# Course Descriptions for the Master's Degree

Mathematics course descriptions for the current academic year may be found at the following link: Catalog of Courses: Mathematics.

The course descriptions below are taken from the 2015-2016 Catalog of Courses. Note that courses numbered 600 and above are graduate/postbaccalaureate courses that may not be taken by undergraduate students.## Upper Division

## 510. Topics in Mathematics

Study of selected areas of advanced mathematics. May be repeated for credit with consent of instructor as topics change. Prerequisite: senior or graduate standing. (4 units)## 529. Advanced Geometry

Topics in affine and projective geometry with applications to Euclidean 2 and 3 space and to modern algebra. Prerequisites: MATH 329, 331 and 345. (4 units)## 531. Advanced Linear Algebra

Inner product spaces; duality of vector spaces; canonical forms; spectral theory; quadratic forms. Formerly a topic under MATH 510. Prerequisite: MATH 331. (4 units)## 545. Abstract Algebra I (FWS)

An introduction to algebraic structures, including groups, rings and fields. Prerequisites: MATH 331, 345 and 355. (4 units)## 546. Abstract Algebra II (S)

Continuation of MATH 545. Prerequisite: MATH 545. (4 units)## 553. Analysis I (FWS)

Continuous and differentiable functions, infinite series. Uniform convergence, computation with series, functions represented by integrals, theory of integration. Prerequisites: MATH 252 and 355. (4 units)## 554. Analysis II (S)

Continuation of MATH 553. Prerequisite: MATH 553. (4 units)## 555. Introduction to Point-Set Topology

Topics to include topological and metric spaces, compactness, product spaces, connectedness, separation properties. Prerequisite: MATH 355. (4 units)## 557. Complex Variables

Analytic and harmonic functions, power series, Cauchy's Theorem and Cauchy's Formula. Prerequisites: MATH 252 and 355. (4 units)## 565. Mathematical Statistics

Likelihood ratio, estimators, distributions of estimators, theory of hypothesis testing, linear statistical models. Prerequisite: MATH 465. (4 units)## 570. Partial Differential Equations

Classification of partial differential equations; heat equation, Laplace's equation, boundary value-problems; separation of variables. Applications of Fourier and Laplace transforms, numerical methods. Prerequisites: MATH 270 and 355. MATH 241 recommended. (4 units)## 576. Introduction to Mathematical Models

Topics from linear and probabilistic models, computer simulation, difference and differential equation models. Prerequisites: CSE 201, MATH 331 and 465. (4 units)## 595. Independent Study

An independent study course for senior mathematics majors. A total of four units may apply toward the major. Prerequisites: MATH 331 and 553, a minimum overall grade point average of 3.0, consent of instructor and departmental approval of a written proposal of a project submitted in advance of the quarter in which the course is to be taken. (1-4 units)## Graduate/Postbaccalaureate

### May not be taken by undergraduate students.

## 601. Assessment Portfolio

Preparation of an acceptable student portfolio assessing and documenting academic progress. For detailed requirements see the MAT graduate coordinator. Prerequisite: advancement to candidacy. (0 units)## 604. Seminar in Problem Solving I

A problem solving seminar emphasizing induction and analogy in the style of George Polya. Prerequisites: MATH 329, 331, 345, 355 and 372. (4 units)## 605. Seminar in Problem Solving II

Continuation of MATH 604. Prerequisite: MATH 604. (4 units)## 610. Topics in Mathematics

Study of selected areas of advanced mathematics to be determined by the instructor. May be repeated for credit with consent of instructor as topics change. Prerequisite: graduate standing. (4 units)## 611. Operations Analysis

Scientific approach to the resolution of operational problems. Structure and function of models and decision strategy commonly used in national policy analysis including measures of effectiveness, uncertainty and the misuse of modeling. May not be counted toward fulfilling the requirements in the mathematics major. Prerequisite: one of the following: MATH 305 or 350, SCM 210, PSYC 210 or equivalent. (4 units)## 614. Studies in Geometry

Advanced topics in affine, projective, elliptic, and hyperbolic geometry. Comparison of synthetic and analytic methods of proof. Prerequisites: MATH 529, 545 and admission to the M.A. in Mathematics program. (4 units)## 616. Studies in Algebra

Advanced topics in algebra to include constructability, transcendence and solvability of groups and equations. Prerequisites: MATH 546 and admission to the M.A. in Mathematics program. (4 units)## 618. Studies in Analysis

Theory of multivariable calculus with applications, to include the Inverse Function Theorem, as well as Stokes' and Green's theorems. Prerequisites: MATH 553; either 554, 555, or 557; and admission to the M.A. in Mathematics program. (4 units)## 631. Algebra from a Teaching and Problem Solving Perspective

