Mathematics

Subject abbreviation: MATH College of Natural and Agricultural Sciences

Vyjayanthi Chari, Ph.D., Chair Department Office, 202 Surge Building

• (951) 827-3113; www.math.ucr.edu

Professors John C. Baez, Ph.D. Mei-Chu Chang, Ph.D. Vyjayanthi Chari, Ph.D. Gerhard Gierz, Ph.D. Michel L. Lapidus, Ph.D. Yat Sun Poon, Ph.D. Ziv Ran, Ph.D. Malempati M. Rao, Ph.D. David E. Rush, Ph.D. Reinhard Schultz, 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. Bruce L. Chalmers, Ph.D. John E. de Pillis, Ph.D. Neil E. Gretsky, Ph.D. Lawrence H. Harper, Ph.D. Frederic T. Metcalf, Ph.D. J. Keith Oddson, Ph.D. Louis J. Ratliff, Jr., Ph.D. Victor L. Shapiro, Ph.D. James D. Stafney, Ph.D. Albert R. Stralka, Ph.D. Associate Professors Wee Liang Gan, Ph.D. Zhang-Dan Guan, Ph.D. Frederick H. Wilhelm, Jr., Ph.D. Stefano Vidussi, Ph.D. Assistant Professors Marta Asaeda, Ph.D. Julia Bergner, Ph.D. Jacob Greenstein, Ph.D. Juhi Jang, Ph.D. James Kelliher, Ph.D. Thomas Laurent, Ph.D. ** Cooperating Faculty Bai-Lian “Larry” Li, Ph.D. (Botany and Plant Sciences)

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 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 mod- erate amount of advanced mathematics in the major. It is selected most often either by students who intend to obtain a teaching cre- dential 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 Mathemat ics program is directed toward students who may wish to pur- sue graduate work in mathematics. The Applied Mathemat ics programs, with options in Biology, Chemistry, Economics, Environmental Sciences, Physics, and Statis tics, 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 comput- ers 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.

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.

Teachers in the public schools in California must have a credential approved by the State Commission on Teacher Credentialing. The cre- dential requires an undergraduate major, bac- calaureate degree, and completion of a gradu- ate credential program such as that of fered by the Graduate School of Education at UCR (see Education in this catalog). The Bachelor of Science 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 pro- ficiency 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 Init ia 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 teach- ers 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.

CaTEACH-SMI at UCR offers undergraduate students paid/unpaid opportunities 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 requirements. The CaTEACH-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 CaTEACH-SMI program, please visit http://smi.ucr.edu or at the Resource Center at 1315 Pierce Hall. 328 / Programs and Courses

See Undergraduate Studies section.

See College of Natural and Agricultural Sciences, Colleges and Programs section.

To fulfill the Natural Sciences requirement, the Dep artment of Mathematics requires the follow ing:

• 1. One of the year sequences

• a) BIOL 002, BIOL 003, BIOL 005C

• b) CHEM 001A, CHEM 001B, CHEM 001C,

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

• c) PHYS 002A, PHYS 002B, PHYS 002C or

PHYS 040A, PHYS 040B, PHYS 040C

• 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: MATH 008B or

MATH 009A, MATH 009B, MATH 009C, MATH 010A, MATH 010B, 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 008B or MATH 009A, MATH 009B, MATH 009C, MATH 010A, MATH 010B, MATH 046, CS 010 (CS 012 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) Twenty (20) additional units of upper-divi-

sion mathematics, upper-division comput- er science, or other related courses approved by the undergraduate advisor (For students who wish to pursue gradu- ate work, courses in complex variables, differential equations, and probability may be particularly useful.)

2. Applied Mathematics programs

MATH 113 or MATH 131, MATH 132, MATH 146A, MATH 146B, MATH 146C and the courses in one of the following options:

• a) Biology option

• (1) BIOL 005A, BIOL 05LA, BIOL 005B,

BIOL 005C

• (2) MATH 149A

• (3) Three courses from MATH 120, MATH 121, MATH 135A, MATH 135B, MATH 149B, MATH 149C

• (4) BIOL 102, BIOL 105, BIOL 108,

BIOL 117

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

division biology

• b) Chemistry option

• (1) CHEM 001A, CHEM 001B, CHEM 001C,

CHEM 01LA, CHEM 01LB, CHEM 01LC

• (2) Either PHYS 040A, PHYS 040B,

PHYS 040C (preferred); or PHYS 002A, PHYS 002B, PHYS 002C

• (3) Four courses from MATH 120,

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

• (4) CHEM 110A, CHEM 110B,

CHEM 111, CHEM 113

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

division chemistry

• c) Economics option

• (1) MATH 120, MATH 121, MATH 149A,

MATH 149B, MATH 149C

• (2) Five 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 111, ECON 134/BUS 106, ECON 135, ECON 143A/ENSC 143A, ECON 143B/ENSC 143B, ECON 143C/ENSC 143C, ECON 156, ECON 206

