| |
|
Mathematics Course Offerings
NOTE: A student who has recently taken a pre-calculus
course in high school should be prepared to enter calculus. A student
with three years of high school mathematics, including two years
of algebra and one year of geometry, should be prepared to take
MATH 1130, or possibly MATH 1300. Such students, and others who
are unsure about what mathematics course to begin with, should call
the Mathematics and Computer Science Department for advice (885-4011).
Also, Assessment and Testing (885-3661) offers placement tests that
can assist students in finding the appropriate starting class.
-
A two-quarter sequence in basic
mathematics and elementary algebra. CR/NC grading only. On successful
completion of this sequence, students should register for MATH
0950. Units will not count toward the baccalaureat degree.
Prerequisite: Appropriate ELM score
(ranges available from the Testing
Office or at
http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
-
A one quarter course in elementary algebra. CR/NC
grading only. On successful completion of this course, students
should register for MATH 0950.
Not open to students who have passed MATH 0802. Units will not count toward
the baccalaureate degree.
Prerequisite:
Appropriate ELM score (ranges available from the Testing
Office or at
http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
-
Operations with algebraic expressions, exponents
and radicals; linear and quadratic equations; systems of equations
and inequalities; linear and quadratic functions and their graphs;
elementary conic sections; word problems. CR/NC grading only.
Units will not count toward baccalaureate degree.
Prerequisite:
Grade of CR in 0802 or MATH 0900 or an appropriate ELM
score (ranges available from the Testing Office or at
http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
-
This course is designed to introduce the student
to mathematics as an art and mathematics as a tool, emphasizing
the place of mathematics in today's world. Will satisfy the
general education education requirement for nonmajors.
Prerequisites: Satisfactory completion of Entry Level Mathematics
requirement.
-
Functions and graphs: polynomials, rational functions,
exponential and logarithmic functions.
Prerequisites: Satisfactory completion of Entry Level Mathematics
requirement.
-
Definitions, properties and graphs of the trigonometric
functions. Applications. Analytic geometry of conic sections.
A preparatory course for calculus.
Prerequisites: MATH 1130 or departmental permission
-
Differential calculus. Limits and continuity.
Exponential and logarithmic functions. Techniques and applications
of differentiation.
Prerequisite: MATH 1300 or departmental permission
-
Integral calculus. The indefinite integral, area,
the Fundemental Theorem and techniques of integration. Applications
of volume, arc length, physical and biological problems.
Prerequisite: MATH 1304 or departmental permission
-
Functions and graphs; exponential and logarithmic functions; mathematics of
accounting and finance; matrices and systems of equations; geometric approach
to linear programming; introduction to differential and integral calculus
with applications to business and social sciences.
Prerequisite: MATH 1130
-
Further topics in derivatives and integration, elementary differential
equations; multivariable calculus, Lagrange multipliers, systems of linear
equations, matrix algebra; inequalities and linear programming; applications
to business and social sciences.
Prerequisite: MATH 1810
-
Structure of number systems, place value, whole numbers,
integers, fractions, decimals, real numbers. Standard and
nonstandard algorithms, mental computation. Algebra as
generalized arithmetic. Divisibility, prime and composite
numbers, GCF, LCM. Ratio, proportion, percents. Not open
to students with credit for MATH 4021.
Prerequisite: satisfactory completion of the Entry Level Mathematics (ELM) requirement.
-
Vector spaces, linear transformations, matrices,
systems of linear equations. Stress on 2 and 3 dimensions, including
geometric and other applications.
Prerequisite: MATH 1305 or 1820 (may be taken simultaneously
with, or after, MATH 2304)
-
Topics in discrete mathematics. Elementary logic,
set theory, and relations; induction, enumeration techniques,
recurrence relations, trees and graphs. Boolean algebra, algorithm
analysis.
Prerequisite: MATH 1304
-
Infinite series, convergence of power series.
Vectors in space. Partial derivatives, chain rule, directional
derivative and gradient. Curves and surfaces. Maxima and minima.
Multiple integrals.
