| Mathematics |
MATH #805 - Probability, Data Analysis, and Discrete Mathematics for the Middle School
Credits:
3.00
Probability, counting techniques, analysis of statistical
data, elementary graph theory, and school curriculum
materials for middle school teachers. Prereq: permission.
MATH 835 - Statistical Methods for Researchers
Credits:
3.00
Emphasis is on applications of statistical methods and
concepts. Topics include: Basic descriptive statistics,
statistical graphs, fundamentals of statistical inference,
analysis of variance (ANOVA), regression analysis,
introduction to statistical design of experiments,
categorical data, time-ordered data, introduction to
multivariate statistical techniques. Recommended to
graduate students with little or no formal training in
statistical methods or to graduate students looking for a
refresher course in statistics.
MATH 837 - Statistical Methods For Quality Improvement
Credits:
3.00
Introduction to scientific data collection and analysis with
an emphasis on industrial applications. Topics include
statistical process control (SPC), engineering process
control, failure modes and effects analysis (FMEA),
Six-Sigma concepts and methods, and confidence intervals
and hypothesis testing. Use of a statistical software
package is an integral part of the course; graphical data
analyses are emphasized. Prereq: basic introductory
statistics.
MATH 839 - Regression Analysis
Credits:
3.00
Estimation, testing, and diagnostic methods for regression
models. Simple linear regression, residual analysis and
model validation, multiple linear regression, model
selection, multicollinearity, polynomial regression,
categorical predictors, analysis of variance, analysis of
covariance.
MATH 840 - Design of Experiments I
Credits:
3.00
Quality control methods; design of experiments for quality
improvement; randomization and blocking; factorial designs;
nested designs; fixed-, and random- and mixed-effects
models; fractional factorial designs; response surface
methods. Industrial and engineering applications.
MATH 841 - Biostatistical Methods
Credits:
3.00
Concepts and methods of nonparametric statistics,
categorical data analysis and failure-time data analysis:
Censored data analysis. Biostatistical techniques.
Reliability and life testing. Poisson regression. (Offered
alternate years.)
MATH 842 - Multivariate Statistics and Modern Regression Methods
Credits:
3.00
Random vectors and matrices, multivariate normal
distribution, Hotelling's T2, multivariate analysis of
variance (MANOVA), principal components, discriminant
analysis, factor analysis, partial least squares, emprical
orthogonal functions, additive and generalized additive
models. (Offered in alternate years.)
MATH 844 - Design of Experiments II
Credits:
3.00
Experimental design strategies and issues that are often
encountered in practice. Topics include: Complete and
incomplete blocking, partially balanced incomplete blocking
(BIB), confounding intra and inter block information, split
plotting and strip plotting, repeated measures, crossover
design strategies, Latin squares and rectangles, Youden
squares, crossed and nested treatment structures, variance
components, mixed effects models, analysis of covariance,
optimizations, missing responses. Prereq: industrial
statistics and design of experiments or permission.
MATH 845 - Foundations of Applied Mathematics
Credits:
3.00
Basic concepts and techniques of applied mathematics
intended for graduate students of mathematics, engineering,
and the sciences. Fourier series and transforms, Laplace
transforms, optimization, linear spaces, eigenvalues,
Sturm-Liouville systems, numerical methods, conformal
mapping, residue theory.
MATH 846 - Foundations of Applied Mathematics
Credits:
3.00
See description for MATH 845.
MATH 847 - Introduction to Nonlinear Dynamics and Chaos
Credits:
3.00
An introduction to the mathematics of chaos and nonlinear
dynamics. Topics include: linear and nonlinear systems of
ordinary differential equations; discrete maps; chaos; phase
plane analysis; bifurcations; and computer simulations.
Prereq: elementary differential equations; linear algebra;
and multidimensional calculus. (Not offered every year.)
MATH 853 - Introduction to Numerical Methods
Credits:
3.00
Introduction to mathematical algorithms and methods of
approximation. A wide survey of approximation methods are
examined including, but not limited to, polynomial
interpolation, root finding, numerical integration,
approximation of differential equations, and techniques used
in conjunction with linear systems. Included in each case is
a study of the accuracy and stability of a given technique,
as well as its efficiency and complexity. It is assumed that
the student is familiar and comfortable with programming a
high-level computer language. (Also offered as CS 853.)
