F, W, Sp, Su notations indicate the quarter(s) each course is normally offered. Unless otherwise specified, the course is offered 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 (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.
|
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. |
STA 120:
Statistics with Applications (4) FWSpSu
Collection and summarization of data; measures of central tendency and dispersion;
probability; binomial and normal distributions, confidence intervals and
hypothesis testing. Not open to mathematics or engineering majors. 4 lecture/problems.
Prerequisites: Minimum placement score on ELM appropriate MDT or C or better
in MAT 012 within two quarters. |
STA 200:
Special Problems for Lower 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. |
STA
210: Statistical Computing (4)
Use of computer packages, inferences about means
of two populations, dependent and independent samples, small and large samples,
inferences about proportions and variances, correlation and regression.
4 lecture/problems. Prerequisite: C or better in STA 120 or consent of instructor.
|
STA
220: Discrete Probability Models (4)
Set-theoretic approach to probability in finite
sample spaces. Conditional probability, independence, binomial, hypergeometric
and related distributions. 4 lecture/problems. Prerequisite: C or better
in MAT 105, or consent of instructor. |
STA
241 (formerly STA 330): Applied Probability Theory (4)
FWSu
Rules of Probability, random variables, expected values of random
variables, distribution of functions of a random variable. Discrete and continuous
probability distributions with applications. Sampling methods.
Descriptive statistics, central limit theorem and estimation. 4
lecture/problem-solving.
Prerequisites: C or better in MAT 116 ot MAT 131 or consent of instructor. Not open
to students with credit in STA 315 or ECE 315. |
STA
299/299A/299L: Special Topics for Lower 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. |
STA
309: Statistical Methods in Engineering and the Physical Sciences (3)
FWSp
The uses of statistics in testing, inspection and production, measures of
central tendency and dispersion, probability, binomial and normal distributions,
sampling theory, hypothesis testing and estimation, comparison of two populations.
Not open to students required to take STA 315 or ECE 315. Not open to math
majors for upper division math elective credit. 3 lecture/problems. Prerequisite:
C or better in MAT 214 or MAT 131 or consent of instructor. |
STA
310: Sampling Survey Methods (4) Sp (odd years)
Simple random sampling, stratified, cluster, systematic, multistage,
multiphase and probability sampling methods, source of errors, sample size
estimation. Not open to math majors for upper division math elective credit.
4 lecture/problems. Prerequisite: C or better in STA 120 or equivalent or
consent of instructor. |
STA
315: Probability and Statistics for Engineers (4)
Statistical and probabilistic concepts for the analysis of electrical and
electronic systems associated with random phenomena. Application to
communication, control, instrumentation and logic systems. 4 lecture/problems.
Prerequisites: C or better in MAT 215 or consent of instructor. Not open
to students with credits in ECE 315, STA 309 or students required to take
STA 241. |
STA
326: Statistical Methods for Computer Scientists (4)
FWSpSu
Rules of Probability. Discrete and continuous distributions including the
multinomial distribution. Sampling distributions. Point and interval estimation.
Hypothesis testing. Large and small sample inferences for means, proportions,
and variances. Introduction to queueing theory and regression. 4 lecture/problems.
Prerequisites: C or better in MAT 214 or consent of instructor. Not open
to students required to take STA 241. |
STA
341 (formerly STA 331): Applied Statistics (4) FWSp
Joint distributions, central limit theorem. Maximum likelihood estimation. Point and interval
estimation and hypothesis testing. Small and large sample inferences. Contingency
table analysis and Chi- square tests. 4 lecture/problems. Prerequisite:
C or better in STA 241 and MAT 215 or consent of instructor. |
STA
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. |
STA
420: Nonparametric Statistics (4) (odd years)
Common nonparametric tests such as permutation tests, sign tests,
Wilcoxon test, chi- square test, and rank correlation tests. Null distributions
and their approximations. 4 lecture/problems. Prerequisite: C or better
in STA 210 or STA 326 or STA 341 or consent of instructor. |
STA
425: Applied Survival Analysis (4) (even years)
Survival models. Types of censoring. Life-tables. Estimation of
survival functions from complete and incomplete mortality data. Actuarial
and maximum likelihood methods. Kaplan-Meier estimator, Mantel-Haenszel
and Log-rank tests. Probit and Logit models. Use of computer package
such as SAS or MINITAB or S-plus. 4 lecture/problem-solving.
Prerequisite: C or better in STA 341 or STA 326 or consent of instructor.
|
STA
430: Introduction to Random Processes (4) (even years)
General types of stochastic processes. Random walks, Poisson processes,
counting processes, Markov chains, and topics from other areas such as Markov
jump processes, Birth-death processes, Gaussian processes. 4 lecture/problems.
Prerequisite: C or better in STA 326 or STA 241 or consent of instructor.
|
STA
432: Applied Regression Analysis (4) (odd years)
Matrix approach to regression models, least square estimation, correlation,
multiple regression, transformation of variables, analysis of residuals,
multicollinearity and auto- correlation. Use of computer packages for applied
problems. 4 lecture/problems. Prerequisites: C or better in STA 326 or STA
341 and
MAT 208 or consent of instructor. |
STA
435: Analysis of Variance and Design of Experiments (4) (even years)
ANOVA techniques, computer solutions, randomized groups and blocks designs,
interactions, analysis of covariance. Latin square, split-plot, simple and
confounded factorial designs; treatment of missing data, incomplete block
designs. 4 lecture/problems. Prerequisite: C or better in STA 326 or STA
341 or consent of instructor. |
STA
440: Mathematical Statistics I (4) (odd years)
Discrete and continuous probability distributions; moments, moment generating
functions, special distributions, distributions of functions of random variables.
4 lecture/problems. Prerequisite: C or better in MAT 215, or consent of
instructor. |
STA
441: Mathematical Statistics II (4) (odd years)
Asymptotic distributions; central limit theorem; point and interval estimation;
completeness and sufficient statistics; Neyman-Pearson theory of testing
hypotheses. 4 lecture/problems. Prerequisite: C or better in STA 440, or
consent of instructor. |
STA
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. |
