowland Hall; (949) 824-5503
Peter Li, Department Chair
Faculty
Takeo Akasaki, Ph.D. University of California, Los Angeles, Professor Emeritus of Mathematics (ring theory)
Bruce M. Bennett, Ph.D. Columbia University, Professor of Mathematics and Cognitive Sciences (algebraic geometry, theory of perception)
Frank B. Cannonito, Ph.D. Adelphi University, Professor Emeritus of Mathematics (group theory)
Larry Chrystal, M.A. University of California, Santa Barbara, Lecturer in Mathematics
Donald Darling, Ph.D. California Institute of Technology, Professor Emeritus of Mathematics
Panagiota Daskalopoulos, Ph.D. University of Chicago, Department Vice Chair for Graduate Studies and Associate Professor of Mathematics (partial differential equations, harmonic analysis, geometric analysis)
Rui J. P. de Figueiredo, Ph.D. Harvard University, Professor of Electrical and Computer Engineering and of Mathematics
William F. Donoghue, Jr., Ph.D. University of Wisconsin, Professor Emeritus of Mathematics (classical function theory)
Paul C. Eklof, Ph.D. Cornell University, Professor of Mathematics (logic and algebra)
Aleksandr Figotin, Ph.D. Tashkent University, Professor of Mathematics (applied mathematics, electromagnetic waves in inhomogeneous media, photonic crystals)
Mark Finkelstein, Ph.D. Stanford University, Associate Professor of Mathematics (analysis)
Matthew D. Foreman, Ph.D. University of California, Berkeley, Professor of Mathematics and Philosophy (logic)
Michael D. Fried, Ph.D. University of Michigan, Professor of Mathematics (arithmetic geometry, complex variables)
Svetlana Jitomirskaya, Ph.D. Moscow State University, Associate Professor of Mathematics (mathematical physics)
Richard K. Juberg, Ph.D. University of Minnesota, Professor Emeritus of Mathematics (analysis, differential equations)
Gerhard K. Kalisch, Ph.D. University of Chicago, Professor Emeritus of Mathematics (functional analysis)
Ludmil Katzarkov, Ph.D. University of Pennsylvania, Associate Professor of Mathematics (algebraic geometry, representation theory)
Abel Klein, Ph.D. Massachusetts Institute of Technology, Professor of Mathematics (mathematical physics)
Peter Li, Ph.D. University of California, Berkeley, Department Chair and Professor of Mathematics (differential geometry)
Song-Ying Li, Ph.D. University of Pittsburgh, Assistant Professor of Mathematics (harmonic analysis, several complex variables)
Penelope Maddy, Ph.D. Princeton University, Department Chair and Professor of Logic and Philosophy of Science and Professor of Mathematics (logic, philosophy, and foundations of mathematics)
Qing Nie, Ph.D. Ohio State University, Assistant Professor of Mathematics (computational applied mathematics)
David L. Rector, Ph.D. Massachusetts Institute of Technology, Associate Professor of Mathematics (algebraic topology, computer algebra)
Robert C. Reilly, Ph.D. University of California, Berkeley, Associate Professor of Mathematics (differential geometry)
Bernard Russo, Ph.D. University of California, Los Angeles, Professor of Mathematics (functional analysis)
Donald G. Saari, Ph.D. Purdue University, UCI Distinguished Professor of Economics and Mathematics (dynamical systems and mathematical economics)
Martin Schechter, Ph.D. New York University, Professor of Mathematics (partial differential equations, functional analysis)
Stephen Scheinberg, Ph.D. Princeton University; M.D. University of California, Irvine, Professor of Mathematics (analysis)
William H. Smoke, Ph.D. University of California, Berkeley, Professor Emeritus of Mathematics (homological algebra)
Ronald J. Stern, Ph.D University of California, Los Angeles, Dean of the School of Physical Sciences and Professor of Mathematics (geometry and topology)
Edriss S. Titi, Ph.D. Indiana University, Professor of Mathematics and of Mechanical and Aerospace Engineering (partial differential equations, nonlinear analysis)
Howard G. Tucker, Ph.D. University of California, Berkeley, Professor of Mathematics (probability and statistics)
Daqing Wan, Ph.D. University of Washington, Associate Professor of Mathematics (number theory, algebraic geometry)
Frederic Yui-Ming Wan, Ph.D. Massachusetts Institute of Technology, Professor of Mathematics and of Mechanical and Aerospace Engineering (applied mathematics)
Richard A. Wentworth, Ph.D. Columbia University, Associate Professor of Mathematics (complex geometry, gauge theory, low-dimensional topology)
Robert W. West, Ph.D. University of Michigan, Professor Emeritus of Mathematics (algebraic topology)
Joel J. Westman, Ph.D. University of California, Los Angeles, Professor Emeritus of Mathematics (analysis)
Robert J. Whitley, Ph.D. New Mexico State University, Department Vice Chair for Undergraduate Studies and Professor of Mathematics (analysis)
Janet L. Williams, Ph.D. Brandeis University, Professor Emerita of Mathematics (probability and statistics)
James J. Yeh, Ph.D. University of Minnesota, Professor of Mathematics (real and stochastic analysis)
Hong-Kai Zhao, Ph.D. University of California, Los Angeles, Assistant Professor of Mathematics (computational applied mathematics)
Weian Zheng, Ph.D. Université de Strasbourg, Professor of Mathematics (probability)
The Department of Mathematics is engaged in teaching and fundamental research in a wide variety of basic mathematical disciplines, and offers undergraduate and graduate students the opportunity to fashion a thorough program of study leading to professional competence in mathematical research, or in an area of application.
