Bulletin--Mathematics Discipline
## MATHEMATICS

### College of Science and Engineering

(See Mathematics in the Academic Programs section for information on degrees)

*Most Mathematics courses are arranged in sequences. A student who has recently passed a higher level course in a sequence may be restricted from enrolling in a lower level course.*
*Undergraduate Courses*

#### 54 Entry Level Mathematics Skills Review (4)

*Prerequisite: grade of C or better in high school algebra, or score of 25 or better on the Entry Level Mathematics (ELM) examination.* Students must bring evidence of prerequisite to class. This is a fast-paced review of the concepts and skills of arithmetic, elementary algebra, and intuitive geometry. Units earned do *not* count towards meeting graduation requirements.

#### 55 Remedial Mathematics Skills (1-5)

Individualized assistance and practice in remedial mathematics skills. Emphasis on personalized audio-tutorial programs. For each unit a student works on skills in the Student Learning Center for 20 hours per semester. May be repeated for a maximum of six units. CR/NC grading. Units earned do *not* count towards meeting graduation requirements.

#### 60 Algebra I (3)

**F,S**

Equivalent to first year high school algebra. Fundamental operations on numbers, polynomials, and rational expressions; factoring, linear equations, and inequalities; applications. Units and grades earned do *not* count towards meeting graduation requirements.

#### 70 Algebra II (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 60.* Equivalent to second year high school algebra. Exponents, radicals, logarithms, systems of linear equations, determinants, complex numbers, quadratic equations. Applications. Units and grades earned do *not* count towards meeting graduation requirements.

#### 107 Plane Trigonometry (3)

**F,S**

*Prerequisites: a grade of C or better in MATH 70 or second year high school algebra and a satisfactory score on a mathematics placement examination.* Equivalent to high school trigonometry. Trigonometric functions, graphs, identities, equations; inverse trigonometric functions. Applications. [CAN MATH 8]

#### 109 Pre-Calculus Mathematics (3)

**F,S**

*Prerequisites: a grade of C or better in MATH 107 and a satisfactory score on a mathematics placement examination.* Continuation of MATH 70 and 107 with an emphasis on the concept of elementary functions, mathematical induction, and graphing. Note: this course is not prerequisite to calculus. [CAN MATH 16]

#### 110 Mathematics for Business Analysis (3) [GE]

**F,S**

*Prerequisites: a score of 550 or above on the Entry Level Mathematics (ELM) examination, or an approved exemption, and a satisfactory score on a mathematics placement examination.* An introduction to the mathematics of finance, probability, and calculus. Satisfies the general education requirement in quantitative reasoning; satisfaction of ELM requirement needed for enrollment.

**F,S**

*Prerequisites: a score of 550 or above on the Entry Level Mathematics (ELM) examination, or an approved exemption; a grade of C or better in MATH 70 or equivalent; and a satisfactory score on a mathematics placement examination.* Statistics as a tool for decision making in the face of uncertainty. Elements of probability; descriptive and inferential statistics. Recommended for students in the many fields where statistics is a means of communication and an instrument in problem solving. (Also offered as STAT 124.) [CAN STAT 2]

#### 165 Concepts of the Number System (3)

**F,S**

*Prerequisites: MATH 70 or equivalent and completion of the Entry Level Mathematics (ELM) requirement.* Designed for prospective multiple subjects credential candidates. Emphasis on understanding operations with whole numbers, fractions, and decimals. Additional topics include problem solving strategies, numeration systems, and elementary number theory. [CAN MATH 4]

#### 220 Calculus and Analytic Geometry I (3) [GE]

**F,S**

*Prerequisites: a score of 550 or above on the Entry Level Mathematics (ELM) examination, or an approved exemption; a grade of C or better in MATH 107; and a satisfactory score on a mathematics placement examination.* Graphs of lines and curves. Differentiation: theory, techniques, and applications to curve plotting and optimization. Integration. Fundamental theorem of calculus. [CAN MATH SEQ C]

#### 221 Calculus and Analytic Geometry II (3)

**F,S**

*Prerequisite: MATH 220 with a grade of C or better.* Applications of integration, transcendental functions. Techniques of integration. [CAN MATH SEQ C]

