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Mathematics

Catalog pages 444-452

Subject abbreviation: MATH College of Natural and Agricultural Sciences

Frederick Wilhelm, Ph.D., Chair Department Office, 238 Skye Hall

  • (951) 827-3113; mathdept.ucr.edu

Professors Mark Alber, Ph.D., Distinguished Professor John C. Baez, Ph.D., F. Burton Jones Endowed Chair Vyjayanthi Chari, Ph.D., Distinguished Professor Wee Liang Gan, Ph.D. Jacob Greenstein, Ph.D. Michel L. Lapidus, Ph.D., Distinguished Professor Yat Sun Poon, Ph.D. Ziv Ran, Ph.D. Reinhard Schultz, Ph.D. Rodolfo Torres, Ph.D., Distinguished Professor Stefano Vidussi, Ph.D. Frederick H. Wilhelm, Jr., Ph.D. Bun Wong, Ph.D. Feng Xu, Ph.D. Qi S. Zhang, Ph.D.

Professor of Teaching Estela Gavosto, Ph.D.

Professors Emeriti 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. Lawrence H. Harper, Ph.D. Frederic T. Metcalf, Ph.D. Malempati M. Rao, Ph.D. Louis J. Ratliff, Jr., Ph.D. David E. Rush, Ph.D. James D. Stafney, Ph.D. Albert R. Stralka, Ph.D.

Associate Professors James Kelliher, Ph.D. Carl Mautner, Ph. D. Amir Moradifam, Ph.D. Associate Professors of Teaching Kevin Costello, Ph.D. David Weisbart, Ph.D.

Assistant Professors Patricio Gallardo Candela, Ph.D. Po-Ning Chen, Ph.D. Weitao Chen, Ph.D. Heyrim Cho, Ph.D. Yat Tin Chow, Ph.D. Brian Collier, Ph.D. Matthew Durham, Ph.D. Jose Gonzalez, Ph.D. Jia Gou, Ph.D. Mykhailo Potomkin, Ph.D. Peter Samuelson, Ph.D. Qixuan Wang, Ph.D. Zhenghe Zhang, Ph.D.

** Assistant Professor of Teaching Sara Lapan, Ph.D.

Visiting Assistant Professors Hassan Attarchi, Ph.D. Liwei Chen, Ph.D. Sayan Das, Ph.D. Javier Gonzalez-Anaya, Ph.D. Fazel Hadadifard, Ph.D. Matthew Harper, Ph.D. Neal Livesay, Ph.D. Francesco Pancaldi, Ph.D. Mohammad Safdari, Ph.D. Mahesh Sunkula, Ph.D. Kevin Tsai, Ph.D. Henry Tucker, Ph.D. Xin Yang, Ph.D. Sarah Yeakel, Ph.D.

Lecturer Michael Curtis

Cooperating Faculty Bai-Lian “Larry” Li, Ph.D. (Botany and Plant Sciences) Academic Coordinator Rob Lam

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 mathe- matics itself or within the many scientific and business fields, which, in today’s technological society, depend on a basic knowledge of math- ematical 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 under- graduate 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/Mathematics Initia- tive (CaTEACH-SMI) California Teach-Science Mathematics Initiative (CaTEACH-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 retire- ment of qualified teachers, this is an essential time to explore and prepare for a career in teaching science or mathematics.

CaTEACH-SMI at UCR offers undergraduate students paid/unpaid opportunities, such as the SMI & Alpha Center Apprentice Programs, to explore STEM teaching as a career option. Through CaTEACH-SMI, students receive ad- vising 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 CaTEACH-SMI Resource Center provides future STEM teachers with ma- terial and financial resources which includes the National Science Foundation (NSF) Noyce Scholarship Program, to promote planning and professional development towards a science/ mathematics education career.

For more information about the CaTEACH-SMI program, please visit smi.ucr.edu, the Resource Center at 1315 Pierce Hall, or on Facebook at facebook.com/ScienceMathInitiativeAtUcr.

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 007A or MATH 009A or MATH 009HA

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

MATH 007A or MATH 009A or MATH 009HA

MATH 007B or MATH 009B or MATH 009HB

MATH 009C or MATH 010A

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

MATH 007A or MATH 009A or MATH 009HA

MATH 007B or MATH 009B or MATH 009HB

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 pro- grams 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 consider- ation 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:

MATH 007A or MATH 009A, MATH 007B or MATH 009B, and MATH 009C (mandatory)

And at least one sequence from:

BIOL 005C, if articulated)

CHEM 01LC

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

or MATH 009A or MATH 09HA, MATH 007B or MATH 009B or MATH 09HB, MATH 010A, MATH 010B, MATH 031, MATH 046

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

upperdivision 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 MATH 007A or MATH 009A or MATH 09HA, MATH 007B or MATH 009B or MATH 09HB, MATH 009C, MATH 010A, MATH 010B, MATH 031, MATH 046, CS 010A (CS 010B is recommended).

  • 1. Pure Mathematics program (56 units)
  • a) Thirty-six (36) units of upper-division

mathematics to include at least 24 units from MATH 131, MATH 132, MATH 145A, MATH 145B, MATH 151A, MATH 151B, MATH 151C, MATH 171, MATH 172

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

must be from MATH 145A, MATH 145B, MATH 151A, MATH 151B, MATH 151C

  • c) Courses in the MATH 190–199 series are

excluded

  • d) Sixteen (16) additional units of upper-

division mathematics, upper-division computer science, or other related courses approved by the undergradu- ate advisor (For students who wish to pursue graduate work, courses in com- plex variables, differential equations, and probability may be particularly useful.)

  • 2. Applied Mathematics programs

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

  • a) General Applied Mathematics option
  • (3) Students will select 16 units from

MATH 120, MATH 121, MATH 126, MATH 141, MATH 147, MATH 148, MATH 149A, MATH 149B, MATH 150B, MATH 151B, 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 112, 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 132, MATH 135A, MATH 135B

  • c) One additional CS course to be chosen

from the list of approved technical elective courses.

  • d) Sixteen (16) units of technical electives

to be chosen from

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

  • 1. Lower-division Mathematics requirements

(24 units) MATH 007A or MATH 009A or MATH 09HA, MATH 007B or MATH 009B or MATH 09HB, MATH 009C, MATH 010A, MATH 010B, MATH 031, MATH 046

  • 2. Upper-division Mathematics requirements

(36 units)

MATH 145B, MATH 149A, MATH 149B, MATH 150B, MATH 151B, MATH 151C, MATH 171, MATH 172

  • 3. Additional Mathematics and related disci-

plines requirements (12 units)

  • 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.

  • 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 Domestic applicants must supply GRE General Test scores (verbal, quantitative, and analyti- cal).

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.

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

sional Development in Mathematics.

The requirements of 1 and 2 above consti- tute 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 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 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 consti- tute 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 qualify- ing examination at most twice for each sequence.

  • 3. Completing four quarter-courses in math-

ematics numbered between 211 and 259.

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

sional Development in Mathematics.

Normative Time to Degree 15 quarters

Courses