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Mathematics

Catalog pages 475-484

Subject abbreviation: MATH College of Natural and Agricultural Sciences

James Kelliher, Ph.D., Chair Department Office, 224 Skye Hall

  • (951) 827-3113; mathdept.ucr.edu

Professors Mark Alber, Ph.D., Distinguished Professor Vyjayanthi Chari, Ph.D., Distinguished Professor, F. Burton Jones Endowed Chair Wee Liang Gan, Ph.D. Jacob Greenstein, Ph.D. James Kelliher, Ph.D. Yat Sun Poon, Ph.D. Ziv Ran, Ph.D. Rodolfo Torres, Ph.D., Distinguished Professor Stefano Vidussi, Ph.D. Frederick H. Wilhelm, Jr., Ph.D. Feng Xu, Ph.D. Qi S. Zhang, Ph.D.

Professor of Teaching Estela Gavosto, Ph.D.

Professors Emeriti John C. Baez, Ph.D. Richard E. Block, Ph.D. Mei-Chu Chang, Ph.D. John E. de Pillis, Ph.D. Gerhard Gierz, Ph.D. Zhuang-dan Guan, Ph.D. Michel L. Lapidus, Ph.D., Distinguished Pro- fessor Emeritus Frederic T. Metcalf, Ph.D. Malempati M. Rao, Ph.D. Louis J. Ratliff, Jr., Ph.D. Reinhard Schultz, Ph.D. James D. Stafney, Ph.D. Albert R. Stralka, Ph.D. Bun Wong, Ph.D.

Associate Professors Po-Ning Chen, Ph.D. Weitao Chen, Ph.D. Brian Collier, Ph.D. Jose Gonzalez, Ph.D. Carl Mautner, Ph. D. Amir Moradifam, Ph.D. Maziar Raissi, Ph.D. Peter Samuelson, Ph.D. Qixuan Wang, Ph.D. Zhenghe Zhang, Ph.D. Associate Professors of Teaching Kevin Costello, Ph.D. Sara Lapan, Ph.D. David Weisbart, Ph.D.

Assistant Professors Thomas Bury, Ph.D. Patricio Gallardo Candela, Ph.D. Yat Tin Chow, Ph.D. Tom A. Gannon, Ph.D. Jia Gou, Ph.D. Siting Liu, Ph.D. Mykhailo Potomkin, Ph.D. Yiwei Wang, Ph.D. Morgan Weiler, Ph.D. Agnieszka Zelerowicz, Ph.D.

Assistant Professor of Teaching Jeffrey Meyer, Ph.D. Sarah Yeakel, Ph.D.

** Adjunct Assistant Professor Heyrim Cho, Ph.D.

Visiting Assistant Professors Esther Banaian, Ph.D. David Clausen, Ph.D. Liping Deng, Ph.D. Becky Eastham, Ph.D. Pallav Goyal, Ph.D. Hussain Ibdah, Ph.D. Hamid Naderiyan, Ph.D. Ivo Terek, Ph. D. Boris Tsvelikhovskiy, Ph.D. William Wood, Ph.D. Keija Zhu, Ph.D.

Lecturer Michael Curtis

Cooperating Faculty Bai-Lian “Larry” Li, Ph.D. (Botany and Plant Sciences) Academic Coordinator Brandon Coya, Ph.D. Savanna Gee, Ph.D.

Major

The Department of Mathematics offers a B.A. and B.S. degree in programs that share a common, solid mathematical foundation but differ in their specializations in the pure and applied areas of mathematics. These programs can provide the basis for careers in mathematics itself or within the many scientific and business fields, which, in today’s technological society, depend on a basic knowledge of mathematical methods.

The B.A. in Mathematics, following the liberal arts tradition, combines a broad coverage of the humanities and social sciences with a moderate amount of advanced mathematics in the major. It is selected most often either by students who intend to obtain a teaching credential with a specialty in mathematics or by students who wish to pursue graduate work in business or the social sciences.