#### 222 Calculus and Analytic Geometry III (3)

*Prerequisite: MATH 221 with a grade of C or better.* Analytic geometry, polar coordinates, vectors, improper integrals. Sequences and series. [CAN MATH SEQ C]

#### 223 Calculus and Analytic Geometry IV (3)

**F,S**

*Prerequisites: MATH 222 with a grade of C or better.* Three dimensional analytic geometry, partial differentiation, multiple integrals, vector calculus. Applications. [CAN MATH SEQ C]

#### 245 Elementary Differential Equations and Linear Algebra (3)

**F,S**

*Corequisite: MATH 223.* First and second order differential equations, Laplace transform methods, Fourier series, matrix algebra. Applications.

#### 246 Introduction to Applied Linear Algebra (3)

**F,S**

*Prerequisites: MATH 221 with a grade of C or better.* Systems of equations, finite dimensional Euclidean vector spaces, matrices, linear transformations, eigenvectors, eigenvalues, and orthogonalization. Applications include: computer graphics, cubic spline, iteration, and computation with software. [CAN MATH 26]

**F,S**

*Prerequisites: CSC 210 and MATH 221 with a grade of C or better.* Basic concepts of probability and statistics. Important probability models presented and illustrated: binomial, hypergeometric, Poisson, exponential, and normal. Statistical procedures, both classical and non-parametric, are introduced and applied. Computer simulations and computations are used throughout the course as an instructional aid. (Also offered as STAT 250.)

#### 300 History of Mathematics (3)

**A**

*Prerequisites: MATH 223 and consent of instructor.* The evolution of those principal ideas and techniques that constitute the world of mathematics. Problem-solving methods and techniques are applied to such diverse areas as Egyptian, Greek, and Babylonian mathematics; geometry, number theory, calculus; modern mathematics.

#### 301 Exploration and Proof (3)

*Prerequisite: MATH 220 or equivalent.* Introduction to informal exploration and proofs in mathematics and to basic concepts of advanced mathematics courses. Topics include exploratory thinking, elementary logic, sets, mathematical induction, the integers, relations, and functions.

#### 309 Computation in Mathematics (3)

*Prerequisite: MATH 220 or equivalent.* Introduction to computing in mathematics, including programming in PASCAL and use of commercial mathematical software.

#### 310 Elementary Number Theory (3)

*Prerequisites: a grade of C or better in MATH 220 and 221.* Divisibility, congruences, power residues, quadratic reciprocity, diophantine equations. Additional topics selected from number theoretic functions, continued fractions and rational approximation, partitions.

#### 320 Modern Algebra (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 325; MATH 260 strongly recommended.* Introduction to groups, rings, integral domains, fields, and ordering.

#### 325 Linear Algebra (3)

**F,S**

*Prerequisites: a grade of C or better in MATH 221.* Vector spaces, linear transformations, elements of matrix algebra including determinants and eigenvalues.

**F,S**

*Prerequisite: concurrent registration or completion of MATH 223 with a grade of C or better. MATH 124 or equivalent recommended.* Probability spaces. Random variables, density functions, moments, selected distributions. Central limit theorem. Introduction to statistical inference. Applications. (Also offered as STAT 340.)

**F**

*Prerequisite: a grade of C or better in MATH 340.* Continuation of MATH 340. Advanced topics in probability theory: combinatorics, conditioning, stochastic processes, limit theorems. Applications. (Also offered as STAT 341.)

**S**

*Prerequisite: a grade of C or better in MATH 340.* Continuation of MATH 340. Sampling distributions, law of large numbers, applications of central limit theorem, estimation, confidence intervals, hypothesis testing, regression. (Also offered as STAT 342.)

#### 370 Real Analysis I (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 223; MATH 260 strongly recommended.* Critical development of analysis: Bolzano-Weierstrass and Heine-Borel theorems; limits, continuity, differentiability, integrability.

#### 371 Real Analysis II (3)

**S**

*Prerequisite: a grade of C or better in MATH 370.* Power series, Fourier series; uniform convergence, partial differentiation, implicit function theorem; theorems of Gauss, Green, and Stokes.

