Course Descriptions
F, W, Sp, Su notations indicate the quarter(s) each course is normally offered.
Unless otherwise specified, the course is offered this year during the indicated
quarter(s). Students subject to the CSU system required Entry Level Mathematics
test (ELM) are required to take the ELM prior to enrolling in any math and statistics
course. Any course listed as a prerequisite must be passed with a C or better
grade.
MAT
400: Special Problems for Upper Division Students (1-2) Individual or group investigation, research, studies
or surveys of selected problems. Total credit limited to 4 units, with a
maximum of 2 units per quarter.
MAT
401: Numerical Analysis (4) F (odd years)
Theoretical error and machine error associated with algorithms. Solutions
of non-linear equations, systems of linear equations and systems of non-linear
equations. 4 lecture/problems. Prerequisite: C or better in MAT 201, MAT
208, MAT 215 and CS 120 or CS 125 or consent of instructor.
MAT
402: Numerical Methods in Differential Equations (4) W (even
years)
Polynomial interpolation, cubic splines, numerical differentiation and integration,
numerical solutions of differential equations including Runga-Kutta methods
and predictor-corrector methods for solving initial value problems and the
shooting method for solving boundary value problems. 4 lecture/problems.
Prerequisites: C or better in MAT 216 and MAT 401 or CS 301 or consent of
instructor.
MAT
413: Advanced Calculus (4)
Differential and integral calculus of functions and transformations in several
real variables. 4 lecture/problems. Prerequisite: C or better in MAT 315,
or consent of instructor.
MAT
415: Foundations of Geometry (4) Sp (even years)
Axiomatic development of selected topics from euclidean and neutral geometries;
introduction to non-euclidean geometry with emphasis on the hyperbolic case.
4 lecture/problems. Prerequisite: C or better in MAT 208 and 215, or consent
of instructor.
MAT
416: Projective Geometry (4) Sp (odd years)
Synthetic and analytic treatment of selected topics from projective geometry;
classical theorems, conics, polarities; quadratic and bilinear forms. 4
lecture/problems. Prerequisite: C or better in MAT 208 and 215, or consent
of instructor.
MAT
417, 418: Modern Algebra I (4) II (4) FW / WSp
Introduction to algebraic structures; groups, rings, integral domains, fields;
mappings with emphasis on morphisms. 4 lecture/problems. Prerequisite for
MAT 417: C or better in MAT 310 or consent of instructor. Prerequisite for
MAT 418: C or better in MAT 417 or consent of instructor.
MAT
419: Abstract Linear Algebra (4) Sp (even years)
Vector spaces and dimension, linear transformations, dual spaces,
adjoints of transformations, multilinear forms, eigen vectors, the Cayley-Hamilton
theorem, inner product spaces, orthogonality, similarity transformations,
the spectral theorem, jordan form. 4 lecture/problems. Prerequisite: C or
better in MAT 208, or consent of instructor.
MAT
420: Differential Geometry (4)
The Frenet formulas, covariant derivatives, frame fields, the structure
equations, differential forms on a surface, normal curvature, Gaussian curvatures;
intrinsic geometry of surfaces in E3, the Gauss and Bonnet theorem. 4 lectures/problems.
Prerequisite: C or better in MAT 314 and MAT 216, or consent of instructor.
MAT
428, 429: Functions of a Complex Variable I (4) II (4)
Algebra and geometry of complex numbers; analyticity, mappings of elementary
functions; Cauchy integral formula, Taylor and Laurent series, the residue
theorem; conformal mapping with applications. 4 lectures/problems. Prerequisites
for MAT 428: C or better in MAT 314 or consent of instructor. Prerequisite
for MAT 429: C or better in MAT 428 or consent of instructor.
MAT
431, 432: Differential Equations (4) (4) WSp
Partial differential equations with applications to wave actions,
heat transfer and fluid flow. Ordinary differential equations; linear with
variable coefficients, linear systems; stability and qualitative behavior
of solutions. 4 lecture/problems. Prerequisite: C or better in MAT 216 and
208 or consent of instructor.