The curriculum in mathematics includes opportunities for supervised individual study and research, and is augmented by seminars and colloquia. It is designed to be compatible with curricular structures at other collegiate institutions in California in order to enable students transferring to UCI to continue their programs of mathematics study.
The Department offers a B.S. degree in Mathematics. Within this program, students have the option of completing a concentration in Mathematics for Economics, a specialization in Applied and Computational Mathematics, a specialization in Statistics, or a specialization in Mathematics for High School Teaching. In addition, the Department offers a minor in Mathematics.
Undergraduate mathematics courses are of several kinds: courses preparatory to advanced work in mathematics, the exact sciences, and engineering; courses for students of the social and biological sciences; and courses for liberal arts students and those planning to enter the teaching field.
Admission to the Major
Students may be admitted to the Mathematics major upon entering the University as freshmen, via change of major, and as transfer students from other colleges and universities. Information about change of major policies is available in the Physical Sciences Student Affairs Office. For transfer student admission, preference will be given to junior-level applicants with the highest grades overall, and who have satisfactorily completed the required course work of one year of approved calculus.
University Requirements: See pages 54-59.
School Requirements: None.
Departmental Requirements
Lower-Division Requirements (for all Mathematics majors except those in the Teaching specialization):
A. Mathematics 2A-B; 2J or 2C, with 2J preferred; 2D-E; 3A; 3D.
B. Computing skills attained through either Information and Computer Science 21, Engineering E10, Engineering CEE10, Engineering ECE10, Engineering MAE10, or Physics 53.
C. One lecture course sequence selected from Chemistry 1A-B-C; Physics 5A-B-C, 7A-B-D, 7A-B-E, or 7B-D-E. (This also satisfies UCI breadth requirement category II if taken with the accompanying laboratories.)
Upper-Division Requirements (for Mathematics majors except those in the Economics concentration, Applied and Computational specialization, or Teaching specialization): Most of the upper-division Mathematics courses are organized into a series of Core Areas. The Core Areas are: Numerical Analysis (courses numbered 100-109); Applied Mathematics (110-119); Algebra (120-129); Probability and Statistics (130-139); Analysis (140-149); Logic (150-159); and Geometry/Topology (160-169). There are also non-Core-Area courses (170-199). Students are required to complete 15 upper-division one-quarter lecture courses in Mathematics (with associated laboratories when applicable) as follows:
A. Mathematics 120A, 121A
B. Mathematics 140A-B
C. A third lecture course from the Algebra Core Area (120-129)
D. A third lecture course from the Analysis Core Area (140-149)
E. One additional lecture course from either the Algebra or the Analysis Core Area
F. Two lecture courses from a third Core Area
G. One lecture course from a fourth Core Area
H. Five additional lecture courses in Mathematics chosen from the Core Areas or from courses numbered 170-189
Concentration in Mathematics for Economics
Admission to this concentration requires approval in advance by the Mathematics Department. This approval should be applied for after the student has completed Economics 20A-B-C, but no later than the end of the junior year.