#### 374 Advanced Calculus (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 223.* Coordinate transformations, Jacobians; vector calculus, line integrals and Green's Theorem, surface integrals and Stokes' Theorem, Divergence Theorem; uniform convergence; Fourier series.

#### 376 Ordinary Differential Equations I (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 223.* Theory of linear differential equations; series solutions with applications to Bessel and Legendre equations; existence and uniqueness theorems; numerical techniques.

#### 378 Ordinary Differential Equations II (3)

**S**

*Prerequisite: a grade of C or better in MATH 376.* Systems of linear differential equations; boundary-value problems, Green's function; further topics such as: introduction to non-linear systems and stability theory, difference equations, operator methods.

#### 379 Partial Differential Equations (3)

**F**

*Prerequisite: a grade of C or better in MATH 374 and 376.* Formulation of initial and boundary value problems; separation of variables, Sturm-Liouville theory; wave propagation method. Applications.

#### 380 Introduction to Functions of a Complex Variable (3)

**F**

*Prerequisite: a grade of C or better in MATH 223 or equivalent.* Analytic functions of a complex variable. Cauchy's theorem, power series, laurent series, singularities, residue theorem with applications to definite integrals. Conformal mappings.

#### 400 Numerical Analysis (3)

**F**

*Prerequisites: a grade of C or better in MATH 223, 246, or 325; CSC 210 or MATH 309.* Numerical solution of algebra and calculus problems. Interpolation and approximations; direct and iterative methods for solutions of linear equations. Gaussian elimination. Numerical differentiation and integration. Numerical solution of ordinary differential equations.

#### 425 Advanced Linear Algebra (3)

*Prerequisites: MATH 320, 325 or equivalent.* Eigenvalue theory, quotient spaces, Jordan canonical form, generalized inverses, operator and matrix norms.

#### 430 Operations Research: Deterministic Methods (3)

*Prerequisites: grade of C or better in MATH 246 or 325.* Introduction to deterministic methods of operations research. Problem formulation, development of solution algorithms and their computer implementation. Topics selected from linear programming, network analysis, and transportation models.

#### 440 Geometry (3)

**A**

*Prerequisites: a grade of C or better in MATH 222.* Introduction to the origin and foundations of geometry: Euclidean, non-Euclidean geometries, more recent approaches. Quick survey of high school geometry. Classification and representation of motions and similarities. Projections, homogeneous coordinates.

#### 455 Set Theory (3)

*Prerequisites: a grade of C or better in MATH 320, CSC 330, or consent of instructor.* Quantifier logic, paradoxes of set theory, cardinal and ordinal arithmetic, and equivalents of the axiom of choice.

#### 460 Mathematical Modeling (3)

**F,S**

*Prerequisites: a grade of C or better in CSC 210 or MATH 309; MATH 325, 250, or 340; and MATH 376.* Deterministic and stochastic techniques used in mathematical modeling, illustrated and developed through problems originating in industry and applied research. Students work on individual or team projects.

#### 500 Mathematics Seminar (3)

**F,S**

*Prerequisite: consent of instructor. Topic to be specified in Class Schedule.* Development of a selected branch of advanced mathematics; e.g., calculus of variations, non-parametric statistics, differential geometry, game theory. May be repeated for credit as topics vary.

#### 560 Computers and Elementary Mathematics (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 165. MATH 565 is also recommended.* Designed for prospective multiple subjects credential candidates. Concepts from geometry, logic, statistics, algebra, and arithmetic introduced via appropriate software. Programming using LOGO is an important element of the course.

#### 565 Concepts of Geometry, Measurement, and Probability (3)

**F,S**

*Prerequisite: a grade of C or better in MATH 165.* Designed for prospective multiple subjects credential candidates. Spatial relationships and inductive reasoning in geometry, measurement emphasizing the metric system, and elementary statistics and probability. Some computer use and programming in LOGO will be included.

#### 567 Problem Solving and Discovery in Mathematics (3)

*Prerequisite: MATH 70 or equivalent.* Intended for non-science majors and prospective teaching credential candidates interested in a mathematics concentration. Suitable for multiple subject credential candidates and liberal studies majors. Problem solving strategies are used to explore topics in algebra, logic, and number theory. Games, puzzles, and brain teasers are investigated.