The B.S. in Mathematics is more technical and contains a greater concentration of work in the major field. The Pure Mathematics program is directed toward students who may wish to pursue graduate work in pure mathematics. The General Applied Math option is directed toward students who may wish to pursue grad- uate work in applied mathematics.

The other Applied Mathematics programs, with options in Biology, Chemistry, Economics, Environmental Sciences, Physics, and Statistics, are designed to provide a rigorous training in mathematics together with a substantial background in the discipline of the option. The Computational Mathematics program is de- signed to prepare the student for professional work with computers and computer systems and for graduate work in computer science.

The B.S. in Mathematics for Secondary Teachers is intended for students planning to pursue a career in secondary education. Its courses cover the high school curriculum from an advanced perspective. Students are required to complete mathematics education and education courses in order to facilitate presence in the classroom early in their undergraduate career and to better prepare them for entry in a credential program.

Academic Advising Each Mathematics major is assigned a faculty advisor who assists the student in formulating educational goals and monitors the student’s subsequent progress in an academic program. Each quarter a study list must be approved by this advisor. Advising for all math majors is conducted by the CNAS Academic Advising Center in 1223 Pierce Hall.

Teaching Credential Teachers in the public schools in California must have a credential approved by the State Commission on Teacher Credentialing. The credential requires an undergraduate major, baccalaureate degree, and completion of a graduate credential program such as that offered by the School of Education at UCR (see Education in this catalog). The Bachelor of Sci- ence in Mathematics for Secondary Teachers assists students in their preparation to face the challenges of a credentialing program.

Before admission and student teaching in a graduate credential program, the candidate must pass the California Basic Education Skills Test (CBEST) and demonstrate subject-matter proficiency in the fields which the candidate will teach. The candidate can demonstrate proficiency either by passing the commission’s subject-matter assessment examination or completing an undergraduate program that is state approved for teacher preparation.

California Teach-Science and Mathematics Initiative (CalTeach-SMI) California Teach-Science and Mathematics Initiative (CalTeach-SMI) has a goal of addressing the critical need of highly qualified K-12 science and mathematics teachers in California. With an economy increasingly reliant on science, technology, engineering, and mathematics (STEM) and the anticipated large scale retirement of qualified teachers, this is an essential time to explore and prepare for a career in teaching science or mathematics.

CalTeach-SMI at UCR offers undergraduate students paid/unpaid opportunities, such as the Scholar Apprentice Program, to explore STEM teaching as a career option. Through CalTeach-SMI, students receive advising and mentoring to prepare for entrance into an intern teaching credential program while diligently coordinating with academic advisors to ensure completion of STEM degree requirements. The CalTeach-SMI Resource Center provides future STEM teachers with material and financial resources to promote planning and professional development towards a science/mathematics education career.

For more information about the CalTeach-SMI program, please visit smi.ucr.edu, the Resource Center at 1114 Pierce Hall, or on Facebook at facebook.com/ScienceMathInitiativeAtUcr and on Instagram at instagram.com/smiatucr/.

Change of Major Criteria All courses taken to fulfill major requirements must be completed with grades of C- or better after repeats.

Freshman (0-44.9 units earned) Completion of the following with grade of “C-“or better and must be in good academic standing. (2.0 quarter and cumulative GPA).

MATH 005B or MATH 007A or MATH 009A or MATH 009HA

Sophomores (45-89.9 earned units) Completion of the following three criteria with grade of “C-“or better and must be in good academic standing. (2.0 quarter and cumulative GPA).

• MATH 005B or MATH 007A or MATH 009A or MATH 009HA

• MATH 005C or MATH 007B or MATH 009B or MATH 009HB

• MATH 005C or MATH 009C or MATH 010A

Juniors & Seniors (90 or more earned units) Completion of the following five criteria with grade of “C-“or better and must be in good academic standing. (2.0 quarter and cumulative GPA).

