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
306: History of Mathematics (4) F
Development of mathematics over four millennia. Recommended for students
preparing to teach mathematics. 4 lectures. Prerequisite: C or better in
MAT 215, or consent of instructor.
MAT
310: Basic Set Theory and Logic (4) FSp
Basic set theory and logic, relations, functions, mathematical induction,
countable and uncountable sets. Emphasis on how to present and understand
mathematical proof. 4 lecture/problems. Prerequisite: C or better in MAT
116, or consent of instructor.
MAT
314, 315: Intermediate Analysis (4) (4) FW / WSp
Metric spaces and continuity. Analysis of functions of a single variable.
Sequences, limits, continuity, differentiation, integration, introduction
to function spaces. 4 lecture/problems. Prerequisite for MAT 314: C or better
in MAT 215 and MAT 310 or consent of instructor. Prerequisite for MAT 315:
C or better in MAT 314, or consent of instructor.
MAT
317: Laplace Transforms and Fourier Series (3)
WSu
Introduction to Fourier Series and Integrals with applications. Elementary
theory of Laplace transformation with applications including the solution
of differential equations. 3 lecture/problems. Prerequisite: C or better
in MAT 216, or consent of instructor.
MAT
318: Mathematical Analysis of Engineering Problems (3) FSp
Introduction to the algebra and calculus of vectors including the divergence
and Stokes’ theorem. Introduction to analytic functions of a complex
variable. Not open to mathematics majors for math elective credit. 3 lecture/problems.
Prerequisite: C or better in MAT 215, or consent of instructor.
MAT
321: Introduction to Topology (4) F (odd years)
Topology of the line and plane, topological spaces, continuity and topological
equivalence, and topics selected from the following: bases and subbases,
metric and normed spaces, countability axioms, separation axioms, compactness,
connectedness, product spaces, completeness, and function spaces. 4 lecture/problems.
Prerequisite: C or better in MAT 310, or consent of instructor.
MAT
325: Introduction to the Theory of Numbers (4) W
Fundamentals of the system of integers, divisibility, congruences, theorems
of Fermat and Wilson, power residues and indices, quadratic reciprocity,
factorization techniques, diophantine equations, theorems of Euler, Gauss
and Lagrange. Elementary results concerning the distribution of primes.
4 lecture/problems. Prerequisite: Junior standing or consent of instructor.
MAT
330: Modern Euclidean Geometry (4) W
Euclidean geometry using modern techniques of transformations, inversions.
Extension of elementary geometry to elegant results on triangles, circles,
polygons, famous theorems of geometry, unsolved problems. Introduction to
deductive reasoning and techniques of proof. 4 lecture/problems. Prerequisite:
Consent of instructor.
MAT
370: Graph Theory (4) Sp
The study of graphs, trees, Eulerian, Hamiltonian, planar graphs, connectivity,
coloring, independence and covering numbers, directed graphs, theorems of
Menger, Ramsey with applications. 4 lecture/problems. Prerequisite: Consent
of instructor.
MAT
380: Mathematics of Operations Research (4) F
Introduction to mathematics of linear programming (LP): algebra and geometry
of simplex method, solution of LP problems by Gauss-Jordan elimination method.
Duality theory and sensitivity analysis. Development of revised and dual
simplex algorithms. Introduction to parametric and separable convex programming.
Applications of LP: computational considerations, case studies. 4 lecture/problems.
Prerequisites: C or better in MAT 208, and 215, or consent of instructor.
MAT
381: Mathematics of Operations Research (4) W
Solution of transportation, transshipment and assignment problems. Formulation
and solution of network problems: maximal flow, minimal spanning tree, shortest
route problems; PERT-CPM techniques. Introduction to dynamic and integer
programming. Elements of game theory, solution of games by linear programming.
Introduction to non- linear programming: Kuhn-Tucker conditions, quadratic
and convex programming; SUMP solution procedure. 4 lecture/problems. Prerequisite:
C or better in MAT 380, or consent of instructor.
MAT
391: Elementary Mathematics from an Advanced Viewpoint (4) FWSpSu
Development of the real number system through the reals; development of
numeration systems; elementary concepts of algebra; introduction to number
theory; elementary group and field theory. Development of problem solving
strategies and application of technology to these topics. 4 lecture-problem.
Prerequisite: C or better in MAT 191. Not open to mathematics majors for
math elective credit.
MAT
392: Elementary Geometry from an Advanced Viewpoint I (4) FWSpSu
Introduction to Metric and non-Metric geometry; development of inductive
and deductive geometric proofs; congruence and similarity; and basic concepts
of topology. 4 lecture- problems. Prerequisites: C or better in MAT 391.
