# Mathematics

## College of Science and Engineering

Dean: Keith Bowman

### Department of Mathematics

TH 937

Phone: 415-338-2251

E-mail: statmath@sfsu.edu

Web Site: http://math.sfsu.edu

Chair: David Bao

Mathematics Undergraduate Advisors: D. Ellis, E. Hsu, S. Li

Mathematics Graduate Coordinators: M. Beck, S. Hosten

Statistics Undergraduate Advisor: M. Kafai

## Program Scope

The Bachelor of Arts is offered for students with a general interest in mathematics; Bachelor of Science 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
- 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, doing research on DNA topology, mathematical cancer biology, or meeting the 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 College of Business, and the College of 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 apply 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.

## Mathematics Faculty

### Professors

Axler, Bao, Beck, Cheung, Ellis, Goetz, Gubeladze, Hosten, Hsu, Kafai, Kysh, Langlois, Li, Ovchinnikov, Robbins, Schuster

### Associate Professors

Ardila, Krause, Piryatinska

### Assistant Professors

He, Lai, Seashore

## Statistics Faculty

### Professor

Kafai

### Associate Professor

Piryatinska

### Assistant Professor

He

## Majors

- Bachelor of Arts in Mathematics: Concentration in Mathematics for Advanced Study
- Bachelor of Arts in Mathematics: Concentration in Liberal Arts
- Bachelor of Arts in Mathematics: Concentration in Teaching
- Bachelor of Science in Applied Mathematics
- Bachelor of Science in Statistics

## Minors

**MATH 50 Preparatory Mathematics for Pathways Courses (Units: 4)**

Prerequisite: ELM scores below 50; restricted to students who have committed to take pathway course such as STAT way.

**Course Attributes:**

- Pre-Collegiate

**MATH 60 Entry Level Math I (Units: 3)**

Equivalent to first year high school algebra.

Fundamental operations on numbers, polynomials, and rational expressions; factoring, linear equations, and inequalities. Units and grades earned do not count towards graduation requirements. (A/A-/B+/B/B-/C+/C/NC grading only)

**Course Attributes:**

- Pre-Collegiate

**MATH 70 Entry Level Math II (Units: 3)**

Prerequisite: A grade of C or better in MATH 59 or MATH 60/ESM 60, or a score of 42 or above on ELM.

**Course Attributes:**

- Pre-Collegiate

**MATH 110 Business Calculus (Units: 3)**

Prerequisite: ELM exempt status, or MATH 70/ESM 70 with grade of C or better.

(Note: In order for this course to satisfy General Education, students must earn a C- or CR or higher grade if taken fall 2014 or later.)

**Course Attributes:**

- B4: Math/QR

**MATH 124 Elementary Statistics (Units: 3)**

Prerequisite: Satisfactory completion of ELM requirement.

(Note: In order for this course to satisfy General Education, students must earn a C- or CR or higher grade if taken fall 2014 or later.)

**Course Attributes:**

- B4: Math/QR

**MATH 165 Concepts of the Number System (Units: 3)**

Prerequisites: Satisfactory completion of ELM requirement.

**MATH 199 Pre-Calculus (Units: 4)**

Prerequisite: Satisfactory completion of ELM requirement.

(Note: In order for this course to satisfy General Education, students must earn a C- or CR or higher grade if taken fall 2014 or later.)

**Course Attributes:**

- B4: Math/QR

**MATH 226 Calculus I (Units: 4)**

Prerequisites: Satisfactory completion of ELM requirement, acceptable score on the department's Calculus readiness test (instructions will be provided after enrollment), and one of the following: MATH 199 [formerly MATH 109] or equivalent with a grade of C or better; passing a high school math analysis or pre-calculus class with a grade of B or better.

(Note: In order for this course to satisfy General Education, students must earn a C- or CR or higher grade if taken fall 2014 or later.)

**Course Attributes:**

- B4: Math/QR

**MATH 227 Calculus II (Units: 4)**

Prerequisite: MATH 226 with a grade of C or better.

