Mathematics

College of Science and Engineering
Dean: Sheldon Axler

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

Mathematics Undergraduate Advisers: D. Ellis, R. Marcucci, S. Li
Mathematics Graduate Coordinator: E. Hayashi

Mathematics Faculty

Professors—Axler, Bao, Ellis, Goetz, Hayashi, Kafai, Langlois, Li, Marcucci, Meredith, Ovchinnikov, Robbins, Schuster

Associate Professors—Beck, Cheung, Gubeladze, Hosten, Hsu, Krause, Kysh

Assistant Professors—Ardila, Arsuaga, Piryatinska, Vazquez

Statistics Undergraduate Adviser: M. Kafai

Statistics Faculty

Professors— Chattopadhyay, Cholette, Eng, Kafai, Mar, Marcucci, Mehrotra, Mui, Soorapanth

Assistant Professor—Piryatinska

Programs

B.A. in Mathematics: Concentration in Mathematics for Advanced Study
B.A. in Mathematics: Concentration in Mathematics for Liberal Arts
B.A. in Mathematics: Concentration in Mathematics for Teaching
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. Copies of program requirements are available in the Mathematics Department Office.

The Bachelor of Arts in Mathematics has three concentrations: liberal arts, teaching, and advanced study.

The liberal arts concentration is for students who desire a broad liberal arts education with an emphasis in mathematics.

The teaching concentration is for students whose goal is to teach mathematics in middle school or high school. These students will obtain a solid understanding of the mathematics needed for teaching and they will gain classroom experience as volunteers in local public schools. They will also have the opportunity to develop the mathematical skills, flexibility and perceptiveness in order to help future students cultivate fruitful wonderful ideas, and to help students connect their thinking to formal mathematical structures. Students who complete this concentration will have satisfied the early field experience requirement and the subject matter competency requirement for a single subject credential in mathematics.

The advanced study concentration is for students who plan to pursue a masters or doctoral degree in mathematics. Students who choose this concentration will obtain a solid foundation in the cornerstones of advanced mathematics: linear algebra, abstract algebra, vector analysis, real analysis and complex analysis.

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 (for example, those with emphasis on DNA topology, mathematical cancer biology, or special needs of biostatistics), 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, government, or biomedical research. 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.

The described degrees, when supplemented by the appropriate courses, can also prepare students for graduate study in other fields such as accounting, mathematical biology, computer science, economics, engineering, physics, and statistics.

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 applies mathematical and statistical concepts. In addition, specific careers in actuarial science, investment firms, computer industry, biomedical research and the government sector (such as NASA and the NSA) 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 at least one semester of trigonometry. Students in doubt as to their satisfaction of these prerequisites should consult the Mathematics Department. MATH 59, 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 regular intervals during their degree programs. MATH 500 through MATH 599 may not be counted as electives toward the mathematics major or minor. CR/NC grades are not acceptable in courses to be counted for a mathematics major or minor program.

The Bachelor of Arts in Mathematics can be earned by completing any one of three concentrations:

Mathematics majors who successfully complete MATH 300 GW spring 2010 or thereafter or MATH 301 GW in spring 2009 or thereafter will have satisfied the University’s Graduation Writing Assessment Requirement (GWAR).

On-line course descriptions are available.

Core Courses Units
MATH 226-228 Calculus I-III (4 units each) 12
MATH 301 GW Exploration and Proof 3
MATH 325 Linear Algebra 3
MATH 335 Modern Algebra I 3
MATH 370 Real Analysis I 3
Total for core 24

Concentration in Mathematics for Advanced Study

Core Courses 24
CSC 210
   or
CSC 309
Introduction to Computer Programming

Computer Programming for Scientists and Engineers
3
MATH 340 Probability and Statistics I 3
MATH 310
   or
MATH 376
Elementary Number Theory

Ordinary Differential Equations
3
MATH 380 Introduction to Functions of a Complex Variable 3
MATH 435 Modern Algebra II 3
MATH 470
   or
MATH 471

Analysis II-Several Variables

Fourier Series and Wavelets

3
Two elective courses numbered 400 or above except MATH 475 6
Total for major 48

Concentration in Mathematics for Liberal Arts

Core Courses 24
CSC 210
   or
CSC 309
   or
MATH 309
Introduction to Computer Programming

