Subcollegiate
Courses 
 081 Intensive Learning Experience I (4)
 Covers first two thirds of MATH 090.
Properties of ordinary arithmetic, integers, rational numbers, real numbers,
linear equations. Graded ABC/NC. Open only to students with ELM score
below 360. No credit toward baccalaureate.

 082 Intensive Learning Experience II (4)
 Prerequisite: MATH 081. Covers last third
of MATH 090 and first third of MATH 091.
Linear equations, inequalities, systems of equations, basic geometry,
polynomials and functions. Open only to students with ELM score below 360.
Graded ABC/NC. No credit toward baccalaureate.

 083 Intensive Learning Experience III (4)
 Prerequisite: MATH 082. Covers last two
thirds of MATH 091. Fractional expressions and equations,
exponents, quadratic equations, exponentials and logarithms. Graded ABC/NC.
Open only to students with ELM score below 360. No credit toward
baccalaureate.

 090 Preparatory Mathematics (4)
 Prerequisite: Score of 470 or less on ELM. For students who
are not prepared for college level mathematics. Fundamentals of arithmetic
including percentages and decimals; introductory algebra including linear
equations, quadratic equations, graphing; basic geometric formulas. Graded
ABC/NC. Students with credit or two NC grades for this course may not
enroll again. No credit toward baccalaureate.

 091 Intermediate Algebra (4)
 Prerequisite: MATH 090 or score of 480 or
more on ELM. Fundamental skills necessary for mathematics beyond arithmetic;
basic topics in algebra, including multiplication, division, and
factorization of polynomials; solutions of equations and systems of
equations, functions, exponents, and logarithms. Graded ABC/NC. Students
with credit or two NC grades for this course may not enroll again. No
credit toward baccalaureate.

Lower
Division Courses 
 100 Introduction to College Mathematics (4)
 Prerequisites: Score of 550 or more on ELM;or MATH 091 with minimum C grade. Introduction to mathematical
methods and reasoning, including: logic, combinatorics and probability,
modular arithmetic, descriptive statistics, geometric topics, algorithms,
elementary number theory, and sequences. No credit toward mathematics or
computer science majors.
 CAN MATH 2

 102 College Algebra (4)
 Prerequisites: Score of 550 or more on ELM; or MATH 091 Logarithmic and exponential functions; polynomial
equations; permutations, combinations, and probability; sequences and
series; matrices and determinants; mathematical induction.
 CAN MATH 7

 103 Algebra and Trigonometry (4)
 Prerequisites: Satisfactory score on (or exemption from)
ELM; MATH 102 with minimum C grade or satisfactory score on
placement examination. Trigonometric functions, identities, and equations;
solution of triangles; inverse trigonometric functions; complex numbers,
DeMoivre's Theorem; parametric equations; polar coordinates.
 CAN MATH 8

 110 Foundations of the Real Number System
for Elementary
 and Middle School Teachers (4)
 Prerequisite: A score of 480 or more on the ELM or
MATTH 90 with minimum grade of C or exemption from the
ELM requirement. Integers and elementary number theory, rational numbers,
decimals and percent, ratio and proportion, alternate bases, and word problems.
Restricted to students in multiple subjects credential programs.

 115 Elements of Algebra and Statistics
for Elementary
 and Middle School Teachers (4)
 Prerequisite: MATH 110 and satisfaction of
or exemption from the ELM requirement.
Functions, relations, sequences, discrete structures, probability, data analysis,
and descriptive statistics.Restricted to students in multiple subjects credential
programs.

 120 Mathematics for Elementary School
Teachers (4)
 Prerequisite: MATH 100 with minimum C
grade within past 3 years or satisfactory score on placement examination.
Selected topics from elementary geometry, units of measurement, areas,
volumes, approximate numbers, square roots.

 225 Explorations in Geometry for Elementary
and
 Middle School Teachers (4)
 Prerequisite: A college level mathematics
course with a minimum grade C. Topics include properties of two and three
dimensional figures, measurement, constructions, structure, spatial
relationships, transformations, and graph theory presented through
multiple teaching modes. No credit for mathematics majors.