Prerequisite: MATH 1305
-
Introduction to methods and proof techniques
in several branches of mathematics, with topics chosen from
logic, set theory, abstract algebra, number theory, analysis,
and graph theory. Provides a transition from lower division
mathematics courses, which concentrate on computation, to upper
division proof-oriented mathematics courses. Mathematics majors
may substitute this course for MATH 2150.
Prerequisite: MATH 2304; co-requisite: MATH 2101
-
Abstract vector spaces, linear transformations,
matrices and determinants. Dual spaces and inner product spaces.
Eigenvalues and eigenvectors.
Prerequisites: MATH 2101 and either 2150 or 3000
-
Equivalence relations, binary operations. Integers:
divisibility, factorization, integers modulo n. Groups: subgroups,
cyclic groups, permutation groups, quotient groups. Homomorphisms
and isomorphisms. Selected topics as time permits.
Prerequisites: MATH 2101 and either 2150 or 3000
-
Rings and fields: integral domains, ideals, quotient
rings polynomial rings, roots of polynomials, algebraic extensions
and finite fields. Selected topics as time permits.
Prerequisite: MATH 3121
-
Theory of counting, including partitions, Stirling
numbers, generating functions. Applications of Burnside's Lemma
from multiple transitivity to the Polya- Redfield Theorem. Ferrers
diagrams, symmetric functions, and majorization.
Prerequisites: MATH 2101 and either 2150 or 3000
-
An axiomatic approach to incidence, Neural, Euclidean,
and non-Euclidean plane geometry. Various models, such as the
Euclidean, hyperbolic, taxicab planes, will be considered throughout
the course.
Prerequisites: MATH 2101 and either 2150 or 3000
-
The real numbers, limits, sequences and series
of real numbers, Bolzano-Weierstrass theorem. Continuity, intermediate
and extreme value theorems, uniform continuity, sequences of
functions. Topology of Rn. Differentiation, chain
rule, implicit and inverse function theorems.
Prerequisites: MATH 2101, 2304 and either 2150 or 3000
-
The real numbers, limits, sequences and series
of real numbers, Bolzano-Weierstrass theorem. Continuity, intermediate
and extreme value theorems, uniform continuity, sequences of
functions. Topology of Rn. Differentiation, chain
rule, implicit and inverse function theorems.
Prerequisite: MATH 3300
-
Differentiation and integration of vector valued
functions; gradient, divergence, and curl; cylindrical and spherical
coordinates; theorems of Green and Stokes.
Prerequisites: MATH 2304 and MATH 2101 (2101 may be taken
concurrently)
-
Methods of solution and applications of first
order differential equations. Linear n-th order equations with
emphasis on equations of 2nd order. Other topics may include
power series solutions, Laplace transforms, linear systems.
Prerequisite: MATH 2304
-
Series solution of linear differential equations
with variable coefficients, two point boundary value problems,
systems of differential equations, phase plane analysis
Prerequisites: MATH 2101 and MATH 3331
-
The theory of probability with applications to
science and engineering. Sample spaces; random variables; joint,
marginal, conditional distributions; expectations; important
distributions (binomial, Poisson, normal, etc.); and moment
generating functions.
Prerequisite or concurrent: MATH 1305
CROSS-LISTED: STAT 3401
-
Generating functions and multivariate distributions.
Conditioning. Chebyshev inequality and limit theorems. Multidimensional
transformations of random variables. Derivation of t and F distributions.
Uses of probability theory in mathematical statistics.
Prerequisites: MATH 2304 or concurrent, MATH/STAT 3401
CROSS-LISTED: STAT 3402
-
Random variables, sampling distributions (binomial,
Poisson, normal, exponential), conditional probability. Estimation,
hypothesis testing. Computer-aided computations. Topics include:
t-tests; correlation, regression; proportions, chi-squared;
ANOVA.
Prerequisites: MATH 1305 or MATH 1820
CROSS-LISTED: STAT 3502
-
General linear hypothesis with emphasis on design
and analysis of experiments. Data from science, engineering,
and quality management. Factorial designs: random effects, nesting.
Optional topics: incomplete blocks, missing data, analysis of
covariance. Computer-aided analysis.
