Dean: James C. Kelley

TH 937

415-338-2251

E-mail: mathstat@math.sfsu.edu

Chair: Sheldon Axler

*Associate Professors*--Haines, Kafai, Krause

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.

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.

CSC 210 Introduction to Computer

Programmingor

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 IIor

MATH 374 Advanced Calculusor

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 Iand

MATH 341 Probability Theoryor

MATH 376 Ordinary Differential

Equations Iand

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

CSC 210 Introduction to Computer

Programmingor

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 Algebraor

MATH 370 Real Analysis I 3

MATH 340 Probability and Statistics I 3

MATH 250 Statistics with Computingor

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

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

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).

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

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 Econometricsor

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

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 Econometricsor

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

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

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

MATH 220-223 Calculus and Analytic

Geometry I-IV (3 each) 12

Upper division electives on advisement 12

Total 24

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.

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

**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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