DEPARTMENT OF MATHEMATICS
103 Multipurpose
Science and Technology Building; (949) 824-5503
John S. Lowengrub, Department
Chair
Faculty
Takeo Akasaki, Ph.D. University of California, Los Angeles, Professor Emeritus of Mathematics (ring theory)
Vladimir Baranovsky, Ph.D. University of Chicago, Assistant Professor of Mathematics (algebraic geometry)
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
Michael C. Cranston, Ph.D. University of Minnesota, Department Vice Chair for Graduate Studies and Professor of Mathematics (probability)
Vittorio Cristini, Ph.D. Yale University, Assistant Professor of Biomedical Engineering and Mathematics
Donald Darling, Ph.D. California Institute of Technology, Professor Emeritus of Mathematics
Lawrence Man Hou Ein, Ph.D. University of California, Berkeley, Professor of Mathematics (algebraic geometry)
Paul C. Eklof, Ph.D. Cornell University, Department Vice Chair for Undergraduate Studies and 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 Emeritus of Mathematics (arithmetic geometry, complex variables)
Patrick Guidotti, Ph.D. University of Zürich, Assistant Professor of Mathematics (applied mathematics)
Svetlana Jitomirskaya, Ph.D. Moscow State University, Professor of Mathematics (mathematical physics)
Richard K. Juberg, Ph.D. University of Minnesota, Professor Emeritus of Mathematics (analysis, differential equations)
Ludmil Katzarkov, Ph.D. University of Pennsylvania, Professor of Mathematics (algebraic geometry, representation theory)
Abel Klein, Ph.D. Massachusetts Institute of Technology, Professor of Mathematics (mathematical physics)
Natalia L. Komarova, Ph.D. University of Arizona, Assistant Professor of Mathematics and of Ecology and Evolutionary Biology (applied mathematics)
Rachel Lehman, Ph.D. University of California, Irvine, Lecturer in Mathematics
Peter Li, Ph.D. University of California, Berkeley, UCI Chancellor's Professor of Mathematics (differential geometry)
Song-Ying Li, Ph.D. University of Pittsburgh, Professor of Mathematics (harmonic analysis, several complex variables)
John S. Lowengrub, Ph.D. New York University, Department Chair and Professor of Mathematics (computational mathematics)
Zhiqin Lu, Ph.D. New York University, Associate Professor of Mathematics (differential geometry)
Penelope Maddy, Ph.D. Princeton University, UCI Chancellor's Professor of Logic and Philosophy of Science and of Mathematics (logic, philosophy, and foundations of mathematics)
Caryl Margulies, Ph.D. University of California, Irvine, Lecturer in Mathematics
Eric D. Mjolsness, Ph.D. California Institute of Technology, Associate Professor of Computer Science and Mathematics
Qing Nie, Ph.D. Ohio State University, UCI Chancellor's Fellow and Professor of Mathematics and Biomedical Engineering (computational applied mathematics)
Timur Oikhberg, Ph.D. Texas A&M University, Associate Professor of Mathematics (analysis)
Richard S. Palais, Ph.D. Harvard University, Adjunct Professor of Mathematics (differential geometry)
David L. Rector, Ph.D. Massachusetts Institute of Technology, Professor Emeritus of Mathematics (algebraic topology, computer algebra)
Robert C. Reilly, Ph.D. University of California, Berkeley, Associate Professor of Mathematics (differential geometry)
Karl C. Rubin, Ph.D. Harvard University, Professor of Mathematics, and Edward and Vivian Thorp Chair in Mathematics (number theory)
Bernard Russo, Ph.D. University of California, Los Angeles, Professor Emeritus of Mathematics (functional analysis)
Donald G. Saari, Ph.D. Purdue University, Director of the Institute for Mathematical Behavioral Sciences and 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 Emeritus of Mathematics (analysis)
Alice Silverberg, Ph.D. Princeton University, Professor of Mathematics and Computer Science (number theory and arithmetic algebraic geometry)
William H. Smoke, Ph.D. University of California, Berkeley, Professor Emeritus of Mathematics (homological algebra)
Knut Solna, Ph.D. Stanford University, Associate Professor of Mathematics (applied mathematics)
Ronald J. Stern, Ph.D University of California, Los Angeles, Dean of the School of Physical Sciences and Professor of Mathematics (geometry and topology)
Chuu-Lian Terng, Ph.D. Brandeis University, Professor of Mathematics and National Science Foundation "ADVANCE" Chair (differential geometry)
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, 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)
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 Emeritus of Mathematics (analysis)
Janet L. Williams, Ph.D. Brandeis University, Professor Emerita of Mathematics (probability and statistics)
Jack Xin, Ph.D. New York University, Professor of Mathematics (applied mathematics)
James J. Yeh, Ph.D. University of Minnesota, Professor of Mathematics (real and stochastic analysis)
Martin Zeman, Ph.D. Humboldt University (Berlin), Associate Professor of Mathematics (logic and combinatorics)
Hong-Kai Zhao, Ph.D. University of California, Los Angeles, Associate Professor of Mathematics and Computer Science (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 there are five tracks; besides
the standard track, there are four specializations or concentrations (in Mathematics
for Economics, Applied and Computational Mathematics, Statistics, and Mathematics
for Education). 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 and at http://www.due.uci.edu/Change_of_Major.html. 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.