Prerequisites: MATH/STAT 3502
CROSS-LISTED: STAT 3503
-
Euclid's algorithm, prime numbers, congruences,
theorems of Fermat and Euler, quadratic residues.
Prerequisites: MATH 2101 and either 2150 or 3000
-
Basic probability rules (independence, Bayes'
Theorem), distributions (binomial, Poisson, normal, exponential),
reliability. Descriptive, inferential statistics (control charts,
estimation, hypothesis testing: one, two samples), correlation,
regression. Emphasizes: computer analysis, simulation; science,
engineering applications.
Prerequisite: MATH 1305 CROSS-LISTED: ENGR 3601
-
Basic numerical methods and analysis; practical
solutions of problems from engineering, science, and mathematics.
Computer representation of real numbers, errors, root finding,
interpolation, numerical integration, ordinary differential
equations.
Prerequisites: CS 1160, MATH 2101 and 2304
-
Problems of maximizing or minimizing a linear
function subject to linear constraints; typical applications
involve planning ("programming") the allocation of limited resources
to achieve an optimal result. Topics include problem formulation,
solution procedures, duality theory, sensitivity analysis, special
problems ( e.g., transportation and assignment problems).
Prerequisites: MATH 2304 and competence in matrix algebra
CROSS-LISTED: ENGR 3841
-
Discrete and continuous mathematical models. General introduction to the use
of difference and differential equations, probability and statistics,
and matrices for solving realistic problems. Computer simulation.
Emphasis on effective written reports.
Prerequisites: MATH 2101 and MATH 2304
CROSS-LISTED: STAT 3865
-
Mathematics theory and methods with applications to physics. In class
physics laboratory explorations will utilize mathematical techniques to
better understand physics phenomena.
Prerequisite: MATH 1305, Co-requisite: MATH 2304
-
Supervised work experience in which student completes
academic assignments integrated with off-campus paid or volunteer
activities. May be repeated for up to 8 units. A maximum of
2 units will be accepted toward the Mathematics major. CR/NC
grading only.
Prerequisites: at least 2.0 GPA; departmental approval of
activity; completion of lower-division Mathematics major requirements
and upper division standing.
-
Properties of 2- and 3-dimensional figures including
congruence, similarity, proportional reasoning, area,
perimeter, volume, surface area. Informal constructive
proofs of properties of angles, polygons, parallel lines
and Pythagorean theorem. Transformational geometry.
Measurement systems, estimation, coordinate geometry. Not
open to students with credit for MATH 4022.
Prerequisite: MATH 2011
-
Displaying and interpreting data via graphs, tables and
charts. Descriptive statistics, including mean, median,
mode and range. Basic Survey design, including possible
sources of biases. Elementary discrete probability.
Dependent and independent events. Cross-listed with STAT
4013. Not open to students with credit for MATH 4023.
Prerequisites: MATH 2011 and satisfactory completion of
the Entry Level Mathematics requirement.
-
Patterns and functional relationships. Linear and
quadratic equations and inequalities. Interpretation of
graphs, multiple representations of functions. Factoring
and completing the square. Proportional reasoning.
Systems of linear equations. Not open to students with
credit for MATH 4024.
Prerequisites: MATH 2011 and
satisfactory completion of the Entry Level Mathematics
requirement.
-
Foundations of school mathematics from an advanced standpoint. An in depth
study of middle and high school level algebra, geometry and number theory and
its applications, theoretical foundations and extensions.
Prerequisites: MATH 2011 and MATH 1130 or consent of instructor
-
The historical development of mathematical ideas
and techniques.
Prerequisite: Calculus or the consent of instructor
-
Introduction to partitions of positive integers; inner product spaces,
including such topics as unitary, hermitian, normal matrices; certain
``combinatorial'' properties of permutation groups. Applications to
matrix representations of finite groups and topics in tensor spaces.
Prerequisites: MATH 3100 and MATH 3121
-
Theory of groups, including factor groups, Jordan-Holder
Theorem, Sylow theorems. Mappings and homomorphisms. Introduction
to rings and fields. Topics continued in MATH 6121.