• MATH 005B or MATH 007A or MATH 009A or MATH 009HA

• MATH 005C or MATH 007B or MATH 009B or MATH 009HB

• MATH 005C or MATH 009C

• MATH 010A

• MATH 031

Major change requests are reviewed during the 2nd, 3rd, 4th & 10th weeks of each quarter. Students are required to complete degree programs without exceeding 216 earned units.

Transfer Selection Criteria Applicants to majors in the College of Natural and Agricultural Sciences are selected on the basis of academic preparation, as assessed by their GPA and the strength of preparation for the intended major. A GPA of at least 2.70 is required. (This is a baseline GPA for consideration and not a guarantee of admission.)

In addition, applicants will need to complete college courses comparable to at least two of the following UCR year-long sequences in order to meet selection criteria for this major. Courses must be completed with “C” grades or better:

At least one sequence from:

or MATH 009B, and MATH 009C (mandatory)

(mandatory)

And at least one sequence from:

(and BIOL 005C, if articulated)

CHEM 01LB, CHEM 001C, and CHEM 01LC

EE 020A or MATH 046

Courses must be completed with a letter grade, with no grade lower than a “C.” Students should visit assist.org for updated and com- prehensive major preparation requirements.

University Requirements

See Undergraduate Studies section.

College Requirements

See College of Natural and Agricultural Scienc- es, Colleges and Programs section.

Major Requirements for the Bachelor of Arts and Bachelor of Science in Mathematics To fulfill the Natural Sciences requirement, the Department of Mathematics requires the following:

  • 1. One of the year sequences:

CHEM 01LA, CHEM 01LB, CHEM 01LC,

  • 2. Either one course in the physical sciences

listed above if (a) above is completed or one course in the biological sciences if (b) or (c) above is completed

The major requirements for the B.A. and B.S. degrees in Mathematics are as follows:

For the Bachelor of Arts

  • 1. Lower-division requirements (25-27 units)

or MATH 09HA

  • 2. Four (4) units of either CS 010A or one

upper-division course in Statistics

  • 3. A minimum of 36 units of upper-division

mathematics, excluding courses in the MATH 190–199 series

For the Bachelor of Science Lower-division requirements for all programs are (33-36 units)

or MATH 09HA

  • b) Thirty-six (36) additional units of

upper-division mathematics or other related courses approved by the un- dergraduate advisor

  • c) At least three courses from (b) above

must be from MATH 132, MATH 145A, MATH 145B, MATH 151C, MATH 171, MATH 172 (For students who wish to pursue graduate work, MATH 132, MATH 145A, MATH 145B, MATH 151C, MATH 165A, MATH 165B, MATH 171, and MATH 172 are recommended)

  • d) Courses in the MATH 190-199 series are

excluded

  • 2. Applied Mathematics programs

(MATH 135A and MATH 135B) or (MATH 149A and MATH 149B), MATH 110, MATH 131, MATH 146A, MATH 146B, MATH 146C and the courses in one of the following options:

  • a) General Applied Mathematics option
  • (3) Students will select sixteen (16) ad-

ditional units from MATH 120, MATH 121, MATH 126, MATH 135A, MATH 135B, MATH 135C, MATH 147, MATH 148, MATH 149A, MATH 149B, MATH 151B, MATH 161, MATH 162, MATH 163, MATH 165A, MATH 165B

  • b) Biology option

BIOL 005C

  • (5) Four (4) additional units of up-

per-division biology

  • c) Chemistry option

CHEM 01LA, CHEM 01LB, CHEM 01LC

CHEM 113

  • (5) Four (4) additional units of up-

per-division chemistry

  • d) Economics option

MATH 149B

  • (2) Four upper-division Economics

courses (17-20 units) including:

  • (b) Three courses to be chosen from

ECON 104B, ECON 104C, ECON 105A, ECON 105B, ECON 107, ECON 108, ECON 110, ECON 117/PHIL 119, ECON 129, ECON 134/BUS 106, ECON 135, ECON 136, ECON 153, ECON 160/BUS 160, ECON 171/BUS 171, ECON 178/BUS 178.

