Mathematics

College of Science and Engineering
Dean: Sheldon Axler

Department of Mathematics
TH 937
415-338-2251
E-mail: mathstat@math.sfsu.edu
Web Site: http://math.sfsu.edu
Chair: David Meredith

Mathematics Undergraduate Advisers: D. Ellis, E. Hayashi
Mathematics Graduate Coordinator: D. Meredith

Mathematics Faculty

Professors—Aiyar, Axler, Ekstrand, Ellis, Fendel, Hayashi, Langlois, Marcucci, Meredith, Novalis, Ovchinnikov, Resek, Robbins, Smith, J., Tabatabaian

Associate Professors—Kafai, Krause, Li

Assistant Professors—Goetz, Hsu, Schuster

Statistics Undergraduate Adviser: M. Kafai

Statistics Faculty

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

Associate Professor—Kafai

Assistant Professors—Mar

Programs

B.A. in Mathematics
B.S. in Applied Mathematics
B.S. in Statistics
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 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 that 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 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 Bachelor of Science in Statistics is for students who are planning careers as statisticians in industry, business, or government. Statistics is basic to quantitative research in the biological, physical, and social sciences. Because its methods are based on mathematics, it requires a firm understanding of mathematical methods as well as an appreciation of scientific method, computation, and practical problems. To give the student both breadth and depth and to introduce the student to a variety of fields where statistics may be applied, three emphases are offered: science, business, and economics.

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

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 60, 70, and 109 may be used to remedy deficiencies. Because of the sequential nature of mathematics courses, all students must consult with a departmental adviser at the beginning of their degree programs. MATH 500 through MATH 599 may not be counted as electives toward the mathematics major. CR/NC grades are not acceptable in courses to be counted for a mathematics major or minor program.

On-line course descriptions are available.

Required Courses Units
MATH 309 Computation in Mathematics or 3
  CSC 210   Introduction to Computer Programming
MATH 226-228 Calculus I-III (4 units each) 12
MATH 325 Linear Algebra 3
MATH 335 Modern Algebra I 3
MATH 370 Real Analysis I 3
MATH 470 Real Analysis II or 3
  MATH 374   Advanced Calculus or
  MATH 380   Introduction to Functions of a Complex Variable
A sequence of two courses in a related area, such as: 6
  MATH 340 and MATH 441 or  
  MATH 376 and MATH 477 or
  MATH 309 and MATH 400 or
  MATH 310 and MATH 375 or
  MATH 350 and MATH 455 or
  MATH 376 and MATH 460 or
  Other sequences can be arranged with consent of adviser
Upper division mathematics courses on advisement 9
Total 42

BACHELOR OF SCIENCE IN APPLIED MATHEMATICS

Required Courses (39 units) Units
CSC 210 Introduction to Computer Programming or 3
  MATH 309   Computation in Mathematics
MATH 226-228 Calculus I-III (4 each) 12
MATH 324 Statistics with Computing or 3
  MATH 441   Mathematical Statistics
MATH 325 Linear Algebra 3
MATH 335 Modern Algebra or 3
  MATH 370   Real Analysis I
MATH 340 Probability and Statistics I 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)
Units selected from the following: 6
  MATH 301 Exploration and Proof  
  MATH 374 Advanced Calculus
  MATH 476 Ordinary Differential Equations II
  MATH 477 Partial Differential Equations
  MATH 380 Introduction to Functions of a Complex Variable
  MATH 442 Probability Theory
  MATH 430 Operations Research: Deterministic Methods
A coherent collection of 3 courses emphasizing 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 pursuing higher education in probability and statistics or careers as statisticians in a wide variety of industrial, scientific, and business activities, as well as government services.

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

On-line course descriptions are available.

