Mathematics

College of Science and Engineering
Dean: James C. Kelley

Department of Mathematics
TH 937
415-338-2251
E-mail: mathstat@math.sfsu.edu
Chair: Sheldon Axler

Mathematics Undergraduate Advisers: D. Ellis, E. Hayashi

Mathematics Graduate Coordinator: J. Lewis

Mathematics Faculty

Professors--Aiyar, Douglas, Ekstrand, Ellis, Fendel, Fisher, Forsey, Gutierrez, Hayashi, Langlois, Lewis, J., Marcucci, Meredith, Novalis, Ovchinnikov, Resek, Robbins, Smith, J., Tabatabaian, Tang

Associate Professors--Haines, Kafai, Krause

Assistant Professor--Li

Statistics Undergraduate Adviser: J. Ekstrand

Statistics Faculty

Professors--Aiyar, Bhimjee, Blecha, Ekstrand, Eng, Forsey, Hunter, Krishnan, P., Marcucci, Osman, Udaybhanu

Associate Professor--Kafai

Assistant Professor--Mar

Programs

B.A. in Mathematics

B.S. in Applied Mathematics

B.S. in Statistics

Minor in Actuarial Science

Minor in Mathematics

M.A. in Mathematics

Program Scope

The Bachelor of Arts is offered for students with a general interest in mathematics; B.S. programs in Applied Mathematics and Statistics are also offered. Courses are offered in mathematics education for prospective elementary and secondary teachers; the approved California Single Subject Teaching Credential Program is closely aligned with the B.A. degree program. A student may readily satisfy both sets of requirements. Copies of program requirements are available in the Mathematics Department Office.

The Bachelor of Arts, for those desiring a general liberal arts program with an emphasis in mathematics, will help students prepare for careers in mathematics teaching and mathematical analysis in industry or for graduate study.

The Bachelor of Science in Applied Mathematics responds to the needs of business and industry for applied mathematical scientists. The program also responds to the needs of those students who enjoy mathematics for its own sake but who also have interests in other fields to which mathematics is applied. Applied mathematicians and statisticians are employed in such areas as operations research, systems analysis, computing, data analysis, biological sciences, communications research, and in the management sciences.

The primary aim of applied mathematics is to elucidate scientific concepts and to describe and predict scientific phenomena through the use of mathematics. The applied mathematician is at once a mathematical specialist and a systems analyst, whose task it is to confront highly complex real-world situations with mathematical analysis. In industry the applied mathematician has an opportunity to test both background and training in solving problems of a practical nature. It is necessary to have not only a grasp of the mathematical theories involved, but also an appreciation for the specific science or technology concerned. In this way, one can arrive at usable mathematical formulations of scientific and engineering problems.

The applied mathematics program prepares students in several areas. First, students acquire a broad knowledge of the techniques and methods of applied mathematics. These techniques include differential equations, optimization, statistics, numerical analysis, computer programming, and operations research. Second, students learn to model scientific phenomena and complex real-world systems, (Mathematical Modeling, Applied Mathematics Project) and to use these models to understand and predict the behavior of these systems. Finally, they learn how to effectively communicate these results to other scientists and managerial decision makers.

The Minor in Mathematics is available for students desiring a program of study in mathematics which is coherent but not as extensive as the B.A. program. It could provide excellent background for prospective secondary school teachers who want to be able to teach in mathematics as well as in their major area, or for students majoring in a science such as biology or economics who want to emphasize the quantitative aspects of their major.

The Minor in Actuarial Science is available for students entering the actuarial field, a field that makes extensive use of mathematics and statistics in the solution of a variety of financial and social problems.

The Colleges of Behavioral and Social Sciences, Business, and Science and Engineering offer the Bachelor of Science in Statistics for students who are planning careers as statisticians in a wide variety of industrial and business activities, and government services.

The Master of Arts in Mathematics is offered with the purpose of extending students' experience in mathematics. A student's goal may be to prepare for a career in government, industry, or community college teaching, to enhance competency as an elementary or secondary school teacher, or to prepare for further graduate study.

Career Outlook

The degree programs in mathematics and statistics prepare students for additional graduate work; teaching careers; and work in business, industry, and government that apply mathematical and statistical concepts. In addition, specific careers in actuarial science and computer analysis are especially attractive.