Computer Programming for Scientists and Engineers

Computation in Mathematics
3
MATH 300 GW History of Mathematics - GWAR 3
Four elective courses numbered 300 or above except MATH 475 12
Total for major 42

Concentration in Mathematics for Teaching

Core Courses 24
MATH 300 GW History of Mathematics 3
MATH 309 Computation in Mathematics 3
MATH 310 Introduction to Number Theory 3
MATH 324 Probability and Statistics with Computing 3
MATH 350 Geometry 3
MATH 375 Field Study for Secondary Teachers 3
MATH 475 Capstone Course for Secondary Teachers of Mathematics 3
Total for major 45

BACHELOR OF SCIENCE IN APPLIED MATHEMATICS

Courses are 3 units unless otherwise indicated. On-line course descriptions are available.

Required Courses (39 units) Units
CSC 210
   or
CSC 309
   or
MATH 309
Introduction to Computer Programming

Computer Programming for Scientists and Engineers

Computation in Mathematics
3
MATH 226-228 Calculus I-III (4 each) 12
MATH 324
   or
MATH 441
Statistics with Computing

Mathematical Statistics
3
MATH 325 Linear Algebra 3
MATH 335
   or
MATH 370
Modern Algebra

Real Analysis I
3
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 GW Exploration and Proof  
MATH 380 Introduction to Functions of a Complex Variable
MATH 430 Operations Research: Deterministic Methods
MATH 442 Probability Theory
PHYS 385 Introduction to Theoretical Physics I
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 intend to pursue an advanced degree, or who are planning careers as statisticians in industry, business, government, or scientific research.

To give the students both breath and depth and to introduce them to a variety of fields where statistics may be applied, we offer three emphases for the degree: science, business, and economics.

Courses are 3 units unless otherwise indicated. On-line course descriptions are available.

Core Requirements Units
CSC 210
   or
CSC 309
Introduction to Computer Programming
 
Computer Programming for Scientists and Engineers
3
MATH 226-228 Calculus I-III (4 units 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 301 Intermediate Microeconomic Theory 3
ECON 302 Intermediate Macroeconomic Theory 3
ECON 312 Introduction to Econometrics 3
ECON 615 Mathematical Economics 3
ECON 630 Introduction to Econometrics 3
ECON 725 Applied Data Analysis in Economics 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 12 units of courses counted toward the minor, including at least six upper division units, must be completed at SFSU.

Courses are 3 units unless otherwise indicated. On-line course descriptions are available.

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

Upper division courses acceptable on an Advancement to Candidacy will be determined by the student with approval of the graduate adviser.

Courses are 3 units unless otherwise indicated. On-line course descriptions are available.

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 mathematics or related courses
At least 3 unpaired graduate units in mathematics must be included1 and at most 9 units may be selected from unpaired upper division courses. Student must complete either a thesis2 with oral defense or take the comprehensive examinations and write an expository paper.
18
Minimum total 30
1 MATH 730 must be included in this category unless the student has completed an undergraduate complex analysis course with a grade of B or higher.
2 MATH 898 Master's Thesis, if chosen will earn 3 units toward this requirement.

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 contain new theorems or algorithms, a novel application, or an original approach to an established result. The resulting manuscript must be prepared according to university guidelines following a style similar to that used by the Notices of the American Mathematical Society. Each MA thesis has a principal adviser and two 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 Graduate Adviser.

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 algebra, analysis, and statistics. Written examinations are administered during the last two weeks of each semester. Examinations last two and a half 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 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. Students who fail an examination may repeat it at least once, with additional attempts requiring the written approval of the graduate adviser.

The expository paper is completed in two stages. First, students must complete a departmental proposal form, including: the title and abstract of the proposed paper, the what-why-how aspects of the research in question, a brief preliminary bibliography, and the approval of the proposal by a committee consisting of a faculty adviser and two additional readers from the Mathematics faculty. Once students have an approved proposal, they may begin work on the project under the guidance of the faculty adviser. Completion of the paper is subject to signed approval by all members of the committee.

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



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