#### 650 Curriculum and Instruction in Mathematics (3)

**F**

The teaching of mathematics in junior and senior high schools including determination of objectives, utilization of modern principles of learning, development of curriculum materials, and investigation of the most effective methods of teaching and evaluating in junior and senior high school mathematics.

#### 655 Projects in Study and Mathematics Skills (3)

*Prerequisites: MATH 221 and consent of instructor.* Students are trained as learning assistants for the Student Learning Center. Students assist peers in improving their skills in remedial mathematics. All work is done in the laboratory in six hours per week. May be repeated once for credit. Credit does *not* count towards the mathematics major or minor requirements.

#### 696 Applied Mathematics Project I (1)

**F,S**

*Corequisite: MATH 460 and consent of instructor.* Preparation under faculty guidance of feasibility study and outline of a project in applied mathematics.

#### 697 Applied Mathematics Project II (2)

**F,S**

*Prerequisite: MATH 696.* Completion of applied mathematics project. Presentation of oral and written report.

#### 699 Special Study in Mathematics (1-3)

**F,S**
*Prerequisites: approval of the department and the instructor concerned.* Special study of a particular problem under the direction of a member of the department. The student must present a written report of the work accomplished to the staff of the department.

*Graduate Courses*

#### 710 Analysis (3)

*Prerequisites: a grade of C or better in MATH 371 or equivalent, and consent of instructor.* Metric spaces, completeness, compactness; normed spaces, linear operators; applications to functional, differential, and integral equations.

#### 730 Theory of Functions of a Complex Variable (3)

**S**

*Prerequisites: a grade of C or better in MATH 371 and consent of instructor.* Elementary topology of the Euclidean plane necessary for a careful development of the theory of differentiation and integration. Integral theorems, residue theorems, power series, Laurent series, analytic continuation. Applications. Additional topics to be selected by the instructor.

#### 740 Functional Analysis (3)

**S**

*Prerequisite: a grade of B or better in MATH 710.* Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems; Hilbert spaces and spectral theory; applications to approximation theory.

#### 750 General Topology (3)

**F**

*Prerequisite: a grade of B or better in MATH 710.* Sets and relations, topological spaces, countability, separation axioms, compactness, connectedness, convergence, product spaces.

#### 760 Introduction to Measure and Lebesgue Integration (3)

**F**

*Prerequisite: a grade of B or better in MATH 710.* Set functions and measure; Lebesgue measure and integral. Convergence theorems, absolute continuity, Fubini's theorem. Applications.

#### 770 Methods of Applied Analysis (3)

**S**

*Prerequisites: a grade of C or better in MATH 371 or 379 and consent of instructor.* Boundary and eigenvalue problems of ordinary and partial differential equations; further topics are selected from such areas as calculus of variations; integral transform; integral equations; generalized functions.

#### 800 Foundations of Mathematics (3)

**F**

*Prerequisite: a grade of C or better in MATH 320; MATH 455 recommended.* Syntax and semantics of formal mathematical theories. Completeness of first order logic. Complete and incomplete theories, decidability and undecidability. Topics from set theory as necessary; e.g., axiom of choice, Zorn's lemma, cardinal arithmetic.

#### 850 Algebra (3)

**S**

*Prerequisites: a grade of C or better in MATH 320, 325, and consent of instructor.* Rings and modules; further material is selected from such topics as Wedderburn theory, Noeterian theory, field theory, and general algebraic systems.

#### 890 Seminar (3)

**F,S**

*Prerequisite: consent of instructor. Topic to be specified in Class Schedule.* Development of a selected branch of advanced mathematics; e.g., history of modern mathematics, ideal theory, foundations of geometry, measure theory, stability theory, numerical solution of differential equations. May be repeated for credit as topic varies.

#### 899 Special Study (1-3)

**F,S**

*Prerequisite: approval of the department and the instructor concerned.* Special study of a particular problem under the direction of a member of the department. The student must present a written report of the work accomplished to the staff of the department.

Course Disciplines Listing, Bulletin 1994-96 Table of Contents, SFSU Home Page

last modified June 21, 1995

Home
Search
Need Help?
1600 Holloway Avenue, San Francisco, CA 94132 (415) 338-1111

Last modified July 13, 2012 by bulletin@sfsu.edu