Prerequisite: MATH 3122
-
Introduction to graph theory. Graphic sequences.
Planar graphs and the theorems of Euler and Kuratowski. Bipartite
graphs. Connectivity and spanning trees. Hamiltonian graphs.
Matching, chromatic and characteristic polynomials. Cospectral
graphs and the graph isomorphism problem. Algorithms.
Prerequisites: MATH 2101 and either 2150 or 3000
-
Formal models of automata, language, and computability
and their relationships. Finite automata and regular languages.
Push-down automata and context-free languages. Turing machines,
recursive functions, algorithms and decidability.
Prerequisites: MATH 2101, MATH 2150, MATH 2304
CROSS-LISTED: CS 4170
-
Topics in geometry such as algebraic, differential,
finite, or projective geometry, convexity, packing and tiling,
polytopes, and isoperimetric problems.
Prerequisites: MATH 3215 or consent of instructor. May be
repeated once for credit with consent of the chair.
-
An introduction to the theory of knots and links.
Reidemeister moves, knot invariants, including 3-colorings, linking number,
Alexander polynomial, Kauffman bracket and Jones polynomial. As time permits
some applications in biology and/or chemistry will be discussed.
Prerequisite: MATH 3121
-
Design, analysis and implementation of algorithms.
Methods of algorithm design, including recursion, divide and
conquer, dynamic programming, backtracking. Time and space complexity
analyses in the best, worst, average cases. NP-completeness;
computationally hard problems. Applications from several areas
of Computer Science.
Prerequisites: MATH 2101, MATH 2304, CS 3240
CROSS-LISTED: CS 4245
-
Introduction to modern differential geometry
and topology. Geometry of curves and surfaces, differential
forms and vector fields, manifolds, curvature, geodesics, topological
invariants.
Prerequisites: MATH 3100, 3300, or consent of instructor
-
Manifolds and smooth maps, vector fields and
differential forms, Riemann integration for functions of several
variables, Fubini theorem, theorem of Green, Gauss, and Stokes,
general Stokes theorem.
Prerequisite: MATH 3301
-
Introduction to theory of functions of complex
variables.
Prerequisites: MATH 3300
-
Pointwise and uniform convergence, Taylor series,
Riemann integration, sets of measure zero, Lebesgue's theorem
on the Riemann integral, the metric space of continuous functions,
and selected topics.
Prerequisite: MATH 3300
-
Topological spaces, metric spaces, continuity,
connectedness and compactness.
Prerequisites: MATH 3300
-
Differential equations of physics: the wave equation,
the heat equation, Laplace's equation; boundary-value problems.
Elementary Sturm-Liouville theory. Fourier series, Fourier and
Laplace transforms, Bessel functions, selected topics.
Prerequisite: MATH 3331
-
Introduction to dynamical systems and applications.
Variational calculus, Lagrangian dynamics, principle of critical
action, Hamiltonian system and symplectic mechanics, Hamilton-Jacobi
equation, chaotic and nonlinear systems, fractals.
Prerequisites: MATH 3100, 3300, 3331, or consent of instructor
-
Introduction to geometrical and topological aspects
of dynamical systems. Manifolds, bundles, vector fields, and
differential forms. Lagrangian and Hamiltonian systems and symplectic
mechanics.
Prerequisites: MATH 3100 and MATH 3300, or consent of instructor
-
Markov chains, birth-death processes, queueing
models, limit theorems. Computer simulation. Science, engineering
applications include inventory models, reliability, epidemiology,
dynamic programming.
Prerequisite: MATH 2304 (or concurrent) and either MATH/STAT
3401 or 3502
CROSS-LISTED: ENGR 4401 and STAT 4401
-
Continuation of MATH 3750. Numerical solution
of linear systems, matrix norms, approximation of functions,
algebraic eigenvalues.
Prerequisite: MATH/CS 3750
CROSS-LISTED: CS 4750
-
Sequel to MATH 3841. Topics to be drawn from
linear and/or nonlinear programming. Linear programming topics
may include integer programming, game theory, network programming;
nonlinear programming topics include optimality conditions and
solution procedures for unconstrained and constrained optimization
problems. May be repeated once for credit with consent of the
chair.