Upper-division requirements:
A. Twelve upper-division Mathematics lecture courses (plus any associated laboratories) including:
1. Nine courses: Mathematics 120, 121A-B, 140A-B-C, 131A-B-C.
2. Three elective lecture courses chosen from Mathematics 105A-B (plus 105LA-LB), 118A-B-C, 130A-B-C, 171A-B.
B. Nine Economics courses: Economics 20A-B-C, 100A-B-C, 123A-B-C.
Specialization in Applied and Computational Mathematics
Upper-division requirements:
A. Thirteen upper-division Mathematics lecture courses (plus any associated laboratories) including:
1. Ten required lecture courses: Mathematics 105A-B, 107 (plus 105LA-LB, 107L); 112A-B-C, 115, 121A, 140A-B.
2. A two-quarter sequence chosen from: Mathematics 118A-B, 120A-B, 130A-B, 131A-B, 140C-D, 162A-B.
3. One additional Mathematics course numbered 100-189.
B. Two approved courses in an area of application outside of Mathematics. Approval must be obtained in advance from the Mathematics Department. The student is responsible for satisfying any prerequisites for these courses.
Specialization in Statistics
Satisfaction of all the requirements for the Mathematics major; in fulfilling requirements F and H, students must include the following courses: Mathematics 131A-B-C, 132A-B-C, and one additional course approved in advance by the Mathematics Department Undergraduate Advisor.
Departmental Requirements for the Mathematics Major with a Specialization in Mathematics for High School Teaching
Admission to this specialization requires approval in advance by the Mathematics Department. The admission process, which includes an interview with the Department's Undergraduate Advisor and its Tutor Supervisor, should be completed no later than the end of the student's junior year.
Lower-Division Requirements:
A. Mathematics 2A-B; 2J or 2C, with 2J preferred; 2D; 3A; 3D; 6A; 13.
B. Computing skills attained through either Information and Computer Science 21, Engineering E10, Engineering CEE10, Engineering ECE10, Engineering MAE10, or Physics 53.
C. One lecture course sequence (plus the indicated laboratories) selected from Chemistry 1A-B-C (plus 1LB-LC); Physics 5A-B-C (plus 5LB-LC), 7A-B-D (plus 7LA-LB-LD), 7A-B-E (plus 7LA-LB), or Physics 7B-D-E (plus 7LB-LD).
D. In addition, students must satisfy an extra science requirement by taking at least three additional approved science lecture courses, including any accompanying laboratories. The following courses are approved:
1. Chemistry 51A-B and 51LA-LB, plus one quarter of Earth System Science 10, 14, 15, 20E, or 20F (for students taking Chemistry 1A-B-C).
2. Physics 5D-E and 5LD-LE, plus one quarter of Physics 20A, 20B, 20C, or 20D (for students taking Physics 5A-B-C);
3. Physics 7E, 51A-B, plus one quarter of Physics 20A, 20B, 20C, or 20D (for students taking Physics 7A-B-D);
4. Physics 7D (plus 7LD) and 51A-B, plus one quarter of Physics 20A, 20B, 20C, or 20D (for students taking Physics 7A-B-E);
5. Physics 51A-B, plus two quarters of Physics 20A, 20B, 20C, or 20D (for students taking Physics 7B-D-E but testing out of Physics 7A);
Although course groupings 1-5 above are the "preferred" ways to satisfy the extra science requirement for this specialization, a student can request approval to substitute other suitable science courses, including certain upper-division Mathematics courses. Such approval is not automatic and should be obtained from the Mathematics Department Undergraduate Advisor before a student takes the courses.
Upper-Division Requirements:
A. Twelve Mathematics lecture courses, numbered 100-189, plus any accompanying laboratories, including: Mathematics 120A-B, 121A, either 121B or 124, 140A-B, 131A, 150, 180, 182, 184.
B. One quarter of Education 100 and two quarters of Mathematics 192.
Requirements for the Minor
One course selected from Mathematics 13, 120A, or 140A, plus six additional upper-division lecture courses in Mathematics (plus the associated laboratories, where applicable) numbered 100-169. (NOTE: Nearly all upper-division courses in Mathematics have Mathematics 2A-B-C as prerequisites, and many courses have additional prerequisites such as Mathematics 2D, 2E, 2F, 3A, and/or 3D.)
There is a variety of career patterns the UCI Mathematics major may select. In many instances, a double major (in Mathematics and an appropriate related field) provides the strongest preparation for the career desired.