MATH 854 - Introduction to Scientific Computing
Credits:
3.00
Introduction to the tools and methodology of scientific
computing via the examination of interdisciplinary case
studies from science and engineering. Emphasis on numerical
approaches to solving linear systems, eigenvalue-eigenvector
problems, and differential equations. Problems solved on
various hardware platforms using a combination of software
and data visualization packages. Prereq: linear algebra;
differential equations; introduction to scientific
programming;/ or permission. (Also offered as CS 854,
PHYS 854.)
MATH 855 - Probability and Stochastic Processes
Credits:
3.00
Introduction to the theory of probability, random variables,
expectation, discrete and continuous probability
distributions, correlation, Markov chains, introduction to
stochastic processes, birth-death processes,
moment-generating functions, limit theorems.
MATH 856 - Principles of Statistical Inference
Credits:
3.00
Theory of statistical inference, principles of point
estimation, maximum likelihood and other methods, exact
and approximate methods, confidence regions, significance
testing, computational methods, Bayesian inference,
decision theory. Prereq: probability and stochastic
processes.
MATH 861 - Abstract Algebra
Credits:
3.00
Basic properties of groups, rings, fields, and their
homomorphisms.
MATH 862 - Linear Algebra
Credits:
3.00
Abstract vector spaces, linear transformations, and
matrices. Determinants, eigenvalues, and eigenvectors.
Prereq: MATH 861.
MATH #864 - Advanced Algebra
Credits:
3.00
Topics to be selected from among rings, modules,
algebraic fields, and group theory. Prereq: MATH 861.
(Not offered every year.)
MATH 867 - One-Dimensional Real Analysis
Credits:
3.00
Theory of limits, continuity, differentiability,
integratbility.
MATH #876 - Logic
Credits:
3.00
Induction and recursion; sentential logic; first-order
logic; completeness, consistency, and decidability;
recursive function. (Not offered every year.)
MATH #883 - Set Theory
Credits:
3.00
Axiomatic set theory, including its history,
Zermelo-Fraenkel axioms, ordinal and cardinal numbers,
consistency, independence, and undecidability. (Not offered
every year.)
MATH 884 - Topology
Credits:
3.00
Open seats, closure, base, and continuous functions.
Connectedness, compactness, separation axioms, and
metrizability.
MATH 888 - Complex Analysis
Credits:
3.00
Complex functions, sequences, limits, differentiability and
Cauchy-Riemann equations, elementary functions, Cauchy's
theorem and formula, Taylor's and Laurent's series,
residues, conformal mapping. Prereq: MATH 867.
MATH 896 - Topics
Credits:
3.00
New or specialized courses not covered in regular course
offerings. Prereq: permission. May be repeated up to
6 credits.
MATH 898 - Master's Project
Credits:
1.00 to 6.00
May be repeated to a maximum of 6 credits. IA (continuous
grading).
MATH 899 - Master's Thesis
Credits:
1.00 to 6.00
Credit/Fail.
MATH #901 - An Introduction to Programming and the Internet for Teachers
Credits:
3.00
An introductory course covering the basics of programming
using Java applets on the internet that can be used as
mathematics teaching tools. Topics include programming
concepts and techniques, the definition and use of classes
and basic graphical user interface components. Necessary
internet topics will also be covered, such as the World Wide
Web and the HTML.
MATH 903 - Higher Algebra for Teachers
Credits:
3.00
The integers, integral domains, and topics from number
theory; equivalence relations and congruences; real numbers,
complex numbers, fields, and polynomials; group theory;
matrix theory; vectors and vector spaces; rings; Boolean
algebra.
MATH 904 - Higher Algebra for Teachers
Credits:
3.00
See description for MATH 903.
MATH 905 - Higher Geometry for Teachers
Credits:
3.00
Systems of postulates of various geometries; geometric
invariants; synthetic and analytic projective geometry; an
introduction to non-Euclidean geometry and topology.
MATH 906 - Higher Geometry for Teachers
Credits:
3.00
See description for MATH 905.
MATH 907 - Higher Analysis for Teachers
Credits:
3.00
The real number system; functions and limits; elements of
set theory; numerical sequences and series; continuity; the
derivative and the Riemann integral; maxima and minima.
