MATH-MATHEMATICS – 2005-07 Catalog
Mathematics Department
Satisfactory completion of
the Entry Level Mathematics (ELM) requirement is a prerequisite for enrollment in
all mathematics courses except MATH 100 and MATH 104. For additional
mathematics placement (MAPE) information , see page 61.
MATH 100 Beginning Algebra Review (3) (CR/NC)
Review of basic algebra
skills at the beginning algebra level intended primarily to prepare students
for MATH 104. Course open only to students who have taken the ELM examination
and are not qualified for MATH 104. Not for baccalaureate credit. Credit/No
Credit grading only. 3 lectures.
MATH 104 Intermediate Algebra (3) (CR/NC)
Review
of basic algebra skills at the intermediate algebra level intended primarily to
prepare students for MATH 116. Not for baccalaureate credit. Credit/No Credit
grading only. 3 lectures. Prerequisite: Appropriate score on the ELM
examination, or credit in MATH 100.
MATH 110 Beginning Algebra Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of beginning algebra. Not
for baccalaureate credit. Credit/No Credit grading only. 1 laboratory.
Corequisite: Concurrent enrollment in the associated section of MATH 100.
MATH 112 The Nature of Modern Mathematics (4) GE B1
Topics from contemporary
mathematics, their development, applications, and role in society. Some typical
topics, to be chosen by the instructor: graph theory, critical path analysis,
statistical inference, coding, game theory, and symmetry. 4 lectures.
Prerequisite: Passing score on ELM examination or an ELM exemption or credit in
MATH 104.
MATH 114 Intermediate Algebra Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of intermediate algebra.
Not for baccalaureate credit. Credit/No Credit grading only. 1 laboratory.
Corequisite: Concurrent enrollment in the associated section of MATH 104.
1 MATH
116, 117 Pre-Calculus Algebra I, II (3)
(3)
For MATH 116 and 117:
GE B1
Pre-calculus college
algebra without trigonometry. Special products and factoring, exponents and
radicals. Fractional and polynomial equations.
Matrices, determinants, and
systems of equations. Polynomial, rational, exponential, and logarithmic
functions. Graphing, inequalities, absolute value, and complex numbers. MATH
116 and MATH 117 are equivalent to MATH 118, but are taught at a slower pace.
Upon completion of MATH 116 and MATH 117, a student will receive 4 units of GE
credit for Area B1. Not open to students with credit in MATH 118. 3 lectures. MATH 116 prerequisite: Passing score
on ELM examination, or an ELM exemption, or credit in MATH 104. MATH 117 prerequisite: MATH 116 with a
grade of C- or better or consent of instructor.
MATH 118 Pre-Calculus Algebra (4) GE B1
Pre-calculus
algebra without trigonometry. Special products and factoring, exponents and
radicals. Fractional and polynomial equations. Matrices, determinants, and
systems of equations. Polynomial, rational, exponential, and logarithmic
functions. Graphing, inequalities, absolute value, and complex numbers. MATH
118 is equivalent to MATH 116 and MATH 117. Not open to students with credit in
MATH 117. 4 lectures. Prerequisite: Completion of ELM requirement and passing
score on appropriate Mathematics Placement examination.
MATH 119 Pre-Calculus Trigonometry (4) GE B1
Rectangular
and polar coordinates. Trigonometric functions, fundamental identities. Inverse
trigonometric functions and relations. Vectors, complex numbers, conic
sections, and analytic geometry. 4 lectures. Prerequisite: Completion of ELM
requirement and passing score on appropriate Mathe-matics Placement
Examination, or MATH 117, or MATH 118 or equivalent.
MATH 126 Pre-Calculus Algebra I Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of pre-calculus algebra.
Credit/No Credit grading only. 1 laboratory. Co-requisite: Concurrent
enrollment in the associated section of MATH 116.
MATH 127 Pre-Calculus Algebra II Laboratory (1)
(CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of pre-calculus algebra.
Credit/No Credit grading only. 1 laboratory. Co-requisite: Concurrent
enrollment in the associated section of MATH 117.
MATH 128 Pre-Calculus Algebra Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of pre-calculus algebra.
Credit/No Credit grading only. 1 laboratory. Co-requisite: Concurrent
enrollment in the associated section of MATH 118.
MATH 129 Pre-Calculus Trigonometry Laboratory (1)
(CR/NC)
Facilitated
study and discussion of the theory, problems, and applications of pre-calculus
trigonometry. Credit/No Credit grading only. 1 laboratory. Corequisite:
Concurrent enrollment in the associated section of MATH 119.
