| Mathematics |
MATH 835 - Statistical Methods for Researchers
Credits:
3.00
Emphasis is on applications of statistical methods andx Emphasis is on applications of statistical methods and conc
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
Introduces scientific data collection and analysis with an
emphasis on industrial and service provider applications.
Topics include descriptive and graphical statistical
methods, confidence intervals and hypothesis testing,
regression, ANOVA, statistical process control (SPC),
failure modes and effects analysis (FMEA), Six-Sigma
concepts and methods, introduction to reliability, quality
tools, MSA, and process capability studies, introduction to
Lean methodology, such as 5S, Kaizen, and VSM. Use of a
statistical software package is an integral part of the
course. Prereq: basic introductory statistics.
MATH 839 - Applied Regression Analysis
Credits:
3.00
Statistical methods for the analysis of relationships
between response and input variables: simple linear
regression, residual analysis model selection,
multicollinearity, nonlinear curve fitting, categorical
predictors, introduction to analysis of variance,
examination of validity of underlying assumptions.
Emphasizes real applications with use of statistical
software. Prereq: basic introductory statistics.
MATH 840 - Design of Experiments I
Credits:
3.00
First course in design of experiments with applications to
quality improvement in industrial manufacturing,
engineering research and development, or research in
physical and biological sciences. Experimental factor
identification, statistical analysis and modeling of
experimental results, randomization and blocking, full
factorial designs, random and mixed effects models,
replication and subsampling strategies, fractional
factorial designs, response surface methods, mixture
designs, and screening designs. Focuses on various
treatment structures for designed experimentation and the
associated statistical analyses. Use of statistical
software. Prereq: basic introductory statistics; permission.
MATH 841 - Survival Analysis
Credits:
3.00
Explorations of models and data-analytic methods used in
medical, biological, and reliability studies. Event-time
data, censored data, reliability models and methods,
Kaplan-Meier estimator, proportional hazards, Poisson
models, loglinear models.
Suitable statistical software,
such as SAS, JMP, S-Plus, or R, are used. Prereq: basic
introductory statistics. (Offered in alternate years.)
MATH 842 - Multivariate Statistics and Modern Regression Methods
Credits:
3.00
Introduces statistical methods for multivariable data,
including exploratory analyses of high-dimensional
observations, data mining and pattern recognition. Random
vectors and matrices, multivariate normal distribution,
multivariate analysis of variance (MANOVA), repeated
measures analysis, dimension reduction methods: principal
components, factor analysis, canonical correlation.
Statistical learning and data mining. Supervised learning:
classification and regression with CART and neural nets.
Unsupervised learning: clustering, multidimensional
scaling.
Prereq: basic introductory statistics. (Offered
in alternate years.)
MATH 844 - Design of Experiments II
Credits:
3.00
Second course in design of experiments, with applications
in quality improvement and industrial manufacturing,
engineering research and development, research in physical
and biological sciences. Covers experimental design
strategies and issues that are often encountered in
practice complete and incomplete blocking, partially
balanced incomplete blocking (PBIB), partial confounding,
intra and inter block information, split plotting and strip
plotting, repeated measures, crossover designs, Latin
squares and rectangles, Youden squares, crossed and nested
treatment structures, variance components, mixed effects
models, analysis of covariance, optimizations, space
filling designs, and modern screening design strategies.
Prereq: MATH 840; 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
Introduces the basic principles and methods of statistical
estimation and model fitting. One- and two-sample
procedures, consistency and efficiency, likelihood methods,
confidence regions, significance testing, Bayesian
inference, nonparametric and resampling methods, decision
theory. Prereq: MATH 855; or permission.
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,
integrability.
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 sets, 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). Cr/F.
MATH 899 - Master's Thesis
Credits:
1.00 to 6.00
May be repeated up to a maximum of 6 credits. Cr/F.
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 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 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. Cr/F
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:
1.00 to 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 941 - Bayesian and Computational Statistics
Credits:
3.00
Current approaches to Bayesian modeling and data analysis
and related statistical methodology based on computational
simulation. Fundamentals of Bayesian estimation and
hypothesis testing. Multi-level and hierarchical Bayesian
modeling for correlated data. Introduction to Markov chain
Monte Carlo based estimation approaches such as the Gibbs
sampler and the Metropolis-Hastings alogrithm. Prereq:
knowledge of intermediate statistics: distributions,
discrete and continuous random variables, transformation of
variables (calculus based), bivariate and multivariate
normal distribution, maximum likelihood estimation; working
knowledge of linear regression and analysis of variance;
basic linear algebra: vectors and matrices, linear spaces,
matrix multiplication, inverse of a matrix, positive
definiteness. Matrix-vector notation for linear regression
and ANOVA.
MATH 942 - Beyond ANOVA: Generalized Linear and Semiparametric Smoothing Methods
Credits:
3.00
Regression model fitting beyond the linear regression and
ANOVA framework. Introduction to generalized linear models
for categorical data, logistic and Poisson regression.
Scatterplot smoothing methods. Spline bases for linear
regression: natural and B-splines, truncated polynomial
splines. Regularization by smoothing splines. Selection by
cross validation and by mixed effects modeling. Application
to multivariable predictor situation; additive and
generalized additive models, interaction and varying
coefficient models. Prereq: Intermediate statistics
including basics of maximum likelihood estimation; linear
regression modeling including familiarity with matrix
notation, basic concepts of calculus including partial
derivatives.
MATH 944 - Spatial Statistics
Credits:
3.00
Frequentist and Bayesian methods for estimation of
characteristics measured in space (usually 2-dimensional
Euclidean space). Spatial averaging. Spatial point
processes: models for clustering and inhibition. Cluster
detection. Point referenced data: varigram estimation,
Kriging, spatial regression. Lattice based data: spatial
autoregression, Markov random field models. Spatial
regression models. Non-Gaussian response variables.
Hierarchical Bayesian spatial models and Markov chain Monte
Carlo methods. Multivariable spatial models. Prereq:
Intermediate statistics including basics of maximum
likelihood estimation; linear regression modeling including
familiarity with matrix notation, basic concepts of
calculus including partial derivatives.
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, Lebesgue
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:
Cr/F.