  • e) Environmental Sciences option

CHEM 01LA, CHEM 01LB, CHEM 01LC

  • (7) Four (4) additional units of upper-

division environmental sciences

  • f) Physics option
  • 3. Computational Mathematics program

MATH 131, MATH 132, (MATH 135A and MATH 135B) or (MATH 149A and MATH 149B)

  • c) Twenty (20) additional units of tech-

nical electives to be chosen from (1) and (2) below. At least 12 units must be chosen from (2).

MATH 135B, MATH 135C, MATH 146A, MATH 146B, MATH 146C, MATH 149A, MATH 149B, MATH 150 or MATH 151A, MATH 161, MATH 162, MATH 163, MATH 171

CS 170, CS 171, CS 173, CS 177

Major Requirements for the Bachelor of Science in Mathematics for Secondary School Teachers

  • 1. Lower-division Mathematics requirements

(27-29 units)

or MATH 09HA

  • 2. Upper-division Mathematics requirements

(36 units)

MATH 149A, MATH 149B, MATH 151B, MATH 151C, MATH 165A, MATH 171, MATH 172

  • 3. Additional Mathematics and related disci-

plines requirements (12 units)

  • c) STAT 155
  • 4. Natural Sciences (16-20 units)

BIOL 05LA

or an additional laboratory Biological science course

  • 5. Social Sciences (16 units)
  • a) One course in ECON or POSC
  • b) One course in ANTH
  • c) One course in PSYC
  • d) One course in SOC
  • 6. Mathematics Education and Education

requirements (18 or 19 units): EDUC 003 or EDUC 004 or EDUC 100B or equivalent, EDUC 104, EDUC 132, EDUC 147, EDUC 162

Mathematics Honors Program Candidates for the Honors Program in Mathe- matics must complete

  • 1. Earn an overall GPA of at least 3.50 in

Mathematics.

  • 2. Earn a grade of “B” or better in each of

MATH 151A, MATH 151B and MATH 151C.

  • 3. Earn a grade of “B” or better in each of

MATH 145B and MATH 171 OR in each of MATH 146A, MATH 146B and MATH 146C OR in each of MATH 149A and MATH 149B.

  • 4. Satisfactorily complete one of the follow-

ing:

  • i) A research project earning a grade of

“A” in MATH 197.

  • ii) Two courses chosen from one of the

sequences: MATH 201A, 201B, 201C; MATH 205A, MATH 205B, MATH 205C: MATH 209A, MATH 209B, MATH 209C; MATH 210A, MATH 210B with a grade of “B” or better in each course.

It is the responsibility of the honors can- didates to notify the department of their eligibility.

Minor

The following are the requirements for a minor in Mathematics.

  • 1. Lower-division courses (18-20 units)

or MATH 009HA

  • 2. Upper-division requirements: 24 units of

upper-division mathematics courses. Of the specified upper-division units, a min- imum of 16 must be unique to the minor and may not be used to satisfy major requirements and no more than 4 units in courses numbered 190–199.

Students with a minor in Mathematics should consult with a faculty advisor in Mathematics to construct a specific program consistent with their goals.

See Minors under the College of Natural and Agricultural Sciences in the Colleges and Programs section of this catalog for additional information on minors.

Education Abroad Education Abroad is an excellent opportunity to learn more about another country and its culture while taking courses to earn units toward graduation. Students should plan study abroad well in advance to ensure that the courses taken fit with their overall program at UCR. Consult the departmental student affairs officer for assistance. For further details, visit Education Abroad at ea.ucr.edu or call (951) 827-4113.

See Education Abroad in the Educational Opportunities section in the beginning of this catalog.

Graduate Programs

The Department of Mathematics offers the M.A., M.S., and Ph.D. degrees in Mathematics.