 206 Calculus l: Differentiation (4)
 Prerequisites: Satisfactory score on (or exemption from)
ELM; MATH 102 and MATH 103, each with a
minimum C grade or satisfactory score on placement examination. Functions,
graphs, conics, limits, continuity and derivatives, antidifferentiation, and
applications.
 MATH206+207+208=CAN MATH SEQ B
 MATH206+207+208+209=CAN MATH SEQ C

 207 Calculus II: Integration (4)
 Prerequisite: MATH 206 with minimum C
grade. The definite integral, Fundamental Theorem of the Calculus,
transcendental functions, methods of integration, improper integrals,
applications to physics and biology.
 MATH206+207+208=CAN MATH SEQ B
 MATH206+207+208+209=CAN MATH SEQ C

 208 Calculus III: Sequences, Series, and
Coordinate
 Systems (4)
 Prerequisite: MATH 207 with minimum C
grade. Limits of sequences and series, indeterminate forms, Taylor Series,
plane coordinate systems, and change of coordinates.

 MATH206+207+208=CAN MATH SEQ B
 MATH206+207+208+209=CAN MATH SEQ C

 209 Calculus IV: Several Variables (4)
 Prerequisite: MATH 208 with minimum C
grade. Three dimensional analytic geometry, partial differentiation,
multiple integration, spherical and cylindrical coordinate systems, line
integrals.
 MATH206+207+208+209=CAN MATH SEQ C

 215 Differential Equations (4)
 Prerequisite: MATH 209. Ordinary
differential equations with concentration on methods of finding solutions;
applications in science and engineering.
 CAN MATH 24

 230 Calculus for Biological Sciences (4)
 Prerequisite: MATH 206. Integration,
ordinary differential equations, difference equations, partial
differentiation, applications to problems arising in biological sciences.

 242 Mathematics for Business and Economics
Majors (4)
 Prerequisites: Satisfactory score on (or exemption from)
ELM; MATH 102 with minimum C grade or satisfactory score
on placement examination. Differential calculus with applications;
introduction to integral calculus.
 CAN MATH 34

 248 Discrete Mathematics (4)
 Prerequisite: MATH 207. Fundamentals
of logic and set theory, counting techniques, relations, induction and
recursion; graphs and trees.

 254 Selected Topics in Mathematics (14)
 Prerequisites: As needed for specific topic.
Current topics of interest to students in mathematics, as
announced in Schedule of Classes. May be repeated for
credit.

 255 Introduction to Matrix Theory (4)
 Prerequisite: MATH 208. Vector spaces,
linear transformations, linear equations, matrices, determinants,
eigenvectors and eigenvalues, canonical forms.
 CAN MATH 26

 274 Introduction to Statistics (4)
 Prerequisite: MATH 091. Statistical
terms; interpretation of statistical data with and without use of
probability, random sampling, confidence limits, and hypothesis tests.
 CAN STAT 2

Upper
Division Courses 
 310 Introduction to Computer Algebra
Systems (4)
 Prerequisite: MATH 206 with grade C or
better; CS 201 recommended. Introduction to computer
algebra systems such as Mathematica, Maple, or Matlab; overview of builtin
functions; 2D and 3D graphs; animations; data manipulation; introduction
to basic programming structures; userdefined functions.

 320 Selected Topics in History of
Mathematics (4)
 Prerequisite or corequisite: MATH 207.
Traces development of fundamental concepts and techniques in fields of
algebra, geometry, trigonometry, and calculus.

 325 Mathematical Notation and Proof (4)
 Prerequisite: MATH 208. Elementary set
theory and number theory with emphasis on notation and types of proof.
Axiomatic method, equivalence relations, ed arguments.

 401 Differential Equations (4)
 Prerequisites: MATH 209, 255, 325. Ordinary differential equations
with concentration on properties of solutions, including existence and
uniqueness. Emphasis on theory as opposed to applications.

 402A Advanced Mathematics I for Engineers
and
 Physicists (4)
 Prerequisite: MATH 215 or 401. Vector analysis to include line and surface integrals,
orthogonal curvilinear coordinates, complex variables to include contour
integration and conformal mapping. Laplace transformation.

 402B Advanced Mathematics II for Engineers and
 Physicists (4)
 Prerequisite: MATH 402A. Implicit
functions and Jacobians, infinite series and integrals, differentiation of
integrals; Taylor series for several variables; Fourier series and boundary
value problems, special functions (Bessel, Legendre, error, elliptic),
calculus of variations.

 403 Partial Differential Equations (4)
 Prerequisite: MATH 215 or 401. Orthogonal sets of functions. Fourier series and
integrals, with applications to the equations of mathematical physics; first
order equations, Cauchy's method of characteristics.