Core Requirements Units
CSC 201 Introduction to Computer Programming for Non-majors or 3
  CSC 210   Introduction to Computer Programming
MATH 226-228 Calculus I-III (4 each) 12
MATH 325 Linear Algebra 3
MATH 338 Introduction to SAS 3
MATH 340 Probability and Statistics I 3
MATH 441 Probability and Statistics II 3
  Total for core 27
Emphasis: Select Business, Economics, or Science as shown below. 27
Total for major 54
Business Emphasis
ACCT 300 Accounting and Finance Reporting 3
DS 312 Data Analysis with Computer Applications 3
DS 412 Operations Management 3
ECON 101 Introduction to Microeconomic Analysis 3
FIN 350 Business Finance 3
ISYS 363 Information Systems for Management 3
Elective units selected with approval of adviser. 9
Total for emphasis 27
Economics Emphasis
ECON 101 Introduction to Microeconomic Analysis 3
ECON 300 Intermediate Macroeconomic Theory 3
ECON 301 Intermediate Microeconomic Theory 3
ECON 312 Statistical Method and Interpretation II 3
ECON 325 Economic Modeling and Computer Simulation 3
ECON 615 Mathematical Economics 3
ECON 630 Introduction to Econometrics 3
Elective units selected with approval of adviser. 6
Total for emphasis 27
Science Emphasis
MATH 400 Numerical Analysis 3
MATH 430 Operations Research 3
MATH 460 Mathematical Modeling 3
MATH 490 Mathematics Seminar 3
Units selected on advisement from a coherent collection of courses in areas of science that use statistical methods. Under advisement, courses from other colleges may be selected. 15
Total for emphasis 27

MINOR IN MATHEMATICS

At least six units of upper division mathematics and half of all units counted toward the minor must be completed at this university.

Program Units
MATH 226-228 Calculus I-III (4 each) 12
Upper division electives on advisement 12
Total 24

MASTER OF ARTS IN MATHEMATICS

Applicants to the master's program must have a 3.0 grade point average in the following three courses, or their equivalent: MATH 325, MATH 335, 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 not be counted as electives toward the M.A. degree).

On-line course descriptions are available.

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

Program Units
MATH 710 Analysis I 3
MATH 850 Algebra 3
Additional units selected from graduate courses other than MATH 895, MATH 898, or MATH 899. 6
Upper division/graduate courses in mathematics or appropriately related subjects with the approval of the graduate adviser. At least 3 graduate units in mathematics must be included in this category.  Students who have not studied complex variable prior to beginning graduate studies should take MATH 380 as one of these courses. Complete either the thesis or the comprehensive examination/expository paper. 18
Minimum total 30

Candidates for the M.A. in Mathematics must complete a culminating experience. Two options are available.

Thesis Option. Students may choose to write a thesis and present an oral defense. Students considering the thesis option should contact the department chair or graduate adviser for further details. A master's thesis should be an original work of twenty or more pages that develops a new theorem or algorithm, a novel application, or an original approach to an established result. The resulting manuscript must be prepared according to university guidelines and—insofar as these to not conflict—following a style similar to that used by the Notices of the American Mathematical Society. Each MA thesis has a principal adviser and tow additional readers. The expected time to completion for this paper is one academic year. Thesis guidelines for students and advisers are available from the Mathematics Department.

Comprehensive Examination/Expository Paper Option. Students selecting this option take two written examinations and write an expository paper. Students must take two examinations selected from three alternatives: algebra, analysis, and statistics. Written examinations are administered twice each year in December and May. Examinations last two hours, and a student takes no more than one examination per day. Departmental syllabi for the examinations are available at least four months in advance of each administration. Each examination requires students to integrate material from several required undergraduate and graduate courses, to demonstrate their ability to write short proofs in correct mathematical English, and to demonstrate the falsity of propositions by counter-examples. Examinations are graded pass/fail, and students who fail an examination may repeat it at least once, with additional attempts requireing the written approval of the graduate adviser and chair.

The expository paper is completed in two stages. First, students must complete a departmental proposal form including:

  1. Title and brief abstract of the proposed paper.
  2. Demonstration of readiness to undertake the topic by prior courses or other study.
  3. Brief preliminary bibliography.
  4. Approval of the proposal by a Mathematics faculty member and the graduate adviser.

Once students have an approved proposal, they may complete their papers wither by enrolling in a course upon advice of the faculty adviser or under the guidance of an individual faculty member.

Further information about these options can be obtained from the department web site: http://math.sfsu.edu.

 



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