BACHELOR OF ARTS IN MATHEMATICS

Courses for this program are listed in alphabetical sequence (consult Index for page reference).

Undergraduate degree programs in mathematics presuppose a background equivalent to two years of high school algebra, one year of plane geometry, and one semester of trigonometry. Students in doubt as to their satisfaction of these prerequisites should consult the department. MATH 55, 60, 70, 107, and 109 may be used to remedy deficiencies. Because of the sequential nature of mathematics courses, all students are urged to consult with the department at the beginning of their degree programs. The following courses may not be counted as electives toward the mathematics major: MATH 560, 565, 650. Students are advised that CR/NC grades are not acceptable in courses to be counted for a mathematics major or minor program.

At least six upper division units in mathematics for this major must be completed at this university.

Units

Program Requirements

CSC 210	Introduction to Computer 
Programming or
MATH 309	Computation in Mathematics		3
MATH 220-223	 Calculus and Analytic 
Geometry I-IV (3 units each) 12
MATH 325	Linear Algebra		3
MATH 320	Modern Algebra I		3
MATH 370	Real Analysis I		3
MATH 371	Real Analysis II or
MATH 374	Advanced Calculus or
MATH 380	Introduction to Functions of a 
Complex Variable 3
A sequence of two courses in a single area, 
such as: 6
MATH 340	Probability and Statistics I and
MATH 341	Probability Theory or
MATH 376	Ordinary Differential 
Equations I and
MATH 379	Partial Differential Equations 
or
Other sequences can be arranged in various 
areas; e.g., computer science
Upper division mathematics courses on advise-
ment (MATH 260 is acceptable in this

category)		9
Total		42

BACHELOR OF SCIENCE IN APPLIED MATHEMATICS

Units

Required Courses (39 units)

CSC 210	Introduction to Computer 
Programming or
MATH 309	Computation in Mathematics		3
MATH 220-223	Calculus and Analytic 
Geometry I-IV (3 each) 12
MATH 325	Linear Algebra		3
MATH 320	Modern Algebra or
MATH 370	Real Analysis I		3
MATH 340	Probability and Statistics I		3
MATH 250	Statistics with Computing or
MATH 342	Mathematical Statistics		3
MATH 376	Ordinary Differential Equations I		3
MATH 400	Numerical Analysis I		3
MATH 460	Mathematical Modeling		3
MATH 696-697	Applied Mathematics 
Project (1-2) 3

Electives (15 units)

Two courses selected from the following:		6
MATH 374	Advanced Calculus
MATH 378	Ordinary Differential Equations II
MATH 379	Partial Differential Equations
MATH 380	Introduction to Functions of a 
Complex Variable
MATH 341	Probability Theory
MATH 430	Operations Research: 
Deterministic Methods
A coherent collection of three courses empha-
sizing applications of mathematics,
chosen with the consent of the Applied

Mathematics adviser			9
Total		54

BACHELOR OF SCIENCE IN STATISTICS

The Bachelor of Science in Statistics is an interdisciplinary program offered for students who are planning careers as statisticians in a wide variety of industrial and business activities, and government services.

The equivalent of two years of high school algebra, one year of plane geometry, and one-half year of trigonometry is prerequisite.

Courses required in this program are listed in alphabetical sequence (consult Index for page reference).

Units

Basic Requirements

CSC 210	Introduction to Computer 
Programming 3
MATH 220-223 Calculus and Analytic 
Geometry I-IV (3 each) 12
MATH 325	Linear Algebra		3
MATH/STAT 340Probability and Statistics I			3
MATH/STAT 342Mathematical Statistics			3
Emphasis:One field in Business, Economics, 

or Science as shown below			30
Total		54

Business Emphasis

BA 212	Business Statistics		3
ACCT 300	Accounting and Finance Reporting		3
BICS 263	Introduction to Computer Informa-
tion Systems 3
BICS 363	Information Systems for 
Management 3
MGMT 405	Introduction to Management and 
Organizational Behavior			3
ECON 101	Introduction to Economics 
Analysis II 3
ECON 320	Introduction to Econometrics or
ECON 325	Economic Modeling and 
Computer Simulation 3
Selection of courses that apply statistics in a 
particular business area with approval of
major adviser 12
For example (notan exhaustive list):
BA 412 plus two courses from BA 408, 
601, 604, 624, MGMT 661
FIN 309, 350, ACCT 303
MKTG 431, 632, PSY 571