**MATH 228 Calculus III (Units: 4)**

Prerequisite: MATH 227 with a grade of C or better.

**MATH 245 Elementary Differential Equations and Linear Algebra (Units: 3)**

Prerequisite: MATH 228 with a grade of C or better.

**MATH 265 Advanced Number Systems (Units: 3)**

Prerequisite: MATH 165 with grade of C or better.

**MATH 300GW History of Mathematics - GWAR (Units: 3)**

Prerequisite: ENG 214 or equivalent with a grade of C- or better; MATH 227 or equivalent with a grade of C or better.

**Course Attributes:**

- Graduation Writing Assessment

**MATH 301GW Exploration and Proof - GWAR (Units: 3)**

Prerequisites: MATH 227 and ENG 214 with grades of C or better.

**Course Attributes:**

- Graduation Writing Assessment

**MATH 310 Elementary Number Theory (Units: 3)**

Prerequisites: MATH 227 and MATH 301GW with grades of C or better.

**MATH 314 Math Circle Seminar (Units: 3)**

Prerequisite: MATH 226 (or equivalent) with a grade of C or better.

**MATH 324 Probability and Statistics with Computing (Units: 3)**

Prerequisites: MATH 227 with grade of C or better, and computer experience that meets the approval of the instructor. Basic concepts of probability and statistics.

**MATH 325 Linear Algebra (Units: 3)**

Prerequisite: MATH 227 with a grade of C or better; CSC 230 or MATH 301GW recommended.

**MATH 335 Modern Algebra (Units: 3)**

Prerequisites: MATH 301GW with grade of C or better or consent of instructor; MATH 325 with grade of C or better.

**MATH 338 Introduction to SAS (Units: 3)**

Prerequisites: MATH 124 (or equivalent) and one of the following: CSC 210, CSC 309, MATH 309, or consent of instructor, with grades of C or better.

**MATH 340 Probability and Statistics I (Units: 3)**

Prerequisite: MATH 228 with a grade of C or better (may be taken concurrently). Recommended: MATH 124 or equivalent. Probability spaces, elementary combinatorics, random variables, independence, expected values, moment generating functions, selected probability distributions, limit theorems and applications.

**MATH 350 Geometry (Units: 3)**

Prerequisites: MATH 228 and MATH 301GW with grades of C or better.

**MATH 370 Real Analysis I (Units: 3)**

Prerequisites: MATH 228 and MATH 301GW with grades of C or better.

**MATH 375 Field Study for Secondary Teachers (Units: 3)**

Prerequisites: MATH 301GW with grade of C or better, or consent of instructor.

**MATH 376 Ordinary Differential Equations I (Units: 3)**

Prerequisites: MATH 228 and MATH 325 with grades of C or better.

**MATH 380 Introduction to Functions of a Complex Variable (Units: 3)**

Prerequisite: MATH 228 with a grade of C or better.

**MATH 400 Numerical Analysis (Units: 3)**

Prerequisites: MATH 228, MATH 325, and either MATH 309 or CSC 210, all with grades of C or better.

**MATH 414 Analyzing DNA Topology with Math/Computational Methods (Units: 3)**

Prerequisite for MATH 414:: MATH 228 (or equivalent) with grade of C or better.

Prerequisite for MATH 714: Graduate standing or consent of instructor.

(MATH 414/MATH 714 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 420 Combinatorics (Units: 3)**

Prerequisites: MATH 301GW and one of the following: MATH 310, MATH 325, CSC 230; with grades of C or better.

(MATH 420/MATH 720 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 424 Introduction to Linear Models (Units: 3)**

Prerequisites: MATH 227 and MATH 325 with grades of C or better.

(MATH 424/MATH 724 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 430 Mathematics of Optimization (Units: 3)**

Prerequisite: MATH 325 with a grade of C or better.

**MATH 435 Modern Algebra II (Units: 3)**

Prerequisite: MATH 335 with a grade of C or better.