REQUIREMENTS FOR THE BACHELOR'S DEGREE
University Requirements: See pages 59-64.
School Requirements: None.
Departmental Requirements
Lower-Division Requirements (for all Mathematics majors except those in the Education specialization):
A. Mathematics 2A-B, 2D (or H2D), 2E (or H2E), 2J, 3A, 3D.
B. Computing skills attained through either Information and Computer Science 21, Engineering E10, Engineering CEE10, Engineering EECS10, Engineering EECS12, Engineering MAE10, or Physics 53.
C. One three-quarter lecture course sequence selected from Chemistry 1A-B-C; Physics 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 Education 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 (170-189). Students are required to complete 15 upper-division one-quarter lecture courses in Mathematics (with associated laboratories when applicable) as follows. (Mathematics Honors Program students follow modified requirements, as explained in a later section.)
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
The Department offers one concentration and three specializations. Note that all require the completion of an application and an interview with an advisor. Mathematics 13 is strongly recommended for all Mathematics majors, as preparation for upper-division courses.
Concentration in Mathematics for Economics
Admission to this concentration requires approval in advance by the Mathematics Department. The admissions process begins with completing a form at the Department office, and includes an interview with the Department's advisor for the concentration. This approval should be applied for after the student has completed Economics 20A-B, 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 120A, 121A-B, 140A-B-C, 131A-B-C (same as Statistics 120A-B-C).
2. Three elective lecture courses chosen from Mathematics 105A-B (plus 105LA-LB), 107 (plus 107L), 112A-B-C, 118A-B-C, 130B-C, 171A-B, 176.
B. Eight Economics courses: Economics 20A-B, 105A-B-C, 123A-B-C.
Specialization in Applied and Computational Mathematics
Admission to this specialization requires approval in advance by the Mathematics Department. The admissions process begins with completing a form at the Department office, and includes an interview with the Department's advisor for the specialization. This approval should be applied for no later than the end of the junior year.
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 114A-B, 114A and 147, 118A-B, 120A-B, 130A-B, 131A-B, 140C-D, 162A-B, 171A-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 advisor for this specialization. The student is responsible for satisfying any prerequisites for these courses.
Specialization in Statistics
Admission to this
specialization requires approval in advance by the Mathematics Department. The admissions
process begins with completing a form at the Department office, and includes an
interview with the Department's advisor for the specialization. All the requirements for the Mathematics
major must be satisfied; in fulfilling requirements F and H, students must include
the following courses: Mathematics 131A-B-C (or Statistics 120A-B-C), either 130B-C
or 132B-C, and two additional courses approved in advance by the advisor for this
specialization.
Specialization in Mathematics for Education
Admission to this specialization requires approval in advance by the Mathematics Department. The admission process begins with completing a form at the Department office, and includes an interview with the Department's Undergraduate Advisor and its Tutor Supervisor. This approval should be applied for no later than the end of the junior year.