1 MATH
141, 142, 143 Calculus I, II, III (4)
(4) (4) GE B1
(Also listed as HNRS 141, 142, 143)
Limits, continuity,
differentiation, integration. Techniques of integration, applications to
physics, transcendental functions. Infinite sequences and series, vector
algebra, curves. 4 lectures. MATH 141
prerequisite: Completion of ELM requirement and passing score on appropriate
Mathematics Placement Examination, or MATH 118 and MATH 119 or equivalent. MATH 142 prerequisite: MATH 141 with a
grade of C- or better or consent of instructor. MATH 143 prerequisite:
MATH 142.
MATH 151, 152, 153 Calculus Laboratories I, II, III (1) (1) (1)
(CR/NC)
Facilitated study and discussion
of the theory, problems, and applications of calculus. Credit/No Credit grading
only. 1 laboratory. Corequisite: Concurrent enrollment in the associated
section of MATH 141, MATH 142, or MATH 143.
MATH 161, 162 Calculus for the Life Sciences I, II (4) (4) GE B1
Review of exponential,
logarithmic, and trigonometric functions. Differential and integral calculus
with applications to the biological sciences. Introduction to differential
equations and mathematical modeling. Examples, exercises and applications to
emphasize problems in life sciences. Not open to students with credit in MATH
141, 142 respectively. 4 lectures. Prerequisite: Completion of ELM requirement
and passing score on appropriate Mathematics Placement Examination, or MATH 118
or equivalent.
MATH 182 Calculus for Architecture and Construction
Management (4) GE B1
Integral calculus with
applications to architecture and construction management. The algebra of
vectors. Polar, cylindrical, and spherical coordinate systems. Not open to
students with credit in MATH 142. 4 lectures. Prerequisite: MATH 141 or
equivalent.
MATH 192 Calculus for Architecture and Construction
Management Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of calculus to
architecture and construction management. Credit/No Credit grading only. 1
laboratory. Corequisite: Concurrent enrollment in the associated section of
MATH 182.
MATH 202 Orientation to the Mathematics Major (1)
(CR/NC)
Career opportunities in the
field of mathematics, preparing a field of study, and a survey of departmental
facilities and procedures related to research, study and graduation. Credit/No
Credit grading only. 1 lecture. Corequisite: Sophomore standing or consent of
instructor.
MATH 206 Linear Algebra I (4)
Matrices, inverses, linear
systems, determinants, eigenvalues, eigenvectors, vector spaces, linear
transformations, applications. 4 lectures. Prerequisite: MATH 143 or consent of
instructor.
MATH 211, 212 Computational Mathematics I, II (4) (4)
Fundamentals of procedural
programming in C/C++ and selected applications to problems in integral and
differential calculus, matrix analysis, geometry, and physics. 4 lectures.
Prerequisite: MATH 141 or consent of instructor.
MATH 221 Calculus for Business and Economics (4) GE B1
Polynomial calculus for
optimization and marginal analysis, and elementary integration. Not open to
students with credit in MATH 142. 4 lectures. Prerequisite: Completion of ELM
requirement and passing score on appropriate Mathematics Placement Examination,
or MATH 118 or equivalent.
MATH 231 Calculus for Business and Economics
Laboratory (1) (CR/NC)
Facilitated study and
discussion of the theory, problems, and applications of business calculus.
Credit/No Credit grading only. 1 laboratory. Corequisite: Concurrent enrollment
in the associated section of MATH 221.
MATH 241 Calculus IV (4) (Also listed as HNRS 241)
Partial derivatives,
multiple integrals, introduction to vector analysis. 4 lectures. Prerequisite:
MATH 143.
MATH 242 Differential Equations (4)
Ordinary differential
equations: introduction with selected applications; classification of equations
and their analytic solutions; study of interrelationships between differential
systems, graphs, and physical problems. Systems of ordinary differential
equations. Not open to CENG students. 4 lectures. Prerequisite: MATH 206 and
MATH 241.
MATH 244 Linear Analysis I (4) (Also listed as HNRS 244)
Separable and linear
ordinary differential equations with selected applications; numerical and
analytical solutions. Linear algebra: vectors in n-space, matrices, linear
transformations, eigenvalues, eigenvectors, diagonalization; applications to
the study of systems of linear differential equations. 4 lectures.
Prerequisite: MATH 143 or consent of instructor.