 410 Vector Analysis (4)
 Prerequisite: MATH 209, MATH 255.
Vector algebra and calculus, vector fields, gradient, divergence, curl, divergence
theorem, Stokes' theorem, applications to geometry and mathematical physics.

 411 Tensor Analysis (4)
 Prerequisite: MATH 410. Contravariant and
covariant vectors and tensors, tensor algebra, Riemannian geometry, the
metric tensor, geodesics, Christoffel symbols, derivatives of tensors,
physical components of tensors. Applications to mechanics and differential
geometry.

 420 Mathematical Logic (4)
 Prerequisite: MATH 325. The statement
calculus, the predicate calculus, mathematical structures, and the deduction
of valid consequences; the completeness theorem.

 430 Modern Geometry (4)
 Prerequisite: MATH 325. Topics selected
from advanced Euclidean geometry, nonEuclidean geometry, projective
geometry. May be repeated once for credit with approval of instructor as
subject matter changes.

 435 Topology (4)
 Prerequisite: MATH 465. Introduction to
point set topology, including continuity, product spaces, compactness,
Tyconoff theorem, connectedness, metric spaces, and Urysohn lemma.

 446 Theory of Numbers (4)
 Prerequisites: MATH 325, upper division
standing. Divisibility, Euclidean algorithm, prime numbers, fundamental
theorem of arithmetic, distribution of primes, congruences, Fermat, Euler,
and Wilson theorems, residues and quadratic reciprocity law. Bernoulli
numbers, quadratic forms, Diophantine equations.

 454 Selected Topics in Advanced Mathematics (14)
 Prerequisites: As needed for specific topic. Current
topics of interest to students in mathematics, as announced in Schedule of
Classes. May be repeated for credit.

 455 Modern Algebra I (4)
 Prerequisites: MATH 255, 325. Groups and rings, including normal subgroups, quotient
groups, ideals, quotient rings, group and ring homomorphisms, and
isomorphisms.

 456 Modern Algebra II (4)
 Prerequisite: MATH 455. Additional topics
in groups and rings, field extensions, modules.

 457 Linear Algebra (4)
 Prerequisite: MATH 455. Vector spaces
over arbitrary fields, special types of linear transformations, eigenvalues
and eigenvectors, canonical forms, scalar product spaces.

 463 Introduction to Complex Analysis (4)
 Prerequisite: MATH 465. Complex
variables, analytic functions, complex integration, conformal mapping,
applications.

 465 Advanced Calculus I (4)
 Prerequisites: MATH 209, 325. Real number system; topology of R" including
compactness and completeness; sequences and series, including limit inferior
and limit superior and continuity.

 466 Advanced Calculus II (4)
 Prerequisite: MATH 465. Differentiation
and integration of function of a real variable: sequences of functions.

 467 Advanced Calculus III (4)
 Prerequisites: MATH 255, 465. Functions of several variables; partial derivatives;
generalized chain rule; inverse and implicit function theorems; line and
surface integrals.

 470 Numerical Analysis I (4)
 Prerequisites: CS 201, MATH 208, facility
in high level programming language. Errors in floating point representation,
nonlinear equations, systems of linear equations, polynomial interpolation,
numerical integration and differentiation.

 471 Numerical Analysis II (4)
 Prerequisites: MATH 215, 470. Numerical solution of ordinary and partial differential
equations, spline and least square approximation. fast Fourier transform.

 472 Linear Programming (4)
 Prerequisite: MATH 255. Geometric
solutions, simplex method, the transportation problem, elementary game
theory.

 474 Theory of Probability (4)
 Prerequisite: MATH 209. General
probability spaces, random variables, joint distributions, random sampling,
law of large numbers, normal, gamma, and binomial distribution.

 475 Introduction to Mathematical Statistics
(4)
 Prerequisite: MATH 474. Estimation and
tests of hypothesis, decision theory and Bayes solutions.

 484 Graph Theory (4)
 Prerequisite: MATH 248,
325. Introduction to graph theory and its applications: graphs, trees,
and directed graphs; isomorphism; connectivity; network flows; Hamiltonian
graphs; planar graphs; coloring problems; matchings; Ramsey theory.

 499 Undergraduate Directed Study (14)
 Prerequisite: Consent of an instructor to act as a sponsor.
Project selected in conference with sponsor before registration; progress
meetings held regularly, and a final report submitted. May be repeated for
credit.