Admission A bachelor’s degree, or its equivalent, from an accredited institution is required. GRE test scores are not required or considered.

M.A. or M.S. in Mathematics General university requirements are listed in the Graduate Studies section of this catalog. Specific requirements are as follows:

  • 1. Completion of two of the following

sequences: MATH 201A, MATH 201B, MATH 201C; MATH 205A, MATH 205B, MATH 205C; MATH 206A, MATH 206B, MATH 206C, MATH 209A, MATH 209B, MATH 209C; or MATH 210A, MATH 210B, MATH 210C with a grade of “C” or better in each course and a GPA of 3.00 in each chosen sequence

  • 2. As a substitute for one or more course se-

quences in (1), passing a Ph.D. qualifying examination fulfills the course require- ment of the corresponding sequence

  • 3. Taking 36 units of courses numbered

between MATH 110 and MATH 189, or be- tween MATH 200 and MATH 210. At least 18 must be from courses numbered between MATH 200 and MATH 210.

Professional Development in Mathematics.

The requirements of 1 and 2 above constitute the comprehensive final examination requirement for the degree.

M.S. in Mathematics (Applied) General university requirements are listed in the Graduate Studies section of this catalog. Specific requirements are as follows:

  • 1. Completion of two sequences of courses

numbered between MATH 206 and MATH 209 with a grade of “C” or better in each course and a GPA of at least 3.00 in each chosen sequence. A sequence consists of all courses with the same course number except for an alphabetical suffix. Any course without an alphabetical suffix is not part of a sequence.

  • 2. As a substitute for one or more course

sequences in (1), passing a Ph.D. qualifying examination fulfills the course requirement of the corresponding sequence.

  • 3. Taking 36 units of courses numbered

between MATH 110 and MATH 189, or between MATH 200 and MATH 210. At least 18 units must be from courses numbered between MATH 200 and MATH 210.

  • 4. Completion of 2 units of MATH 401, Profes-

sional Development in Mathematics.

The requirements of 1 and 2 above constitute the comprehensive final examination requirement for the degree.

Doctoral Degree

The Department of Mathematics offers the Ph.D. degree in Mathematics.

Specific requirements are as follows:

  • 1. Passing four sequences numbered

between MATH 200 and MATH 210. A sequence consists of all courses with the same course number except for an alpha- betical suffix. Any course without an al- phabetical suffix is not part of a sequence.

  • 2. For two of the four chosen sequences

in (1), a qualifying examination must be taken. The qualifying examinations, which are associated with two of the year-long sequences, must be passed with a grade of “A”.

A student is allowed to take the qualifying examination at most twice for each sequence. Students must attempt at least one of these examinations in their 2nd year and are expected to pass both no later than the 3rd year of their Ph.D. program.

  • 3. Completing four quarter-courses in math-

ematics numbered between 211 and 259.

  • 4. The oral qualifying must be passed no

later than the end of the 12th quarter of the student’s graduate training. Excep- tions can be made based on the approval of the Graduate Advisor. The student must pass both written qualifying exams

  • (2) and complete the four required core

sequences (1) before attempting the oral qualifying exam.

  • 5. Advancement to candidacy occurs after

a student completes requirements (1) through (4). Students must advance to candidacy before being able to defend their dissertation.

6 Completion of 2 units of MATH 401, Profes- sional Development in Mathematics.

  • 7. Having completed requirements (1)

through (6), a student must write and defend their dissertation.

  • 8. The acceptable modalities for the oral

qualifying exam and dissertation de- fense are:

  • a) In-person;
  • b) Hybrid, provided the student and at

least two committee members attend in person. If the Chairperson is attend- ing remotely, a committee member who will be attending in person must be designated in advance as a Co- Chairperson;

  • c) Remote.

The modality is to be decided by the Oral Qualifying Exam or Dissertation Com- mittee Chairperson or Co-Chairpersons, after consultations with the committee members and the student.

Normative Time to Degree 15 quarters

Courses