Assistance in planning a program of study is available from faculty advisors and the Mathematics Department Undergraduate Advisor.
| Sample Program -- Mathematics Major Interested in Pure Mathematics or Preparing for Graduate Study in Mathematics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2D |
| Physics 7A, 7LA | Physics 7B, 7LB | Physics 7D, 7LD |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 2E | Math. 3A | Math. 3D |
| Math. 2J | ICS 21 | Math. 13 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Junior | ||
| Math. 120A | Math. 120B | Math. 121B |
| Math. 140A | Math. 121A | Math. 140C |
| Breadth/Elective | Math. 140B | Math. 146 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 140D | Math. 151 | Math. 141A |
| Math. 150 | Math. 162A | Math. 152 |
| Breadth/Elective | Breadth/Elective | Math. 162B |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sample Program -- Mathematics Major Concentrating in Mathematics for Economics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2D |
| Physics 7A, 7LA | Physics 7B, 7LB | Physics 7D, 7LD |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 2E | Math. 3A | Math. 3D |
| Math. 2J | ICS 21 | Math. 13 |
| Economics 20A | Economics 20B | Economics 20C |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Junior | ||
| Math. 131A | Math. 131B | Math. 131C |
| Math. 140A | Math. 140B | Math. 140C |
| Economics 100A | Economics 100B | Economics 100C |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 120A | Math. 121A | Math. 121B |
| Math. 105A, LA | Math. 171A | Math. 171B |
| Economics 123A | Economics 123B | Economics 123C |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sample Program -- Mathematics Major Specializing in Applied and Computational Mathematics | |||||
| FALL | WINTER | SPRING | |||
| Freshman | |||||
| Math. 2A | Math. 2B | Math. 2D | |||
| Physics 7A, 7LA | Physics 7B, 7LB | Physics 7D, 7LD | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Sophomore | |||||
| Math. 2J | Math. 2E | Math. 3D | |||
| ICS 21 | Math. 3A | Math. 13 | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | Junior | ||
| Math. 112A | |||||
| Math. 112B | Math. 112C | ||||
| Math. 140A | Math. 140B | Math. 115 | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Senior | |||||
| Math. 105A, LA | Math. 105B, LB | Math. 107, 107L | |||
| Math. 118A | Math. 118B | Math. 118C | |||
| Technical Elective | Technical Elective | Math. 121A | |||
| Breadth/Elective | Breadth/Elective | Breadth/Elective | |||
| Sample Program -- Mathematics Major Specializing in Statistics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2D |
| Physics 7A, 7LA | Physics 7B, 7LB | Physics 7D, 7LD |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 2E | Math. 3A | Math. 3D |
| Math. 2J | ICS 21 | Math. 13 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Junior | ||
| Math. 120A | Math. 121A | Math. 121B |
| Math. 132A | Math. 132B | Math. 132C |
| Math. 140A | Math. 140B | Math. 140C |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 105A, 105LA | Math. 105B, 105LB | Math. 131C |
| Math. 131A | Math. 131B | Math. 146 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sample Program -- Mathematics Major Specializing in Mathematics for High School Teaching | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2D |
| Physics 7A, 7LA | Physics 7B, 7LB | Physics 7D, 7LD |
| Physics 20A | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 2J | Math. 3A | Math. 3D |
| Math. 6A | Physics 51A | Math. 13 |
| Physics 7E | ICS 21 | Physics 51B |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Junior | ||
| Math. 120A | Math. 120B | Math. 121A |
| Math. 140A | Math. 140B | Math. 124 |
| Math. 192 | Math. 192 | Education 100 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 131A | Math. 151 or 131B | Math. 182 |
| Math. 150 | Math. 180 | Math. 184 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Elective | Elective | Elective |
Graduate courses are designed to meet the needs of students doing graduate work in mathematics and in those disciplines that require graduate-level mathematics for their study. Among the fields covered are analysis, algebra, functional analysis, geometry and topology, probability and statistics, ordinary and partial differential equations, and mathematical logic.
In addition to formal courses, there are seminars for advanced study toward the Ph.D. in various fields of mathematics. Topics will vary from year to year. Each seminar is conducted by a staff member specializing in the subject studied. Enrollment will be subject to the approval of the instructor in charge.
The Department offers three pathways which lead to the Master of Science in Mathematics degree: Pure Mathematics, Applied Mathematics, and the Master of Science with a Teaching Credential. The first two programs are described below; the third is described in the next section.