• d) Environmental Sciences option

• (1) CHEM 001A, CHEM 001B, CHEM 001C,

CHEM 01LA, CHEM 01LB, CHEM 01LC

• (2) ECON 006/ENSC 006

• (3) GEO 001 is recommended

• (4) MATH 149A

• (5) Three courses from MATH 120, MATH 121, MATH 135A, MATH 135B, MATH 149B, MATH 149C, CS 177, STAT 155

• (6) ENSC 100/SWSC 100, ENSC 101,

ENSC 102

• (7) Eight (8) additional units of upper-

division environmental sciences

• e) Physics option

• (1) MATH 135A, MATH 165A, MATH 165B

• (2) Either MATH 120 or MATH 171

• (3) PHYS 130A, PHYS 130B

• (4) Either PHYS 135A, PHYS 135B,

PHYS 136 or PHYS 156A, PHYS 156B

• f) Statistics option

• (1) MATH 120, MATH 149A, MATH 149B,

MATH 149C

• (2) Either STAT 130 or STAT 146

• (3) STAT 161, STAT 170A, STAT 170B,

STAT 171

3. Computational Mathematics program

• a) MATH 011/CS 011, MATH 113 or

MATH 131, MATH 120, MATH 132, MATH 135A, MATH 135B

• b) CS 012, CS 014, CS 141, CS 150

• c) One additional CS course to be chosen

from the list of approved technical elective courses.

• d) Twenty-four (24) units of technical elec-

tives to be chosen from

• (1) MATH 111/CS 111, MATH 121,

MATH 126, MATH 146A, MATH 146B, MATH 146C, MATH 149A, MATH 149B, MATH 149C, MATH 171

• (2) CS 130, CS 133, CS 166, CS 170,

CS 177

• 1. Lower-division Mathematics requirements (24 units)

MATH 009A, MATH 009B, MATH 009C, MATH 010A, MATH 010B, MATH 046

• 2. Upper-division Mathematics requirements (36

units)

• a. MATH 131, MATH 133, MATH 140, MATH 144,

MATH 153

• b. MATH 150A or MATH 151A

• c. Three courses from: MATH 132, MATH 136,

MATH 137, MATH 138A, MATH 145A, MATH 145B, MATH 149A, MATH 149B, MATH 149C, MATH 150B, MATH 151B, MATH 151C, MATH 171, MATH 172

• 3. Additional Mathematics and related disciplines

requirements (12 units)

• a. CS 010

• b. CS 011/MATH 011

• c. STAT 155

• 4. Natural Sciences (16-20 units)

• a. BIOL 002 or BIOL 003 or BIOL 005A and BIOL 05LA

• b. CHEM 001A and CHEM 01LA or CHEM 001HA

and CHEM 1HLA

• c. PHYS 002A or PHYS 040A

• d. CHEM 001B and CHEM 01LB or CHEM 001HB

and CHEM 1HLB or PHYS 002B or PHYS 040B 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

Mathematics / 329

• d. One course in SOC

• 6. Mathematics Education and Education

requirements (18 or 19 units): EDUC 104/MATH 104, EDUC 003 or EDUC 004 or EDUC 100B or equivalent, EDUC 109, EDUC 110, EDUC 139

• 7. Recommended Courses

LING 020 or LING 021, EDUC 116, EDUC 174, EDUC 177A

Candidates for the Honors Program in Math ematics 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, MATH 149B and MATH 149C.

• 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 ofthe

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.

The following are the requirements for a mi nor in Mathematics.

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

MATH 008B or MATH 009A, MATH 009B, 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 Agricultural Sciences in the Colleges and Programs section of this catalog for additional information on minors.

The EAP is an excellent opportunity to travel and learn more about another country and its culture while taking courses to earn units toward gradu- ation. Stu dents should plan study abroad well in advance to en sure that the courses taken fit with their overall program at UCR. Con sult the depart- mental student affairs officer for assistance. For further details visit UCR’s International Education Center at internationalcenter.ucr.edu or call

• (951) 827-4113.

See Education Abroad Program under International Education Center in the Student Services section of this catalog. A list of partici- pating countries is found under Education Abroad Program in the Programs and Courses section. Search for programs by specific areas at eap.ucop.edu/programwizard.