MATH 908 - Higher Analysis for Teachers
Credits:
3.00
See description for MATH 907.
MATH 909 - Probability and Statistics for Teachers
Credits:
3.00
Permutations and combinations; finite sample spaces; random
variables; binomial distributions; statistical applications.
MATH 910 - Mathematics Education
Credits:
1.00 to 4.00
Current developments and issues in mathematics education;
content, curricula, methods, and psychology of teaching
mathematics.
MATH #911 - Technology in Teaching Mathematics
Credits:
3.00
Consideration of the role of technology in teaching
mathematics; preparation of classroom materials for
Macintosh and IBM; exchange of ideas and software.
MATH 912 - Exploring Data and Planning Investigations
Credits:
3.00
Covers basic concepts and methodologies behind exploratory
statistics and design of experiments, and provides
background for teaching AP statistics. Graphical displays,
distributions, summary measures and their distributions,
confidence intervals, hypothesis tests, factorial and
fractional factorial designs, randomization, blocking,
response surface methods. JMP software will be used
extensively.
MATH 914 - Topology for Teachers
Credits:
3.00
Fundamental concepts of elementary topology; network and
map problems; sets, spaces, and transformations.
MATH 916 - Theory of Numbers for Teachers
Credits:
3.00
Divisibility and primes; congruences; quadratic reciprocity;
number theoretic functions; Diophantine equations; perfect
and amicable numbers.
MATH 917 - Mathematical Proof and Problem Solving
Credits:
3.00
Introduction to abstract mathematics with an emphasis on
problem solving and proof structure, methods and techniques.
Content includes logic, set theory and basic number theory.
MATH #919 - Real Number System
Credits:
3.00
A postulational approach to fundamentals of algebraic
structure; sequences, limits, and continuity.
MATH 920 - History of Mathematics
Credits:
3.00
A problem-study approach to mathematical problems from the
period of Greek mathematics until the modern era.
MATH #921 - A Modern Approach to Geometry
Credits:
3.00
The foundations and development of Euclidean geometry, with
emphasis on the recent recommendations in the field of
high school geometry.
MATH 925 - Problem Solving Seminar
Credits:
3.00
A study of variety of problem solving strategies and
techniques in the context of solving mathematical problems.
Problems will emphasize the connections between the core
areas of algebra, geometry and analysis. Other mathematical
topics may be included. Typically taken in conjunction with
the Concluding Experience Problem Set. Credit/Fail.
MATH 928 - Selected Topics in Mathematics for Teachers
Credits:
1.00 to 3.00
New or specialized topics not covered in the regular course
offerings. May be repeated for credit.
MATH 929 - Directed Reading
Credits:
3.00
A directed reading project on a selected topic in
mathematics or mathematics education, planned in
collaboration with a faculty member. May be repeated up to
6 credits.
MATH 931 - Mathematical Physics
Credits:
3.00
Complex variables, differential equations, asymptotic
methods, integral transforms, special functions, linear
vector spaces and matrices, Green's functions, and
additional topics selected from integral equations,
variational methods, numerical methods, tensor analysis,
and group theory. Prereq: differential equations; linear
algebra; multidimensional calculus. (Also offered as
PHYS 931.)
MATH 932 - Mathematical Physics
Credits:
3.00
Complex variables, differential equations, asymptotic
methods, integral transforms, special functions, linear
vector spaces and matrices. Green's functions, and
additional topics selected from integral equations,
variational methods, numerical methods, tensor analysis,
and group theory. Prereq: differential equations; linear
algebra; multidimensional calculus. (Also offered as
PHYS 932.)
MATH 951 - Algebra I
Credits:
3.00
Groups and their homomorphisms, products and sums, structure
of groups; rings and their homomorphisms, ideals,
factorization properties. Prereq: MATH 861.
MATH 952 - Algebra II
Credits:
3.00
Field extensions; Galois theory; module theory. Prereq:
MATH 951.
MATH 953 - Analysis I
Credits:
3.00
Measurable spaces and functions, measures, Lebesque
integrals, convergence theorems. Prereq: MATH 867.
MATH 954 - Analysis II
Credits:
3.00
Cauchy theory and local properties of analytic functions,
Riemann mapping theorem, representation theorems, harmonic
functions. Prereq: MATH 888.