Prerequisite: MATH 3841
-
Function spaces, general variation of a functional, Euler-Lagrange equations,
Noether's theorem and conservation laws, Hamilton-Jacobi theory, canonical
transformations and symplectic geometry.
Prerequisite: MATH 3100 and MATH 3331
-
Prerequisites: Permission from Instructor and Dept Chair
-
Exploration of topics in mathematics. Topics
selected from the literature to illustrate relationships among
various areas of mathematics. Oral presentations and paper required.
Prerequisite: senior standing in mathematics (completion
of 32 units of mathematics courses) or permission of the instructor.
-
Theory, methodology, and practical experience in the teaching of mathematics
at the university level. Includes discussion of lecturing techniques,
analysis of tests and supporting material, preparation and grading of
examinations, and related topics. Required of departmental teaching associates.
May be repeated for credit but only two units can be used toward the M.S. degree.
Prerequisite: permission of department (normally available to
teaching associates only)
-
Research and analysis of selected topics pertinent
to Mathematics in the elementary school. Reports on current
research, contemporary and experimental programs, and new materials.
May be repeated for credit.
Prerequisite: consent of instructor
CROSS-LISTED: T ED 6010
-
Polynomials, groups, fields and rings from an
advanced standpoint as they relate to the high school algebra
curriculum. Discussion of strategies to help secondary students develop
their algebraic thinking skills.
Prerequisite: permission of instructor
-
Causes and effect of mathematics learning disabilities.
Methods and instruments useful in diagnosis and treatment. Evaluation
of materials for the correction of mathematical learning problems.
Prerequisite: consent of instructor
CROSS-LISTED: T ED 6021
-
Rigorous development of a non-Euclidean geometry,
such as spherical, projective, or hyperbolic geometry. Models
and technology will be used where appropriate. Discussion of implementation strategies for teaching geometry and proof techniques for high school students.
Prerequisite: permission of instructor
-
A rigorous development of calculus. The real line, functions, limits, continuity, differential and
integral calculus. Technology used to develop
an intuitive understanding of calculus which can be implemented
in the high school classroom.
Prerequisite: permission of instructor
-
Historical and philosophical study of curriculum
trends, modern curricular developments including use of newer
instructional media, individualization of instruction, school
computer usage, and evaluation techniques.
Prerequisite: consent of instructor
CROSS-LISTED: T ED 6040
-
Mathematics as found throughout the sciences. Mathematics used to model phenomena in Biology, Chemistry, and/or Physics. Students discover some of this mathematics through scientific experiments.
Prerequisite: permission of instructor
-
Topics in discrete mathematics relating to the
high school curriculum such as combinatorics, number theory,
and graph theory.
Prerequisite: permission of instructor
-
Topics which illustrate connections between different
fields and applications of mathematics such as neural networks,
tomography, coding theory, symmetry groups, optimization theory, and applications found in differential equations or complex
analysis.
Prerequisite: permission of instructor
-
A survey course covering significant areas of
applied algebra. Topics might include applied matrix theory,
game theory, convexity and inequalities, and/or algebraic coding
theory.
Prerequisite: MATH 3100 or equivalent. May be repeated once
for credit with consent of Mathematics Graduate Studies Committee.
Introduction to partitions of positive integers; inner product spaces,
including such topics as unitary, hermitian, normal matrices; certain
``combinatorial'' properties of permutation groups. Applications to
matrix representations of finite groups and topics in tensor spaces.
Graduate applications module.
Prerequisites: MATH 3100 and MATH 3121. Not open to students with credit for MATH 4105
-
Continuation of MATH 4121. Topics include ideals,
commutative rings, modules; field extensions and Galois theory.
Prerequisite: MATH 4121
-
An introduction to the theory of semisimple Lie
algebras. Theorems of Lie, Engel, and Weyl; Cartan's Criterion;
the classification of root systems; and abstract theory of weights.