MATH 248 Methods of Proof in Mathematics (4)
Methods of proof (direct,
contradiction, conditional, contraposition); valid and invalid arguments.
Examples from set theory. Quantified statements and their negations. Functions,
indexed sets, set functions. Proofs in number theory, algebra, geometry and
analysis. Proof by induction.
Equivalence and
well-defined operations and functions. The axiomatic method. 4 lectures.
Prerequisite: MATH 143 or consent of instructor.
MATH 258 Methods of Proof in Mathematics Laboratory
(1) (CR/NC)
Facilitated study and
discussion of the methods and techniques of proof in mathematics. Credit/No
Credit grading only. 1 laboratory. Corequisite: Concurrent enrollment in the
associated section of MATH 248.
MATH 300 Technology in Mathematics Education (4)
Examination of existing
hardware and software designed for educational uses. Discussion of mathematical
topics appropriate for computer enhancement. Special methods and techniques for
educational uses of computers. Emphasis on activity learning and applications.
Computer as a classroom management device. 4 lectures. Prerequisite: MATH 141
or MATH 329, and a course in CSC or MATH 211, or consent of instructor.
MATH 304 Vector Analysis (4) GE B6
Algebra of free vectors
with applications. Differential and integral calculus of vectors. Development
of theory and application of vector operations. Green’s Theorem, Stokes’
Theorem, and the Divergence Theorem. 4 lectures. Prerequisite: MATH 206 or MATH
244, and MATH 241, or consent of instructor.
MATH 306 Linear Algebra II (4)
Inner product spaces,
orthogonality, Fourier series and orthogonal bases, linear transformations and
similarity, eigenvalues and diagonalization. 4 lectures. Prerequisite: MATH 206
and MATH 242, or MATH 241 and MATH 244, and a C- or better in MATH 248, or
consent of instructor.
MATH 326 Mathematics and Visual Art (4) GE B5
Topics connecting
mathematics and visual art including regular polygons, symmetry groups,
repetition and pattern, perspective, straightedge and compass constructions,
and origami. Examples of mathematical art including historic and contemporary
art. 4 lectures. Prerequisite: Completion of GE Area B1 and a college course in
art or design.
1 MATH
327, 328, 329 Mathematics for Elementary
Teaching I, II, III (4) (4) (4)
Introduction to set theory,
number theory, real numbers, probability, statistics, and geometry. Computer
applications. 2 lectures, 2 activities. MATH 327 prerequisite:
Completion of ELM requirement, and passing score on appropriate Mathematics
Placement Examination, or MATH 118 or equivalent. MATH 328 prerequisite: MATH 327 with a grade of C- or better or
consent of instructor. MATH 329 prerequisite: MATH 328.
MATH 331 Topics in Mathematics for Teachers (1-6)
(CR/NC)
Topics in mathematics for
practicing credentialed teachers. Content will vary according to teaching
level. Class Schedule will list topic selected. Total credit limited to
12 units. Credit/No Credit grading only. 1-6 activities. Prerequisite: Multiple
Subject or Single Subject teaching credential or consent of instructor.
MATH 333 Numerical Analysis I (4)
Topics in interpolation and
approximation methods, initial value problems, and boundary value problems of
ordinary differential equations. 4 lectures. Prerequisite: MATH 206 and MATH
242, or MATH 241 and MATH 244, or consent of instructor.
MATH 335 Graph Theory (4)
Introduction to graph
theory and its applications: isomorphism, paths and searching, connectedness,
trees, tournaments, planarity, graph colorings, matching theory, network flow,
adjacency and incidence matrices. Further topics to be selected from the theory
of finite state machines, Ramsey theory, extremal theory, and graphical enumeration.
4 lectures. Prerequisite: Junior standing or consent of instructor.
MATH 336 Combinatorial Mathematics (4)
Methods of enumerative
combinatorics: sum, product, and division rules, bijective and recursive
techniques, inclusion and exclusion, generating functions, and the finite
difference calculus. Advanced topics to be selected from the theory of
partitions, Polya theory, designs, and codes. 4 lectures. Prerequisite: Junior
standing or consent of instructor.
MATH 341 Theory of Numbers (4)
Properties of numbers.
MATH 344 Linear Analysis II (4) GE B6
Linear methods applied to
the solution of differential equations.
MATH 350 Mathematical Software (4)
Problem-solving using
mathematical software. 4 lectures. Prerequisite: CSC/CPE 101 or CSC/CPE 235,
and MATH 206 or MATH 244, and MATH 241, or consent of instructor.