(MATH 435/MATH 735 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 441 Probability and Statistics II (Units: 3)**

Prerequisite: MATH 340 with a grade of C or better.

(MATH 441/MATH 741 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 442 Probability Models (Units: 3)**

Prerequisite: MATH 340 with a grade of C or better.

**MATH 447 Design and Analysis of Experiments (Units: 3)**

Prerequisites: MATH 325 and MATH 340 with a grade of C or better.

**MATH 448 Introduction to Statistical Learning and Data Mining (Units: 3)**

Prerequisite: MATH 340 with grade of C or better or consent of instructor.

**MATH 449 Categorical Data Analysis (Units: 3)**

Prerequisite: MATH 340 with grade of C or better or consent of instructor.

**MATH 450 Topology (Units: 3)**

Prerequisite: MATH 370 with grade of C or better.

**MATH 451 Introduction to Differential Geometry (Units: 3)**

Prerequisite: MATH 228 and MATH 325 with grades of C or better, and either MATH 370 or MATH 450. These requirements may be waived upon the consent of instructor.

**MATH 460 Mathematical Modeling (Units: 3)**

Prerequisites: MATH 325 and either MATH 245 or MATH 376, with grades of C or better.

**MATH 470 Real Analysis II - Several Variables (Units: 3)**

Prerequisite: MATH 370 with a grade of C or better, or consent of instructor.

(MATH 470/MATH 770 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 471 Introduction to Fourier and Wavelet Analysis (Units: 3)**

Prerequisite for MATH 471: MATH 370 with a grade of C or better.

Prerequisite for MATH 771: MATH 370 with a grade of C or better; graduate standing or consent of instructor.

(MATH 471/MATH 771 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 475 Capstone Course for Secondary Teachers of Mathematics (Units: 3)**

Prerequisites: MATH 335 with grade of C or better and one of the following: concurrent enrollment in MATH 370 or consent of instructor.

**MATH 477 Partial Differential Equations (Units: 3)**

Prerequisite: MATH 376 with grade of C or better.

(MATH 477/MATH 777 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 490 Mathematics Seminar (Units: 3)**

Prerequisite: Consent of instructor.

**MATH 491 Game Theory (Units: 3)**

Prerequisite: MATH 227 with a grade of C or better.

**MATH 565 Concepts of Geometry, Measurement, and Probability (Units: 3)**

Prerequisite: A grade of C or better in MATH 165.

**MATH 575 Mathematics in the Middle School Classroom (Units: 3)**

Prerequisite: MATH 565 with grade of C or better, or consent of instructor.

**MATH 576 Math in Middle Schools II (Units: 3)**

Prerequisite: MATH 575 with grade of C or better.

**MATH 577 Math in Middle School III (Units: 3)**

Prerequisite: MATH 576 with grade of C or better.

**MATH 578 Mathematics in the High School (Units: 3)**

Prerequisites: MATH 577 or MATH 227 with grade of C or better, or consent of instructor.

**MATH 690 Capstone Research for Mathematics Majors (Units: 3)**

Prerequisites: Grades of C or better in MATH 325, MATH 335, and MATH 370; grades of C or better in a subset of the following MATH courses: MATH 310, MATH 324 or MATH 340, MATH 376, MATH 380, MATH 400, MATH 420, or MATH 490, or consent of instructor.

**MATH 696 Applied Mathematics Project I (Unit: 1)**

Prerequisite: MATH 460 with grade of C or better. May be replaced by consent of instructor.

**MATH 697 Applied Mathematics Project II (Units: 2)**

Prerequisite: Successful completion of MATH 696 in a previous year. May not be taken concurrently with MATH 696.

**MATH 699 Independent Study (Units: 1-3)**

Prerequisites: Approval of department and consent of instructor.

**MATH 700 Graduate Teaching Workshop (Units: 3)**

Prerequisite: GTA status.

**MATH 710 Analysis I (Units: 3)**

Prerequisite: MATH 470 with grade of C or better, or consent of instructor.