This specialization helps to prepare students for teaching mathematics. Students wishing to go on and teach at the intermediate and high school levels should also consult with an academic advisor in the Department of Education. A California Commission on Teaching Credentialing (CCTC)-approved subject-matter program (SMP) in Mathematics can be easily satisfied in tandem with this specialization, and enables students to waive a subject matter exam for teachers. Specific SMP requirements and enrollment procedures are available from the Department of Education.
Lower-Division Requirements: The same as for other tracks except that Mathematics 13 may replace Mathematics 2E (or H2E).
Upper-Division Requirements:
A. Mathematics 120A-B, 121A, 124, 140A-B, 131A-B (or Statistics 120A-B), 150, 161, 180, 184; plus one additional Mathematics course numbered 100-189.
B. One quarter of Education 172B and two quarters of Mathematics 192.
HONORS PROGRAM IN MATHEMATICS
The Honors Program in Mathematics is open to all junior and senior Mathematics majors who meet the minimum academic qualifications of a 3.5 GPA in Mathematics courses and a 3.2 GPA overall. In addition to satisfying the requirements for the major in Mathematics (in any one of its tracks), participants must complete at least one of the two series Mathematics 205A-B-C (Introduction to Graduate Analysis) or 206A-B-C (Introduction to Graduate Algebra) with a grade of C or better. If Mathematics 205A-B-C is not taken, then 140A-B-C-D must all be completed. If Mathematics 206A-B-C is not taken, then 120A-B and 121A-B must all be completed.
In terms of satisfaction of the Mathematics major requirements, Mathematics 205A-B-C counts as the equivalent of four upper-division courses, specifically 140A-B-C-D; and 206A-B-C counts as the equivalent of four upper-division courses, specifically, 120A-B and 121A-B. The graduate sequences may be taken in place of or in addition to the undergraduate courses named.
Students must apply for the Honors Program no later than the fall quarter of their senior year. Those who are accepted enroll in the Honors Seminar (Mathematics H195A-B) during the winter and spring quarter of their senior year. At the end of the spring quarter students submit an Honors thesis, which is designed and completed under the supervision of the Honors Seminar faculty. (Mathematics H195B may be counted toward the major requirements as one of the five additional courses in area H.) Upon approval of the thesis by the Department's Honors Committee and completion of all other requirements, students graduate with Honors in Mathematics, and this distinction is noted on their transcript.
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 100-188. NOTE: Nearly all upper-division courses in Mathematics have Mathematics 2A-B-J as prerequisites, and many courses have additional prerequisites such as Mathematics 2D, 2E, 3A, and/or 3D.
PLANNING A PROGRAM OF STUDY
The application process for the specializations and concentrations is designed to make sure the student gets suitable advising in planning a program of study. For all Mathematics majors, or prospective majors, assistance in planning a program of study is available from the Mathematics Department Undergraduate Advisor and the advisors for the various tracks, as well as from the academic counselors for the School of Physical Sciences. The accompanying sample programs are only examples.
Majors should consider taking Mathematics H2D in place of 2D and H2E in place of 2E. Those in the specialization for Education should note that Mathematics 124, 161, 180, and 184 may not be offered more than once every other year and thus should be taken when offered.
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, applied and computational mathematics, mathematical biology, functional analysis, geometry and topology, probability, 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 faculty member specializing in the subject studied. Enrollment will be subject to the approval of the instructor in charge.
MASTER OF SCIENCE IN MATHEMATICS
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 and residency requirements, and pass Comprehensive Examinations administered by the Graduate Studies Committee of the Department.
The total number of required courses for the M.S. degree is 12 courses, completed with satisfactory performance. Students are required to complete at least one series of the following courses: Mathematics 210A-B-C, 220A-B-C, or 230A-B-C. At most one undergraduate course may count as an elective course, provided it is sponsored by rank faculty and approved by the Graduate Advisor. At most one elective course (of at least three units) is allowed outside the Department.
Students will take Advisory Examinations in Algebra and Analysis upon entrance to the graduate program. The Advisory Examination in Algebra is based on the courses Mathematics 120A and 121A-B plus some advanced topics in group theory and linear algebra; students who do not pass this examination will be asked to take the Mathematics 206A-B-C sequence. The Advisory Examination in Analysis is based on the courses Mathematics 140A-B-C-D; students who do not pass this examination will be asked to take the Mathematics 205A-B-C sequence.