The Master's program serves a dual purpose. For some students it will be a terminal program of mathematics education; for others it will lead to study and research at the doctoral level. To earn the Master of Science degree, the student must satisfy course, language, and residency requirements, and pass a comprehensive examination administered by the Graduate Studies Committee of the Department.
There are two areas of concentration: Pure Mathematics and Applied Mathematics. Each concentration requires the satisfactory completion of 12 upper-division or graduate lecture courses; this includes a core of nine courses (36 units), in each of which the student must earn a grade of B (3.0) or better, and three elective courses (9 to 12 units). At least eight of these courses must be at the graduate level (200-series courses). The specific requirements are described below. A grade point average of at least B (3.0) is required for all courses applicable to the M.S. degree. The student's selection of alternative or elective courses must be approved by the Graduate Studies Committee.
The nine required core courses for the Pure Mathematics concentration are Mathematics 210A-B-C, 220A-B-C, and 230A-B-C. The student must complete three additional approved courses.
The nine required core courses for the Applied Mathematics concentration are Mathematics 210A-B-C, 220A-B-C, and the A-B-C sequence of one of the following: Mathematics 201, 292, 295, or Physics 212. The student must complete three additional approved courses; these may be selected from the preceding list.
In order to satisfy the Comprehensive Examination requirement in the regular Master's program in Mathematics, a student in either the Pure Mathematics concentration or the Applied Mathematics concentration must pass two of the three written Area Examinations (see the Ph.D. program below) at the Master's level or better.
Students must satisfy the language requirement by demonstrating reading proficiency in French, German, or Russian.
The residency requirement ordinarily is satisfied by full-time enrollment for three quarters immediately preceding the award of the M.S. degree. When appropriate, a leave of absence may be granted between matriculation and the final quarters of study.
Master of Science in Mathematics with a Teaching Credential
In cooperation with the UCI Department of Education, the Department of Mathematics sponsors a coordinated two-year program leading to the M.S. degree in Mathematics and the California Single Subject Teaching Credential. In this program the M.S. degree can be obtained under one of two plans: either Plan I (Thesis) or Plan II (Comprehensive Examination). Prospective graduate students interested in this program should so indicate on their applications and should request a detailed description of the program from the Department of Mathematics or the Department of Education.
A student seeking the Ph.D. in Mathematics must demonstrate mastery in the three basic areas of Real Analysis, Complex Analysis, and Algebra, by (a) passing Mathematics 210A-B-C, 220A-B-C, and 230A-B-C (or approved equivalents) with a grade of B or better; and (b) passing three written Area Examinations, one for each of these basic areas, at the Ph.D. level. The Area Examinations, which include both undergraduate and graduate material, are normally given twice each year, just before the start of the fall and winter quarters. All students seeking the Ph.D. degree must successfully complete these examinations within two years of entering the graduate program; students admitted to the Ph.D. program with a Master's degree in mathematics from another institution must successfully complete at least one of these examinations within one year (and complete the rest within two years).
The Department also requires the following for advancement to candidacy for the Ph.D. degree: satisfactory performance at the post-Master's level in nine approved one-quarter graduate lecture courses, which must exclude Mathematics 201, 202, 204, 210, 220, 230, 298, 299, and 399; satisfactory performance in one language examination (French, German, or Russian); and satisfactory performance in the oral qualifying examination.
The oral qualifying examination is conducted by a candidacy committee, appointed by Department on behalf of the Dean of Graduate Studies and the Graduate Council, including at least one member of the faculty outside of the Mathematics Department.
After the student meets the requirements, the Graduate Studies Committee recommends to the Dean of Graduate Studies the advancement to candidacy for the Ph.D. degree.
Teaching experience and training is an integral part of the Ph.D. program. All doctoral students are expected to participate in the teaching program of the Department.
The candidate must demonstrate independent, creative research in mathematics by writing and defending a dissertation that makes a new and valuable contribution to mathematics in the candidate's area of concentration. Following advancement to candidacy, a doctoral committee, appointed by the Department Chair on behalf of the Dean of Graduate Studies and the Graduate Council, guides and supervises the candidate's research, study, and writing of the dissertation; conducts an oral defense of the dissertation; and recommends that the Ph.D. be conferred upon approval of the doctoral dissertation.
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