Graduate
Courses 
 501 Nonlinear Differential Equations (4)
 Prerequisites: MATH 215 or
401; 466. Vector matrix notation,
stability in nonlinear systems, Poincare phase plane, method of
Liapounov, perturbation techniques.
 502A Applied Linear Analysis I (4)
 Prerequisites: MATH 215 or 401;
255; 410 or 467. Function spaces,
convergence, inner product, bounded linear operators, integral
operators and integral equations, adjoint operators, expansion
in eigenfunctions, resolvent kernel.
 502B Applied Linear Analysis II (4)
 Prerequisites: MATH 502A. Unbounded operators,
differential operators of second order, SturmLiouville operators,
eigenvalues and eigenfunctions, Green functions, and additional topics.
 520 Calculus of Variations (4)
 Prerequisites: MATH 255, 466.
EulerLagrange equation for various types of extremal problems; fixed and variable
and points; broken extremals; variational problems with constraints; canonical forms,
direct methods.
 521 Mathematical Models and Optimizations (4)
 Prerequisites: MATH 215, 255,
474. Topics from: Markov chains
and decision theory, game theory, programming algorithms, models
for growth processes, applied graph theory, and theory of maxima
and minima.
 530 Topology (4)
 Prerequisite: MATH 465. Basic concepts of point set topology:
mappings, compactness, connectedness, separation properties, and
metrization.

 540A Abstract Algebra I (4)
 Prerequisite: MATH 455. Theory of groups,
introduction to rings.
 540B Abstract Algebra II (4)
 Prerequisite: MATH 540A. Theory of rings
and fields.
 550 Seminar: Algebra (4)
 Prerequisite: Approval of instructor. Readings and discussion
of topics from group theory, ring theory, linear algebra, discrete
mathematics, and combinatorics. May be repeated to maximum of
8 units.
 551 Seminar: Analysis (4)
 Prerequisite: Approval of instructor. Readings and discussion
of topics from real analysis, complex analysis, functional analysis,
and applied analysis. May be repeated to maximum of 8 units with
approval of Graduate adviser.
 552 Seminar: Topology and Geometry (4)
 Prerequisite: Approval of instructor. Readings and discussion
of topics from general and algebraic topology, differential topology
and geometry, and geometrical foundations. May be repeated to
maximum of 8 units with approval of graduate adviser.
 553 Seminar: Applied Mathematics (4)
 Prerequisite: Approval of instructor. Readings and discussions
of selected topics in field. May be repeated to maximum of 8 units
with approval of graduate adviser.
 559 Mathematical Exposition (1)
 Prerequisite: Completion of at least 12 units
of 500level courses. Students will select an advanced topic
in mathematics with the instructorÂs approval, prepare an
expository paper, and give an oral presentation on the topic.
 562 Advanced Complex Analysis (4)
 Prerequisite: MATH 463. Laurent series, singularities, residue
problems, contour integration, conformal mapping, and additional
topics.
 570A Advanced Numerical Analysis I (4)
 Prerequisite: MATH 470. Numerical solutions
of linear systems of equations, finite difference approximation
to elliptic partial differential equations.
 570B Advanced Numerical Analysis II (4)
 Prerequisite: MATH 570A. Numerical solution
of parabolic and hyperbolic partial differential equations;
consistency, convergence, stability.
 570C Advanced Numerical Analysis III (4)
 Prerequisite: MATH 570B. Numerical solution
of ordinary and partial differential equations, eigenvalue
problems, nonlinear systems, approximation theory, finite
elements, integral equations.
 580 Real Analysis (4)
 Prerequisite: MATH 466. Theory of Lebesgue measure on the real
line; theory of the Lebesgue integral and related convergence theorems.
 584 Advanced Probability Theory (4)
 Prerequisite: MATH 580. Probability spaces; random variables;
abstract probability integrals, moments, convergence theorems;
distribution and characteristic functions: central limit theorems:
dependence.
 591 Functional Analysis (4)
 Prerequisite: MATH 466. Banach spaces, Hilbert spaces, linear
functionals and operators, spectral theory.
 598 Graduate Directed Study (14)
 Prerequisite: Instructor consent. Independent study of advanced
topics in mathematics; regular conferences with instructor. May
be repeated once.
 599 Thesis (14)
 Prerequisites: Advancement to candidacy, instructor consent
to act as sponsor, departmental approval of topic prior to Independent
research resulting in a thesis. May be repeated to maximum of
4 units. Graded CR/NC.