MAT
444: Vector and Tensor Analysis (4) An integrated course in the algebra and calculus of vectors and tensors;
topics in differential geometry; applications to mechanics of deformable
media, hydrodynamics, general relativity. 4 lecture/problems. Prerequisite:
C or better in MAT 208 and 216. PHY 321 is recommended, or consent of instructor.
MAT
450: Foundations of Mathematics (4) F (even years)
Introduction to axiom systems including consistency, independence,
satisfiability, and completeness; transfinite arithmetic; the continuum
hypothesis; well ordering and its equivalents. 4 lecture/problems. Prerequisite:
C or better in MAT 310 or consent of the instructor.
MAT
461, 462: Senior Project (2) (2) Selection and completion of a project under faculty supervision.
Projects typical of problems which graduates must solve in their fields
of employment. Project results are presented in a formal report. Minimum
of 120 hours total time.
MAT
463: Undergraduate Seminar (2)
Discussions through seminar methods of new developments in the fields of
student’s particular interests. 2 lecture/discussions. Prerequisite:
Senior standing in mathematics.
MAT
470: Combinatorics (4) F
Study of enumeration techniques, permutations, combinations, principle of
inclusion and exclusion, finite fields, combinatorial designs, error-correcting
codes. 4 lecture/problems. Prerequisite: C or better in Mat 208 or consent
of instructor.
MAT
480: Mathematical Programming (4) Sp (odd years)
Treatment of linear inequalities, duality, general algorithms, application
of linear programming. Introduction to discrete and nonlinear programming.
4 lecture/problems. Prerequisite: C or better in MAT 208 and CS 125, or
120, or consent of instructor.
MAT
485, 486: Mathematical Modeling and Simulation I (4) II (4) WSp
Introduction to the general principles of modeling. Models will be selected
from the areas such as physics, biology, political science, chemistry, engineering,
and business. Analytical, numerical, and simulation methods will be used
to solve the models. 4 lecture/problems. Prerequisites: C or better in the
following courses: CS 120 or CS 125, MAT 201, MAT 208, MAT 216, and STA
330 or consent of instructor.
MAT
491: Elementary Geometry from an Advanced Viewpoint II (4) FWSpSu
Introduction to congruence and similarity through constructions and deductive
proofs; motion geometry involving translations, rotations, and flips; tesselations;
topology; coordinate geometry programming in LOGO. 4 lecture/problems. Prerequisite:
C or better in MAT 392. Not open to math majors for upper division mathematics
elective credit.
MAT
492: Technological Applications in Mathematics (4) WSu
Use of computers, microcomputers, calculators and other technologies in
doing mathematics. Evaluation and utilization of instructional software
in mathematics; use of application software including databases and spreadsheets;
social issues related to microcomputer use. 4 lecture/problems. Prerequisite:
C or better in MAT 491 or consent of instructor. Not open to math majors
for upper division mathematics elective credit.
MAT
493: Algebraic Structures and Computing for Elementary and Middle School
Teachers (4) FSp
Development of algebraic structures from groups to fields. Study of modular
arithmetic, relationships and functions. Use of the computer, including
programming in BASIC, to investigate algebraic relationships and algorithms.
4 lecture/problems. Prerequisite: C or better in MAT 491 or permission of
the instructor. Not open to math majors for upper division mathematics elective
credit.
MAT
495/495A, 496/496A, 497/497A: Topics in Contemporary Secondary Mathematics
I, II, III (3/1) (3/1) (3/1) FWSp
Examination of the high school mathematics curriculum from an advanced viewpoint.
Analysis of current issues and trends in secondary school mathematics. Use
of technology in learning mathematics. Assessment of students’ competency
in mathematics. Field experiences in educational and non-educational settings.
The first two quarters of the sequence are graded on a CR/NC basis and do
not count as upper division math elective credit. 3 hours lecture, one two-hour
activity. Prerequisites: Completion of 28 units of 300 and 400-level mathematics
courses including MAT 417, 325, 306 and a course in Geometry selected from
MAT 330, 415, or 416 or the equivalent of these three courses.
MAT
499/499A/499L: Special Topics for Upper Division Students (1-4)
Group study of a selected topic, the title to be specified in advance. Total
credit limited to 8 units with a maximum of 4 units per quarter. Prerequisite:
consent of instructor. Lecture/Activity/Lab.