MATH 955 - Topology I
Credits:
3.00
Subspace, product, and quotient topologies; embedding;
separation and countability axioms; connectedness;
compactness and compactifications; paracompactness,
metrization, and metric completions. Prereq: MATH 884.
MATH #956 - Topology II
Credits:
3.00
Chain complexes; homology of simplicial complexes, singular
homology and cohomology; axiomatic homology; cup and cap
products. Prereq: MATH 861 and 884.
MATH 958 - Foundations of Math Education
Credits:
3.00
Topics will include: major issues, trends, and programs in
mathematics education research, the research process,
theoretical perspectives to guide research, the profession
and infrastructure of mathematics education, cultural and
historical aspects of mathematics education, and the
research-practice interface. Examples span the K-16
spectrum. Prereq: permission.
MATH 961 - Topics in Algebra I
Credits:
3.00
An introduction to topics chosen from algebra and number
theory. Prereq: MATH 951-952. May be repeated.
MATH 963 - Functional Analysis
Credits:
3.00
Banach and Hilbert spaces, Hahn-Banach theorem, open mapping
and closed graph theorems, dual spaces, topological vector
spaces. Prereq: MATH 953.
MATH 964 - Topics in Analysis I
Credits:
3.00
An introduction to topics in analysis. Prereq: permission.
May be repeated.
MATH #965 - Topics in General Topology I
Credits:
3.00
An introduction to topics in general topology. Prereq:
MATH 955. May be repeated.
MATH #966 - Topics in Algebraic Topology I
Credits:
3.00
An introduction to topics in algebraic topology. Prereq:
MATH 956. May be repeated.
MATH 967 - Topics in Applied Mathematics I
Credits:
3.00
An introduction to topics in applied mathematics. Prereq:
permission. May be repeated.
MATH 968 - Topics in Mathematics Education I
Credits:
3.00
A) The Teaching and Learning of Mathematics; B) Curriculum
and History in Mathematics Education. Topics selected from:
epistemologies of knowledge applied to mathematics; theories
of learning and teaching mathematics; theoretical
perspectives in research; mathematics education research
programs K-16; research methods for studying mathematics
teaching, learning, and curricula; theoretical frameworks
for curriculum development, implementation of new curricula,
and research on curricula; historical perspectives of
research in mathematics education; the evolution and history
or K-16 mathematics curricula both in United States and
internationally. Versions A and B offered alternately.
Prereq: MATH 958 or permission. May be repeated.
MATH 969 - Topics in Probability and Statistics I
Credits:
3.00
Selected advanced topics from one or several of the
following areas: probability, stochastic processes, design
of experiments, biostatistics, Bayesian theory and methods,
spatial and spatio-temporal statistics, time series
analysis, nonparametric statistics. Prereq: permission. May
be repeated.
MATH #971 - Topics in Algebra II
Credits:
3.00
An introduction to advanced topics chosen from algebra and
number theory. Prereq: MATH 951-952; permission. May be
repeated.
MATH 973 - Topics in Operator Theory
Credits:
3.00
Selected topics in operator theory. Prereq: MATH 963. May be
repeated.
MATH 977 - Topics in Applied Mathematics II
Credits:
3.00
An exploration of an area of research in applied
mathematics. Prereq: permission. May be repeated.
MATH 978 - Topics in Mathematics Education II
Credits:
3.00
An exploration of an area of research in mathematics
education. Prereq: permission. May be repeated.
MATH 979 - Research Topics in Statistics
Credits:
3.00
An exploration of the main statistical issues and
computational methods associated with research problems
from such areas as survival analysis, reliability,
latitudinal data, categorical data, spatio-temporal data,
and industrial processes. Student term projects require:
literature searches, presentation, use of modern statistical
software, and written reports. Prereq: permission. May be
repeated.
MATH 998 - Reading Courses
Credits:
1.00 to 6.00
A) Algebra; B) Analysis; C) Operator Theory; D) Geometry;
E) General Topology; F) Algebraic Topology; G) Applied
Mathematics; H) Mathematics Education; I) Probability and
Statistics. Prereq: permission.
MATH 999 - Doctoral Research
Credits: