From the 2006-2007 catalog:
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)
545. Abstract Algebra I
An introduction to algebraic structures, including groups, rings and
fields. Prerequisites: MATH 331, 345 and 355. (4 units)
546 Abstract Algebra II
Continuation of MATH 545. Prerequisite: MATH 545. (4 units)
553. Analysis I
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
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, 355 and 553.
(4 units)
565. Mathematical Statistics
Likelihood ratio, estimators, distributions of estimators, theory of hypothesis
testing, linear statistical models. Prerequisite: MATH 465.
(4 units)
573. Mathematical Methods of Physics III
A continuation of MATH 473/PHYS 473 with emphasis on advanced
topics relevant to physics. (Also offered as PHYS 573. Students may
not receive credit for both.) Prerequisites: MATH 331 and 473 or
PHYS 473. (4 units)
576. Introduction to Mathematical Models
Topics from linear and probabilistic models, computer simulation, difference
and differential equation models. Prerequisites: CSCI 201,
MATH 331 and 465. (4 units)
595. Independent Study
An independent study course for senior mathematics majors. 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 to 4 units)
599. Senior Seminar for Future Mathematics
Educators
Summative assessment of subject matter competence for prospective
mathematics teachers. Each student will complete and present a
project relating advanced mathematics to the high school curriculum,
and complete and submit a portfolio of their undergraduate work in
mathematics for assessment. Meets four hours per week during the
first week and the last four weeks of the quarter. Graded A,B,C/no
credit. Prerequisites: MATH 199, 480 and 499. (2 units)
Graduate/Postbaccalaureate
May not be taken by undergraduate students.
600. Master of Arts in Teaching Mathematics
Project
Written project, an oral presentation of the project 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 project proposal by the graduate committee
and submission of at least three contributions to the Assessment
Portfolio. 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 600. (4 units)
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)
606. Seminar in Problem Solving III
Continuation of MATH 605. Prerequisite: MATH 605. (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: PSYC 210, SSCI 215, MATH 305 or 350, SCM 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)
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. 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 to 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. Students who enroll in 698 through the university have full
use of all university facilities. See Page 331, 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.
(0 units)