Prerequisite: MATH 3100 or consent of instructor
-
Reducible and irreducible representations, Maschke's
theorem, characters, Schur's lemmas, orthogonality theorems,
the group algebra, induced representations and Frobenius reciprocity,
Young tableaux and representations of the symmetric group, applications
in chemistry and physics.
Prerequisites: MATH 3100 and 3121 or consent of instructor
-
An advanced course in graph theory. Connectivity, planarity, and graph
coloring. Advanced topics which may include substructures in graphs and Ramsey
Theory, Random Graphs, Spectral Graph Theory.
Prerequisites: MATH 3100 and graduate standing. May be repeated once
for credit with consent of instructor and when content varies, for a
maximum of 8 units. A-F grading.
-
Selected topics from advanced counting theory,
including formal power series, partially ordered sets, symmetric
groups, and related algorithms plus an additional graduate module.
Prerequisites: MATH 3121 or 3151 or consent of instructor
and graduate status. Not open to students with credit for MATH
4155
-
Continuation of MATH 4360 topics may include
countability and separation axioms, Tychonoff theorem, metrization
theorems, homotopy theory.
Prerequisite: MATH 4360
-
Convex sets including conex hulls, supporting
hyperplanes and duality. Convex polytopes, including simple,
simplicial, and cyclic polytopes. Combinatorial theory, including
Euler's Relations, Dehn-Somerville Relations and Upper Bound
Theorem.
Prerequisite: MATH 3100 and MATH 3300 or consent of instructor
-
An introduction to the theory of knots and links.
Reidemeister moves, knot invariants, including 3-colorings, linking number,
Alexander polynomial, Kauffman bracket and Jones polynomial. As time permits
some applications in biology and/or chemistry will be discussed.
Additional work required for graduate level credit.
Prerequisite: MATH 3121
-
Topics in differential geometry and topology
such as manifolds, bundles, differential forms, curvature, theorems
of Sard-Smale, Poincare-Hopf, Gauss-Bonnet, de Rham and Hodge.
Prerequisites: MATH 3100, MATH 3301 or consent of instructor
-
Introduction to Symplectic Geometry. Symplectic linear algebra, groups, Lie alg
ebras, and manifolds. Darboux-Weinstein theorem, relation to optics and Hamiltonian dynamics, m
oment maps, and geometric quantization.
Prerequisites: MATH 3100 and MATH 3300 or consent of instructor
-
Languages and algorithms; decision problems; Turing machines and
Turing-Completeness; decidability; measures and classes of time and
space complexity (e.g. P, NP, PSPACE); NP-Completeness.
Prerequisites: CS/MATH 4170 (or CS 6170) and CS/MATH 4245; or consent of instructor
CROSS-LISTED: CS 6260
-
Topics selected from the theory of ordinary and
partial differential equations. may be repeated for credit with
consent of Mathematics Graduate Studies Committee.
Prerequisite: MATH 3100, MATH 3331, MATH 3301 or consent of instructor
-
Cauchy integral formula, Mittag-Leffler's theorem,
Weierstrass' factorization theorem, normal families, Riemann
mapping theorem and selected topics.
Prerequisite: MATH 4340
-
Introduction to the geometry and arithmetic of elliptic
curves. Elliptic integrals and functions, theta functions,
automorphic functions, and modular forms. Algebraic curves
over finite fields. Elliptic curve factorization
algorithms and cryptosystems.
Prerequisites: MATH 4340 or consent of the instructor.
-
Theory of Lebesgue measure and integration on
the real line. Selected topics and applications.
Prerequisite: MATH 4350
-
Introduction to geometrical and topological aspects
of dynamical systems. Manifolds, bundles, vector fields, and
differential forms. Lagrangian and Hamiltonian systems and symplectic
mechanics.
Prerequisites: MATH 3100 and MATH 3300 or consent of instructor
-
Advanced treatment of probability theory and
its applications. May include: conditioning, generating/characteristic
functions, modes of convergence, limit theorems, renewal theory,
Markov processes, combinatorial techniques, measure and integration.