MATH 370 Putnam Exam Seminar (2)
Directed group study of
mathematical problem solving techniques. Open to undergraduate students only.
Class members are expected to participate in the annual William Lowell Putnam
Mathematical Competition. Course may be repeated up to eight units. 2 seminars.
Prerequisite: Consent of instructor.
MATH 371 Math Modeling Seminar (2)
Directed group study of
mathematical modeling techniques. Open to undergraduate students only. Class
members are expected to participate in the annual Mathematical Competition in
Modeling. Total credit limited to 8 units. 2 seminars. Prerequisite: Consent of
instructor.
MATH 372 Mathematical Community Service Projects (2)
(CR/NC)
Directed group
mathematical research in support of volunteer community service projects. Total
credit limited to 8 units. 2 seminars. Prerequisite: consent of instructor and
consent of department chair.
MATH 400 Special Problems for Advanced Undergraduates
(1-4)
Individual investigation,
research, studies, or surveys of selected problems. Total credit limited to 8
units. Prerequisite: Junior standing and consent of department chair.
MATH 404 Introduction to Differential Geometry and
Topology (4)
Theory of curves and
surfaces in space. Topics such as curvature, geodesics, Gauss map, Gauss-Bonnet
Theorem, combinatorial topology, point set topology. 4 lectures. Prerequisite:
MATH 304 or consent of instructor.
MATH 406 Linear Algebra III (4)
Complex vector spaces,
unitary and self-adjoint matrices, Spectral Theorem,
1 MATH
408, 409 Complex Analysis I, II (4) (4) MATH 408: GE B6
Elementary analytic
functions and mappings. Cauchy’s Integral Theorem; Poisson’s Integral Formula.
Taylor and Laurent series, theory of residues, and the evaluation of integrals.
Harmonic functions, conformal mappings. 4 lectures. Prerequisite: MATH 242, or
MATH 241 and MATH 244, or consent of instructor.
MATH 412 Introduction to Analysis I (4)
Introduction to concepts
and methods basic to real analysis. Topics such as the real number system,
sequences, continuity, uniform continuity and differentiation. 4 lectures.
Prerequisite: MATH 306 or consent of instructor.
1 MATH
413, 414 Introduction to Analysis II, III (4) (4)
A continuation of
Introduction to Analysis I covering such topics as integration, infinite
series, uniform convergence and functions of several variables. Highly recommended
for students planning to enter graduate programs or secondary teaching and
those interested in applied mathematics. 4 lectures. Prerequisite: MATH 412 or
consent of instructor.
MATH 417 Introduction to Dynamical Systems (4)
Theory of dynamical systems
in one and two dimensions. Topics such as bifurcation theory, chaos,
attractors, limit cycles, nonlinear dynamics. 4 lectures. Prerequisite: MATH
206 and MATH 242, or MATH 241 and MATH 244, or consent of instructor.
MATH 418 Partial Differential Equations (4)
Mathematical formulation of
physical laws. Separation of variables. Orthogonal functions and generalized
Fourier series. Bessel functions, Legendre polynomials. Sturm-Liouville
problem. Boundary value problems; nonhomogeneous techniques. Applications to
heat flow, potential theory, vibrating strings and membranes. 4 lectures.
Prerequisite: MATH 344 or consent of instructor. Recommended: MATH 304.
MATH 419 Introduction to the History of Mathematics
(4)
Evolution of mathematics
from earliest to modern times. Major trends in mathematical thought, the
interplay of mathematical and technological innovations, and the contributions
of great mathematicians. Appropriate for prospective and in-service teachers. 4
lectures. Prerequisite: MATH 248 with a grade of C- or better and at least one
upper division course in mathematics, or consent of instructor.
MATH 422 Introduction to Analysis I Laboratory (1)
(CR/NC)
Facilitated
study and discussion of the methods and techniques of proof in introductory
analysis. Credit/No Credit grading only. 1 laboratory. Corequisite: Concurrent
enrollment in the associated section of MATH 412.
MATH 423 Advanced Mathematics for Teaching (4)
Introduction to mathematics
education research and advanced exploration of the rational number system, real
number system, complex number system, functions, equations, distance and
similarity, trigonometry, area and volume, and the Cartesian model for
Euclidean geometry. 4 lectures. Prerequisite: MATH 442 and MATH 481.