Students must pass two Comprehensive Examinations, one in Algebra and one in Analysis, before the beginning of their second year in the graduate program and will be given, at most, two chances to pass each examination. Students who have passed the Advisory Examination will be exempted from taking the corresponding Comprehensive Examination.
Mathematics 199, 297, 298, 299, and 399 may not be used to fulfill course requirements.
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 program for the M.S. degree in Mathematics and the California Single Subject Teaching Credential. This option requires 12 courses, at least eight of which must be graduate courses. Three thesis courses (Mathematics 299) may be used as part of the course work for this option. The Advisory and Comprehensive Examination requirements are the same as for the regular Master's degree. Prospective graduate students interested in this program should so indicate on their applications and can request a detailed description of the program from the Department of Mathematics or the Department of Education.
DOCTOR OF PHILOSOPHY IN MATHEMATICS
When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. Qualifying Examinations, Advancement to Candidacy Examination, and dissertation.
All students will take Advisory Examinations in Algebra and Analysis upon entrance to the graduate program. The Advisory Examination in Algebra is based on the courses Mathematics 120A and 121A-B, plus some advanced topics in group theory and linear algebra; students who do not pass this examination will be asked to take the Mathematics 206A-B-C sequence. The Advisory Examination in Analysis is based on material covered in Mathematics 140A-B-C-D; students who do not pass this examination will be asked to take the Mathematics 205A-B-C sequence. All students who take Mathematics 205A-B-C (Analysis) and 206A-B-C (Algebra) must pass, at the beginning of their second year in the graduate program, the corresponding Comprehensive Examination, which covers the material of the Advisory Examination plus Mathematics 205 or 206, respectively.
Each student must choose at least two series of the following three series of courses—Mathematics 210A-B-C (Real Analysis), 220A-B-C (Complex Analysis), or 230A-B-C (Algebra)—and pass two written Qualifying Examinations from these courses before the end of their third year. Each examination may be taken twice. A student who passes the examination prior to taking the corresponding course will be exempted from taking the course. The Department will offer the Qualifying Examinations twice each year, during orientation week before the fall quarter and at the end of spring quarter.
By the end of their second year, students must declare a major specialization from the following areas: Algebra, Analysis, Applied and Computational Mathematics, Geometry and Topology, Logic, or Probability. Students are required to take two series of courses from their chosen area. (Students who later decide to change their area must also take two series of courses from the new area.) Additionally, all students must take two series of course outside their declared major area of specialization. Special topics courses within certain areas of specialization and courses counted toward the M.S. degree, other than Mathematics 205A-B-C and 206A-B-C, will count toward the fulfillment of the major specialization requirement.
By the beginning of their third year, students must have an advisor specialist in their major area. With the advisor's aid, the student forms a committee for the Advancement to Candidacy oral examination. This committee will be approved by the Department on behalf of the Dean of Graduate Studies and the Graduate Council and will have five faculty members. At least one, and at most two, of the members must be faculty from outside the Department. Before the end of the third year, students must have a written proposal, approved by their committee, for the Advancement to Candidacy examination. The proposal should explain the role of at least two series of courses from the student's major area of specialization and of additional research reading material, and should have a plan for investigating specific topics under the direction of the student's adviser(s). The courses Mathematics 210A-B-C, 220A-B-C, and 230A-B-C cannot count for both Qualifying and Advancement to Candidacy Examinations. 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. Students should advance to candidacy by the beginning of their fourth year.
Teaching experience and training is an integral part of the Ph.D. program. All doctoral students are expected to participate in the Department's teaching program.
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. Upon advancement to candidacy a student must form a Thesis Committee, ideally a subcommittee of the Advancement Examination Committee, consisting of at least three faculty members and chaired by the student's advisor. The committee 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. The normal time for completion of the Ph.D. is five years, and the maximum time permitted is seven years.
GRADUATE PROGRAM IN MATHEMATICAL AND COMPUTATION BIOLOGY
The graduate program in Mathematical and Computational Biology (MCB) is a one-year "gateway" program designed to function in concert with selected department programs, including the Ph.D. in Mathematics. Detailed information is available online at http://mcsb.bio.uci.edu/ and in the School of Biological Sciences section of the Catalogue, page 156.