BICS 461, 562, BA 408 
Total for emphasis		30

Economics Emphasis

ECON 101	Introduction to Economics 
Analysis II 3
ECON 300	Intermediate Macroeconomic 
Theory 3
ECON 301	Intermediate Microeconomic 
Theory 3
ECON 312	Statistical Method and Interpreta-
tion II 3
ECON 320	Introduction to Econometrics or
ECON 325	Economic Modeling and 
Computer Simulation 3
Selection of courses in business, economics, 
and related areas with approval of major

adviser			15
Total for emphasis		30

Science Emphasis

Units to be selected upon advisement from 
upper division Mathematics and Statistics
courses, with at least nine (9) units from
the following: 18
MATH/STAT 341 Probability Theory
MATH/STAT 500 Mathematics Seminar, 
with topics to be selected from:
Nonparametic Methods
Analysis on Variance and Covariance
General Linear Models
Sampling Theory
Bayesian Inference
Multivariate Analysis
Additional units from a coherent collection of 
courses in an area/areas of science that
uses statistical methods, with prior

approval of the adviser		12
Total for emphasis		30

MINOR IN ACTUARIAL SCIENCE

The purpose of the Minor in Actuarial Science is to introduce the student to the field of actuarial science. Actuaries play a vital role in the solution of a growing variety of financial and social problems through the use of their analytic and business skills. The minor will assist the student in getting a well-rounded education that includes course work in mathematics and actuarial science.

MATH 220-223	Calculus and Analytic 
Geometry I-IV (3 each) 12
MATH 325	Linear Algebra		3
MATH/STAT 340 Probability and Statistics I			3
MATH/STAT 342 Mathematical Statistics			3
MATH 500	Introduction to Actuarial Mathe-

	matics [topic course]		3
Total for minor		24

MINOR IN MATHEMATICS

At least six units of upper division mathematics for this minor must be completed at this university.

Units

MATH 220-223	 Calculus and Analytic 
Geometry I-IV (3 each) 12

Upper division electives on advisement		12
Total		24

MASTER OF ARTS IN MATHEMATICS

Admission to Program

Applicants to the master's program must have a 3.0 grade point average in the following three courses, or their equivalent: MATH 320, MATH 325, and MATH 370. Applicants who fail to satisfy this requirement but who are qualified in all other respects may be admitted on condition that they bring their grades in these courses up to the 3.0 average during their first two semesters of graduate study (these three courses, however, may notbe counted as electives toward the M.A. degree).

Courses for this discipline are listed in alphabetical sequence (consult Index for page reference).

Upper division courses acceptable on a Graduate Approved Program will be determined by the student with approval of the graduate adviser.

Units

Program

MATH 710	Analysis		3
MATH 730	Theory of Functions of a Complex 
Variable 3
MATH 850	Algebra		3
One course from the following:		3
MATH 740	Functional Analysis
MATH 750	General Topology
MATH 760	Introduction to Measure and 
Lebesque Integration
Upper division or graduate courses in mathe-
matics or appropriately related subjects
with the approval of the graduate adviser.
At least three units of graduate course
work in Mathematics must be included
in this category. 18
Minimum total		30
andMaster's Comprehensive Oral Examination

Master's Comprehensive Oral Examination.The examination covers three areas of mathematics. Two areas are algebra (both abstract and linear) and analysis (both real and complex). The third area is elected by the student, with the approval of the graduate adviser. Examples of choices for the third area are: probability and statistics; foundations; differential equations; topology; applied mathematics; numerical analysis; geometry; and computer science. The examination is comprehensive. The student will choose one area in which he or she will be expected to go somewhat more deeply than the other two.

If the student fails the examination, it may be recommended that the student take all or part of it again. The examination or parts of it may be repeated only once.

Thesis Option.Students expressing an interest may be invited to write a thesis with an oral defense of the thesis in lieu of a comprehensive oral examination. Students considering the thesis option should contact the department chair or graduate adviser for further details.



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