420 Physical Sciences I; (714) 824-5503
Abel Klein, 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)
René A. Carmona, Ph.D. Université de Marseille, Professor of Mathematics (probability, mathematical physics)
Larry Chrystal, M.A. University of California, Irvine, Lecturer in Mathematics
Donald Darling, Ph.D. California Institute of Technology, Professor Emeritus of Mathematics
Panagiota Daskalopoulos, Ph.D. University of Chicago, Assistant 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)
Mark Finkelstein, Ph.D. Stanford University, Associate Professor of Mathematics (analysis)
Matthew D. Foreman, Ph.D. University of California, Berkeley, Professor of Mathematics and of 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, Assistant Professor of Mathematics (algebraic geometry, representation theory)
Abel Klein, Ph.D. Massachusetts Institute of Technology, Department Chair and Professor of Mathematics (mathematical physics)
Peter Li, Ph.D. University of California, Berkeley, 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, Professor of Philosophy and of Mathematics (logic, philosophy, and foundations of mathematics)
George S. McCarty, Ph.D. University of California, Los Angeles, Professor Emeritus of Mathematics (algebraic topology)
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, Department Vice Chair for Administration and Undergraduate Studies and Associate Professor of Mathematics (differential geometry)
Bernard Russo, Ph.D. University of California, Los Angeles, Department Vice Chair for Graduate Studies and Professor of Mathematics (functional analysis)
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)
Senya Shlosman, Ph.D. Kiev University, Professor of Mathematics (probability, mathematical physics)
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, Professor of Mathematics (geometry and topology)
Edriss S. Titi, Ph.D. Indiana University, Associate 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)
Frederic Yui-Ming Wan, Ph.D. Massachusetts Institute of Technology, Vice Chancellor for Research and Dean of Graduate Studies, and Professor of Mathematics and 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, 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 (analysis)
Weian Zheng, Ph.D. Université de Strasbourg, Associate 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 major in Mathematics, a specialization in Statistics, and 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 following required course work of one year of approved calculus.
University Requirements: See pages 5155.
School Requirements: None.
Departmental Requirements
Lower Division Requirements:
A. Mathematics 2A-B-C-D-E; 3A; 2F or 3D (with 3D recommended).
B. Computing skills attained through either Information and Computer Science 21, Engineering E10, or Engineering ECE11.
C. Physics 5A-B-C or Chemistry 1A-B-C. (This also satisfies UCI breadth requirement category II if taken with the accompanying laboratories.)
Upper Division Requirements: Most of the upper-division Mathematics courses are organized into a series of Core Areas. The Core Areas are: Numerical Analysis (courses numbered 100109); Applied Mathematics (110119); Algebra (120129); Probability and Statistics (130139); Analysis (140149); Logic (150159); and Geometry/Topology (160169). There are also non-Core-Area courses (170199). 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 (120129)
D. A third lecture course from the Analysis Core Area (140149)
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 170189
NOTE:
1. Under some circumstances (e.g., double majors), students with prior approval from the Mathematics Department Undergraduate Advisor may substitute appropriate upper-division courses from another department for up to three of the five courses for requirement H.
2. Mathematics courses numbered 190199 may not be used to fulfill the course requirements for the major.
3. Undergraduates who wish to enroll in graduate Mathematics courses should obtain the prior approval of the Mathematics Department Undergraduate Advisor.
Mathematics Major with 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 (plus the associated laboratories), and one additional course approved in advance by the Mathematics Department Undergraduate Advisor.
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 100169. (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.)
| Sample Program -- Mathematics Major Interested in Pure Mathematics or Preparing for Graduate Study in Mathematics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2C |
| Breadth/Elective | Physics 5A | Physics 5B, 5LB |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 3A | Math. 2D | Math. 2E |
| Physics 5C, 5LC | Math 3D | ICS 22 |
| Breadth/Elective | ICS 21 | Math. 13 |
| 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 |
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 Applied Mathematics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2C |
| Breadth/Elective | Physics 5A | Physics 5B, 5LB |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 2D | Math. 3A | Math. 2E |
| Physics 5C, 5LC | Physics 5D, 5LD | Math. 3D |
| ICS 21 | ICS 22 | Physics 5E, 5LE |
| Breadth/Elective | Breadth/Elective | Math. 13 |
| Junior | ||
| Math. 120A | Math. 121A | Math. 121B |
| Math. 140A | Math. 140B | Math. 140C |
| Breadth/Elective | Math. 171A | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 105A, 105LA | Math. 105B, 105LB | Math. 107, 107L |
| Math. 114A | Math. 112A | Math. 112B |
| Math. 140D | Math. 114B | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sample Program -- Mathematics Major Specializing in | ||
| Mathematical Statistics | ||
| FALL | WINTER | SPRING |
| Freshman | ||
| Math. 2A | Math. 2B | Math. 2C |
| Breadth/Elective | Physics 5A | Physics 5B, 5LB |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Sophomore | ||
| Math. 3A | Math. 2D | Math. 2E |
| Physics 5C, 5LC | Math. 3D | ICS 22 |
| Breadth/Elective | ICS 21 | Math. 13 |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Junior | ||
| Math. 120A | Math. 121A | Math. 121B |
| Math. 132A, 132LA | Math. 132B, 132LB | Math. 132C, 132LC |
| Math. 140A | Math. 140B | Math. 140C |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Senior | ||
| Math. 105A, 105LA | Math. 105B, 105LB | Math. 131C, 131LC |
| Math. 131A, 131LA | Math. 131B, 131LB | Breadth/Elective |
| Breadth/Elective | Breadth/Elective | Breadth/Elective |
| Math. 140D | Breadth/Elective | Breadth/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.
