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: D. Meredith

Mathematics Faculty

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

Associate Professors—Haines, Kafai, Krause

Assistant Professors—Li, Sherman

Statistics Undergraduate Adviser: J. Ekstrand

Statistics Faculty

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

Associate Professor—Kafai

Assistant Professors—Mar, Sherman

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 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 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

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, 107, 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. 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.

Online course descriptions are available.

Program Requirements Units
CSC 210 Introduction to Computer Programming or 3
MATH 309 Computation in Mathematics
MATH 226-228 Calculus I-III (4 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 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 342 or
MATH 376 and MATH 379 or
MATH 309 and MATH 400 or
MATH 440 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 325 Linear Algebra 3
MATH 320 Modern Algebra or 3
MATH 370 Real Analysis I
MATH 340 Probability and Statistics I 3
MATH 250 Statistics with Computing or 3
MATH 342 Mathematical Statistics
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 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 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.

Online course descriptions are available.

Basic Requirements Units
CSC 210 Introduction to Computer Programming 3
MATH 226-228 Calculus I-III (4 each) 12
MATH 325 Linear Algebra 3
MATH/STAT 340 Probability and Statistics I 3
MATH/STAT 342 Mathematical 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 Information 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 3
ECON 325 Economic Modeling and Computer Simulation
Selection of courses that apply statistics in a particular business area with approval of major adviser 12
For example (not an 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 Interpretation II 3
ECON 320 Introduction to Econometrics or 3
ECON 325 Economic Modeling and Computer Simulation
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.

Program Units
MATH 226-228 Calculus I-III (4 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 Mathematics [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.

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 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 not be counted as electives toward the M.A. degree).

Online 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 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
MATH 770 Methods of Applied Analysis
MATH 800 Foundations of Mathematics
Upper division or graduate courses in mathematics 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
and Master'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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