**MATH 711 Introductory Functional Analysis (Units: 3)**

Prerequisites: MATH 470 and MATH 725 with grades of B- or better, or consent of instructor.

**MATH 714 Analyzing DNA Topology with Math/Computational Methods (Units: 3)**

Prerequisite for MATH 414:: MATH 228 (or equivalent) with grade of C or better.

Prerequisite for MATH 714: Graduate standing or consent of instructor.

(MATH 414/MATH 714 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 720 Combinatorics (Units: 3)**

Prerequisites: MATH 301GW and one of the following: MATH 310, MATH 325, CSC 230; with grades of C or better.

(MATH 420/MATH 720 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 724 Introduction to Linear Models (Units: 3)**

Prerequisites: MATH 227 and MATH 325 with grades of C or better.

(MATH 424/MATH 724 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 725 Advanced Linear Algebra (Units: 3)**

Prerequisite: MATH 335 with a grade of C or better.

**MATH 728 Mathematical Projects and Partnerships (Unit: 1)**

Prerequisite: Graduate standing or consent of instructor.

**MATH 729 Communicating Mathematics (Units: 3)**

Prerequisite: Formal commitment to write an MA thesis or expository paper.

**MATH 730 Theory of Functions of a Complex Variable (Units: 3)**

Prerequisites: MATH 470 with a grade of C or better, and consent of instructor.

**MATH 735 Modern Algebra II (Units: 3)**

Prerequisite: MATH 335 with a grade of C or better.

(MATH 435/MATH 735 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 741 Probability and Statistics II (Units: 3)**

Prerequisite: MATH 340 with a grade of C or better.

(MATH 441/MATH 741 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 770 Real Analysis II - Several Variables (Units: 3)**

Prerequisite: MATH 370 with a grade of C or better, or consent of instructor.

(MATH 470/MATH 770 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 771 Introduction to Fourier and Wavelet Analysis (Units: 3)**

Prerequisite for MATH 471: MATH 370 with a grade of C or better.

Prerequisite for MATH 771: MATH 370 with a grade of C or better; graduate standing or consent of instructor.

(MATH 471/MATH 771 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 777 Partial Differential Equations (Units: 3)**

Prerequisite: MATH 376 with grade of C or better.

(MATH 477/MATH 777 is a paired course offering. Students who complete the course at one level may not repeat the course at the other level.)

**MATH 814 Seminar on Modern Math Methods in Molecular Biology (Units: 3)**

Prerequisite: Consent of instructor.

**MATH 850 Algebra (Units: 3)**

Prerequisite: MATH 435/MATH 735 with grade of C or better, or consent of instructor.

**MATH 870 Computational Discrete Geometry (Units: 3)**

Prerequisites: CSC 210, CSC 230 [formerly CSC 330], MATH 325, or consent of instructor.

(This course is offered as MATH 870 and CSC 870. Students may not repeat the course under an alternate prefix.)

**MATH 884 Algebraic Geometry (Units: 3)**

Prerequisites: Graduate standing or consent of instructor.

**MATH 890 Seminar (Units: 3)**

Prerequisite: Graduate standing or consent of instructor.

**MATH 896EXM Culminating Experience Examination (Units: 0-3)**

Prerequisite: Consent of instructor, committee chair, and approval of Advancement to Candidacy (ATC) and Culminating Experience (CE) forms by Graduate Studies. ATC and Proposal for Culminating Experience Requirement forms must be approved by the Graduate Division before registration.

**MATH 898 Master's Thesis (Units: 3)**

Prerequisites: Consent of instructor and graduate adviser; and approval of Advancement to Candidacy (ATC) and Culminating Experience (CE) forms by Graduate Studies. ATC and Proposal for Culminating Experience Requirement forms must be approved by the Graduate Division before registration. (CR/NC grading only.)

**MATH 899 Independent Study (Units: 1-3)**

Prerequisites: Approval of the department and consent of the instructor.