Bulletin--Mathematics Program

Mathematics


College of Science and Engineering
Dean: James C. Kelley

Department of Mathematics
TH 937
415-338-2251
Chair: Newman Fisher

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

Mathematics Faculty
Professors—Aiyar, Astromoff, Bruno, Douglas, Ekstrand, Ellis, Fendel, Fisher, Forsey, Gutierrez, Hayashi, Lakness, Lewis, J., Marcucci, Meredith, Novalis, Ovchinnikov, Resek, Robbins, Smith, J., Tabatabaian, Tang

Associate Professors—Haines, Krause, Langlois

Assistant Professor—Kafai

Lecturer—Pollatchek

Statistics Undergraduate Adviser: J. Ekstrand

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

Assistant Professors—Kafai, 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 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 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 (see Mathematics discipline in the Announcement of Courses section).

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.

Program Requirements				Units
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 246	Introduction to Applied 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 Func-
			tions 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 advisement 
(MATH 260 is acceptable in this category)	 9
		Total				42

BACHELOR OF SCIENCE IN APPLIED MATHEMATICS

Courses for this program are listed in alphabetical sequence (see Mathematics discipline in the Announcement of Courses section).

Required Courses (39 units)			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 246	Introduction to Applied Linear 
		Algebra				 3
MATH 320	Modern Algebra or
	MATH 370	Real Analysis I		 3
MATH 340	Mathematical Statistics I	 3
MATH 250	Statistics with Computing or
	MATH 342	Mathematical 
			Statistics II		 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 Func-
			tions 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 (see Statistics discipline in the Announcement of Courses section).

Basic Requirements				Units
CSC 210		Introduction to Computer 
		Programming			 3
MATH 220-223	Calculus and Analytic 
		Geometry I-IV (3 each)		12
MATH 246	Introduction to Applied Linear 
		Algebra or
	MATH 325	Linear Algebra		 3
MATH/STAT 340	Introduction to Probability and 
		Statistics			 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 & Finance Reporting*	 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 (not an exhaustive list):
	BA 412 plus three courses from BA 408, 
		601, 604, 624, MGMT 661
	FIN 309, 350, ACCT 303; one course from 
		BICS 265 and BA 601
	MKTG 431, 632, PSY 571; one course from 
		BICS 265 and BA 601
	BICS 461, 562, BA 408; one course from 
		BICS 265 and BA 601
		Total for emphasis		30
*Students particularly interested in accounting should choose among the electives ACCT 100-101 (6 units) in place of ACCT 300.

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
	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 & 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 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 four courses, or their equivalent: MATH 320, MATH 325, MATH 370, and MATH 371. 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 four courses, however, may not be counted as electives toward the M.A. degree).

Courses for this discipline are listed in alphabetical sequence (see Mathemathics discipline in the Announcement of Courses section).

Upper division courses acceptable on a Graduate Approved Program are: MATH 310, 340, 341, 342, 378, 379, 400, 440, 500; CSC 510, 520.

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
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 Mathe-
matics 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.


Bulletin 1994-96 Table of Contents, SFSU Home Page

last modified June 23, 1995


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