MATH 424 Organizing and Teaching Mathematics (4)
Organization, selection,
presentation, application and interpretation of subject matter in mathematics.
Introduction to current issues in mathematics education. For students who will
be teaching in secondary schools. 4 lectures. Prerequisite: Senior standing or
consent of instructor.
1 MATH
431, 432 Mathematical Optimization I, II
(4) (4)
Classical optimization.
Maximum/minimum of functions, linear and nonlinear optimization problems,
duality, constrained optimization. Model building and applications to various
fields. 4 lectures. Prerequisite: MATH 206 or MATH 244, and MATH 241, or
consent of instructor.
MATH 433 Numerical Analysis II (4)
Numerical techniques for
solving partial differential equations of the parabolic, hyperbolic and
elliptic type. Further topics in approximation theory. 4 lectures.
Prerequisite: MATH 333 or equivalent.
MATH
437 Game Theory (4)
Development of the
mathematical concepts, techniques, and models used to investigate optimal
strategies in competitive situations; games in extensive, normal, and
characteristic form, Nash equilibrium points and Nash Bargaining Model. 4
lectures. Prerequisite: MATH 206 or MATH 244, and MATH 248 with a grade of C-
or better, or consent of instructor.
MATH 440 Topology I (4)
Introduction to general
topological spaces with emphasis on surfaces and manifolds. Open and closed
sets, continuity, compactness, connectedness,. Quotient spaces. 4 lectures.
Prerequisite: MATH 412 and concurrent enrollment in or completion of MATH 481,
or consent of instructor.
MATH 441 Topology II (4)
Introduction to general
topological spaces with emphasis on surfaces and manifolds. Fundamental group.
Triangulations of spaces, classification of surfaces. Other topics may include
covering spaces, simplicial homology, homotopy theory and topics from
differential topology. 4 lectures. Prerequisite: MATH 440 or consent of
instructor. Recommended: MATH 304.
MATH
442 Euclidean Geometry (4)
Foundations of Euclidean
geometry, finite geometries, congruence, similarities, polygonal regions,
circles and spheres. Constructions, mensuration, the parallel postulate.
Appropriate for prospective and in-service mathematics teachers. 4 lectures.
Prerequisite: MATH 248 with a grade of C- or better or consent of instructor.
Recommended: MATH 300 or familiarity with dynamic geometry software.
MATH 443 Modern Geometries (4)
Non-Euclidean and projective geometries. Properties of parallels,
biangles, Saccheri and Lambert quadrilaterals, angle-sum and area. Limiting
curves, hyperbolic trigonometry, duality, perspectivity, quadrangles,
fundamental theorems of projective geometry, conics. 4 lectures. Prerequisite:
MATH 442.
MATH
459 Senior Seminar (4)
Written and oral analyses
and presentations by students on topics from advanced mathematics and
mathematical modeling. 4 seminars. Prerequisite: MATH 306, and completion of at
least two additional upper-division courses in the math major, or consent of
instructor.
1 MATH 461, 462
Senior Project I, II (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 120 hours total time. Prerequisite: MATH
459.
MATH
470 Selected Advanced Topics (1-4)
Directed group study of
selected topics for advanced students. Open to undergraduate and graduate
students. Class Schedule will list
topic selected. Total credit limited to 8 units. 1 to 4 lectures. Prerequisite:
Junior standing and consent of instructor.
1 MATH
481, 482 Abstract Algebra I, II (4) (4)
Fundamental algebraic
structures and types of algebras, including opera-tions within them and
relations among them. Groups, rings and fields. 4 lectures. Prerequisite: MATH
306 or MATH 341 or consent of instructor.
MATH 485 Cooperative Education Experience (6) (CR/NC)
Part-time work experience
in business, industry, government, and other areas of student career interest.
Positions are paid and usually require relocation and registration in course
for two consecutive quarters. Formal report and evaluation by work supervisor
required. Total credit limited to 16 units. Credit/No Credit grading only.
Prerequisite: Sophomore standing and consent of instructor.
MATH 491 Abstract Algebra I Laboratory (1) (CR/NC)
Facilitated study and
discussion of the methods and techniques of proof in abstract algebra.
Credit/No Credit grading only. 1 laboratory. Corequisite: Concurrent enrollment
in the associated section of MATH 481.
MATH 495 Cooperative Education Experience (12) (CR/NC)
Full-time work experience
in business, industry, government, and other areas of student career interest.
