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MATHEMATICS

Catalog pages 402-410

Subject abbreviation: MATH College of Natural and Agricultural Sciences

Yat Sun Poon, Ph.D. Chair Department Office, 202 Skye Hall

  • (951) 827-3113; mathdept.ucr.edu

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

Professors Emeriti Theodore J. Barth, 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. 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 Wee Liang Gan, Ph.D. James Kelliher, Ph.D.

Associate Professor of Teaching Kevin Costello, Ph.D.

Assistant Professors Po-Ning Chen, Ph.D. Weitao Chen, Ph.D. Yat Tin Chow, Ph.D. Matthew Durham, Ph.D. Jose Gonzalez, Ph.D. Carl Mautner, Ph.D. Amir Moradifam, Ph.D. Peter Samuelson, Ph.D. Qixuan Wang, Ph.D. Zhenghe Zhang, Ph.D.

** Assistant Professors of Teaching Sara Lapan, Ph.D. David Weisbart, Ph.D.

Visiting Assistant Professors Scott Atkinson, Ph.D. Brian Benson, Ph.D. Zhanar Berikkyzy, Ph.D. Bradley Burdick, Ph.D. Liwei Chen, Ph.D. Alessandra Costantini, Ph.D. Neal Livesay, Ph.D. Mohammad Safdari, Ph.D. Karl Schmidt, Ph.D. Zilong Song, Ph.D. Bin Sun, Ph.D. Mahesh Sunkula, Ph.D. Henry Tucker, Ph.D. Zhixian Zhu, Ph.D.

Lecturers 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 com- mon, solid mathematical foundation but differ in their specializations in the pure and applied areas of mathematics. These programs can pro- vide 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 graduate work in applied mathematics.

The other Applied Mathematics programs, with options in Biology, Chemistry, Economics, Envi- ronmental Sciences, Physics, and Statistics, are designed to provide a rigorous training in mathe- matics together with a substantial background in the discipline of the option. The Computational Mathematics program is designed 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 ed- ucation 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 con- ducted 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 Com- mission on Teacher Credentialing. The credential requires an undergraduate major, baccalaureate degree, and completion of a graduate credential program such as that offered by the Graduate School of Education at UCR (see Education in this catalog). The Bachelor of Science in Mathe- matics 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 com- pleting an undergraduate program that is state approved for teacher preparation.

California Teach-Science/Mathematics Initiative (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, tech- nology, 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.

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 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 require- ments. The CaTEACH-SMI Resource Center provides future STEM teachers with material 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.Stu- dents 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 re- quired. (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:

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

And at least one sequence from:

(and BIOL 005C, if articulated)

CHEM 01LB, CHEM 001C, and 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 comprehensive 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 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 009HA, MATH 007B or MATH 009B or MATH 009HB, MATH 010A, MATH 010B, MATH 031, MATH 046

  • 2. Four (4) units of either CS 010 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 MATH 007A or MATH 009A or MATH 009HA, MATH 007B or MATH 009B or MATH 009HB, MATH 009C, MATH 010A, MATH 010B, MATH 031, MATH 046, CS 010 (CS 012 is recom- mended).

  • 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 upperdi-

vision mathematics, upper-division com- puter science, or other related courses approved by the undergraduate advisor (For students who wish to pursue grad- uate work, courses in complex 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 149C, MATH 150B, MATH 151B, MATH 165A, MATH 165B

  • b) Biology option

BIOL 005C

  • (5) Four (4) additional units of upper-divi-

sion biology

  • c) Chemistry option

CHEM 01LC

MATH 135A, MATH 135B, MATH . 149A, MATH 149B, MATH 149C, MATH 165A, MATH 165B

  • (5) Four (4) additional units of upper-divi-

sion chemistry

  • d) Economics option

MATH 149B

  • (2) Four upper-division economics

courses at least 20 units) to consist of ECON 102A and four courses to be chosen from ECON 102B, ECON 103A, ECON 103B, ECON 107, ECON 108, ECON 110, ECON 134/ BUS 106, ECON 135, ECON 143A/ ENSC 143A, ECON 143B/ ENSC 143B, ECON 143C/ENSC 143C, ECON 156, ECON 206

  • e) Environmental Sciences option

CHEM 01LC

MATH 149B, MATH 149C, CS 177, STAT 155

ENSC 102

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

sion environmental sciences

  • f) Physics option

PHYS 136 or PHYS 156A, PHYS 156B

  • 3. Computational Mathematics program
  • c) One additional CS course to be chosen

from the list of approved technical elec- tive courses.

  • d) Sixteen (16) units of technical electives to

be chosen from

MATH 146A, MATH 146B, MATH 146C, MATH 149A, MATH 149B, MATH 149C, MATH 171

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

  • 2. Upper-division Mathematics requirements

(36 units)

MATH 144, MATH 153

  • 3. Additional Mathematics and related disci-

plines requirements (12 units)

  • 4. Natural Sciences (16-20 units)

and 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 109/EDUC 109S, EDUC 110, EDUC 139

EDUC 175S

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 following:
  • 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 candidates to notify the department of their eligibility.

Minor

The following are the requirements for a minor in Mathematics.

MATH 007B or MATH 009B or MATH 009HB, MATH 009C, MATH 010A, MATH 010B

  • 2. Upper-division requirements: 24 units of

upper-division mathematics courses. Of the specified upper-division units, a minimum 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 num- bered 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 Ag- ricultural 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 analytical).

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 se-

quences: 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

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 must be from courses numbered between MATH 200 and MATH 210.

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

fessional Development in Mathematics.

The requirements of 1 and 2 above constitute the comprehensive final examination require- ment for the degree.

M.S. in Mathematics (Applied) General university requirements are listed in the Graduate Studies section of this catalog. Specif- ic 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 num- ber 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 be- tween 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, Pro-

fessional Development in Mathematics.

The requirements of 1 and 2 above constitute the comprehensive final examination require- ment 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 alpha- betical 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.

  • 3. Completing four quarter-courses in mathe-

matics numbered between 211 and 259.

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

fessional Development in Mathematics.

Normative Time to Degree 15 quarters

Courses