Algebraic structure and its development. Equations and systems of
equations. Teaching strategies and curriculum issues. Applications
and problem solving will be stressed throughout. Students will adapt
methods from this course to a teaching setting and report on this experience.
Prerequisites: admission to the MAT in Mathematics program
and MATH 345, or consent of instructor. (6 units)
## 632. Geometry from a Teaching and Problem Solving Perspective

The transition from geometry as an empirical study first to "local" proofs and then to axiomatic systems. Comparisons of traditional approaches to geometric proof with those of analytic geometry. Focus on construction to illustrate and motivate teaching strategies and curriculum issues. Students will adapt methods from this course to a teaching setting and report on this experience. Prerequisite: MATH 329 and admission to the MAT in Mathematics program, or consent of instructor. (6 units)## 633. Trigonometry from a Teaching and Problem Solving Perspective

Trigonometric functions, identities and equations as foundation for study of the complex numbers, the complex plane, polar coordinates, de Moivre's theorem, and definition of trigonometric functions in terms of exponential functions. Geometric and analytic properties of the conic sections. Problem solving, curricular and pedagogical issues emphasized throughout. Students will adapt methods from this course to a teaching setting and report on this experience. Prerequisites: MATH 213, 251, 631, 632, and admission to the MAT in Mathematics program, or consent of instructor. (6 units)## 634. Calculus from a Teaching and Problem Solving Perspective

Focus on non-standard problems and theoretical issues in calculus that lend themselves to multiple problem-solving approaches and pedagogical strategies. Students will adapt methods from this course to a teaching setting and report on this experience. Prerequisites: MATH 213, 251, 631, 632, 633, and admission to the MAT in Mathematics program, or consent of instructor. (6 units)## 635. Statistics and Probability from a Teaching and Problem Solving Perspective

Basic probability and descriptive and inferential statistics emphasizing active learning teaching strategies. Students will design and carry out an investigative project. Students will adapt methods from this course to a teaching setting and report on this experience. Prerequisites: MATH 372, 631, 632, and 633, and admission to the MAT in Mathematics program, or consent of instructor. (6 units)## 664. Project Design in Teaching Mathematics

Steps and processes involved in the design and development of research proposals with emphasis on the master's project. Graded credit/no credit. Prerequisites: advancement to candidacy and consent of instructor. (2 units)## 678. Teaching Practicum

Supervised practice in individual and/or classroom teaching. May be repeated for a total of four units. Prerequisite: admission to the master's program in teaching with a major in mathematics. (2 units)## 695. Graduate Independent Study

An independent study course for graduate students in mathematics. Prerequisites: advancement to candidacy in the M.A. or M.A.T. in Mathematics program; a grade point average of at least 3.5 in courses in the program; consent of the instructor and approval by the graduate committee. A written proposal for a project must be submitted to the graduate committee no later than the ninth week of the quarter preceding that in which the independent study is to be pursued. (2-4 units)## 696. Master's Degree Project I

Dissertation preparation and assessment portfolio completion. A written proposal for a project must be submitted to the graduate committee no later than the ninth week of the quarter preceding enrollment in MATH 696. Prerequisites: graduate standing, consent of instructor, approval of the project proposal by the graduate committee and approval of at least five contributions to the assessment portfolio of the seven listed under 6b and 6c in the requirements for graduation. (3 units)## 697. Master's Degree Project II

Finalizing the master's project including approval of the dissertation format by the Office of Graduate Studies, an oral presentation of the project to the department, and formal acceptance of the completed dissertation. Prerequisites: Math 696 and consent of instructor. (1 unit)## 698. Continuous Enrollment for Graduate Candidacy Standing

Independent study leading to completion of requirements (other than course work) for the master's degree. To retain classified standing in the master's program, a student must enroll in 698 each quarter until the project or thesis is accepted or the comprehensive examination passed. Cannot be used to satisfy degree requirements. Students who enroll in 698 through the university have full use of all university facilities. See Page 375, Culminating Experience: Exam, Thesis, or Project. Prerequisites: advancement to candidacy and approval of program graduate coordinator or, if an interdisciplinary studies major, consent of the Dean of Graduate Studies. 698 is a variable unit course, see Page 43 for fee schedule. Earned units are not degree applicable nor will they qualify for financial aid. (0-6 units)## 699. Master of Arts in Teaching Mathematics Thesis

Written thesis, an oral presentation of the thesis to the department and a complete Assessment Portfolio. May not be counted toward fulfilling the requirements of the Master of Arts in Mathematics. Graded credit/no credit. Prerequisites: graduate standing, consent of the instructor, approval of the thesis proposal by the graduate committee and submission of at least three contributions to the Assessment Portfolio. A written proposal for a thesis following departmental guidelines must be submitted to the graduate committee no later than the ninth week of the quarter preceding enrollment in MATH 699. Formerly MATH 600 (4 units)