Positions are paid and usually require relocation and registration in course
for two consecutive quarters. Formal report and evaluation by work supervisor
required. Total credit limited to 16 units. Credit/No Credit grading only.
Prerequisite: Sophomore standing and consent of instructor.
MATH 500 Individual Study (1-4)
Individual research or
advanced study planned and completed under the direction of a departmental
faculty member. Open only to graduate students demonstrating ability to do
independent work. Prerequisite: Graduate standing and consent of department
chair.
1 MATH
501, 502 Methods of Applied Mathematics
I, II (4) (4)
Introduction to advanced
methods of mathematics useful in the analysis of engineering problems. Theory
of vector fields, Fourier analysis, Sturm-Liouville theory, functions of a
complex variable. Selected topics in asymptotic analysis, special functions,
perturbation theory. Not open to students in major or master’s degree program
in mathematics. MATH 501: Distance Learning Lab fee may be required–see Class Schedule. 4 lectures.
Prerequisite: MATH 344 or AERO 300 or equivalent, and graduate standing, or
consent of instructor.
MATH 510 Survey of Modern Mathematics (4)
Selected topics from the field of modern mathematics.
Projective and synthetic geometry, topology, logic, matrices, vectors. Theory
of games, probability, linear and modern algebra and convex sets. Boolean
algebras, graph theory, lattice theory, geometry of complex numbers. 4
seminars. Prerequisite: Graduate standing or consent of instructor.
1 MATH
520, 521 Applied Analysis I, II (4) (4)
Advanced mathematical
methods of analysis in science and engineering, integrated with modeling of
physical phenomena. Topics include applications of complex analysis, Fourier
analysis, ordinary and partial differential equations. Additional topics to be
drawn from perturbation methods, asymptotic analysis, dynamical systems,
numerical methods, optimization, and the calculus of variations. 4 lectures.
Prerequisite: MATH 408, MATH 412 and graduate standing, or consent of the
instructor. Recommended: MATH 418.
1 MATH
530, 531 Discrete Mathematics with
Applications I, II (4) (4)
Advanced
mathematical methods of discrete mathematics with applications. Topics will
include probability theory with generating functions, difference equations and
number theory. Additional topics to be drawn from the theory of algorithms,
coding theory, set theory, and the relation of discrete mathematics to complex
analysis. 4 lectures. Prerequisite: MATH 481, MATH 306 and graduate standing,
or consent of instructor.
MATH 540 Topology I (4)
Introduction to general
topological spaces with emphasis on surfaces and manifolds. Open and closed
sets, continuity, compactness, connectedness,. Quotient spaces. 4 lectures. Not
open to students with credit in MATH 440. Prerequisite: MATH 412, concurrent
enrollment in or completion of MATH 481, and graduate standing, or consent of
instructor.
MATH 541 Topology II (4)
Introduction to general
topological spaces with emphasis on surfaces and manifolds. Fundamental group.
Triangulations of spaces, classification of surfaces. Other topics may include
covering spaces, simplicial homology, homotopy theory and topics from
differential topology. 4 lectures. Not open to students with credit in MATH
441. Prerequisite: MATH 540 and graduate standing, or consent of instructor.
Recommended: MATH 304.
MATH 550 Real Analysis (4)
Introduction to Lebesgue
measure and integration, convergence theorems, L1 spaces, Radon-Nikodym Theorem and Fubini’s
Theorem. 4 seminars. Prerequisite: Satisfactory completion of the Graduate
Written Examination in Analysis or consent of the Graduate Committee.
MATH 560 Field Theory (4)
Polynomial rings, field
extensions, normal and separable extensions, automorphisms of fields,
fundamental theorem of Galois theory, solvable groups, solution by radicals,
insolvability of the quintic. 4 lectures. Prerequisite: Satisfactory completion
of the Graduate Written Examination in Algebra or consent of the Graduate
Committee.
MATH 580 Seminar (1–4)
Built around topics in advanced
mathematics chosen according to the common interests and needs of the students
enrolled. Each seminar will have a subtitle according to the nature of the
content. Total credit limited to 12 units. 1–4 seminars. Prerequisite: Graduate
standing and consent of instructor.
MATH 596 Thesis (3)
Serious research endeavor
devoted to the development, pedagogy or learning of mathematics. Course to be
taken twice for a total of 6 units. Prerequisite: Graduate standing and consent
of instructor.
_____
1 Each course in a combined listing of sequentially
numbered courses is a prerequisite to its successor in the same listing.