Prerequisites: MATH 3300 and either MATH/STAT 3402 or 4401
CROSS-LISTED: STAT 6401
-
Advanced treatment of probability theory and
its applications. May include: conditioning, generating/characteristic
functions, modes of convergence, limit theorems, renewal theory,
Markov processes, combinatorial techniques, measure and integration.
Prerequisite: MATH/STAT 6401
CROSS-LISTED: STAT 6402
-
Theory of point and interval estimation and hypothesis
testing. May include: decision theory, nonparametric inference,
sequential analysis, multivariate analysis, robustness, Bayesian
methods, computer intensive methods.
Prerequisites: MATH 3300 and MATH/STAT 3402
CROSS-LISTED: STAT 6501
-
Theory of point and interval estimation and hypothesis
testing. May include: decision theory, nonparametric inference,
sequential analysis, multivariate analysis, robustness, Bayesian
methods, computer intensive methods.
Prerequisite: MATH/STAT 6501
CROSS-LISTED: STAT 6502
-
The theory and application of the general linear
model; the analysis of variance and covariance; application
of generalized inverses and decomposition theorems from linear
algebra.
Prerequisites: MATH 2101 and MATH/STAT 3503
CROSS-LISTED: STAT 6510
-
Topics in Number Theory such as algebraic number fields, continued
fractions, geometry of numbers, theory of partitions, distribution
of primes, factoring algorithms and quadratic forms. May be repeated
once for credit with consent of chair.
Prerequisites: MATH 3121 and MATH 3600
-
Topics selecte from approximation theory; spline
theory; numerical linear algebra; the algebraic eigenvalue problem;
numerical solutions to non-linear systems of equations, partial
differential equations and boundary value problems. May be repeated
for credit with consent of Mathematics Graduate studies Committee.
Prerequisite: MATH/CS 4750 and MATH 3301 or consent of instructor
CROSS-LISTED: CS 6750
-
Optimality conditions and solution procedures for unconstrained and
constrained optimization problems.
Prerequisite: MATH 3841
-
Topics selected from quasi-Newton methods for multi-variable unconstrained
optimization; nonlinear least squares; quadratic programming; constrained
optimization with nonlinear constraints; convex optimization. May be
repeated for credit with consent of Mathematics Graduate Studies Committee.
Prerequisites: MATH 3750 and MATH 3841, or permission of instructor.
-
Function spaces, general variation of a functional, Euler-Lagrange equations,
Noether's theorem and conservation laws, Hamilton-Jacobi theory, canonical
transformations and symplectic geometry.
Applications to science and engineering.
Prerequisite: MATH 3100 and MATH 3331
-
Discrete and continuous mathematical models. General introduction to the use
of difference and differential equations, probability and statistics,
and matrices for solving realistic problems. Computer simulation.
Emphasis on effective written reports. Additional graduate applications module.
Prerequisites: MATH 2101 and MATH 2304. Not open to students with credit for MATH 3865
CROSS-LISTED: STAT 6865
-
Introduction to construction and analysis of
models by computer simulation. Study of one discrete and one
continuous simulation language. Application to modeling biological,
industrial, and physical processes.
Prerequisites: MATH 3100, MATH 3331, and a course in computer
programming
CROSS-LISTED: CS 6870
-
Advanced mathematics theory and methods with applications to physics.
Prerequisite: MATH 1305, Co-requisite: MATH 2304
-
Development of an original project
which is summarized in a written abstract. Both the project
and the abstract are submitted to the department which specifies
their format. Supervision by a departmental committee, at least
one of whom must be a Cal State East Bay faculty member.
Oral defense may be required.
Prerequisite: graduate status. Maximum of 5 units per students
-
Prerequisites: Permission from Instructor and Dept Chair
-
Development and writing of a formal research
paper for submission to the university in the specified bound
format. Supervision by a departmental committee, at least one
of whom must be a Cal State East Bay faculty member. Oral defense
normally required.
Prequisite: Graduate standing. Maximum of 6 units per student.
(See also, University Thesis Writing Guide)
For any questions, please contact the Department
of Mathematics and Computer Science at 510-885-3414.
|
