625.401 Real Analysis
Instructor: Stacy D. Hill
Time and location: Thursdays, 7:15 − 10:00PM, Applied
Physics Laboratory (southern Howard County)
This course presents a rigorous treatment of fundamental
concepts in analysis. Emphasis is placed on careful reasoning and proofs. Topics
covered include the completeness and order properties of real numbers; limits
and continuity; conditions for integrability and differentiability; infinite
sequences and series. Basic notions of topology and measure are also introduced.
Prerequisite: Multivariate calculus
Instructor: Sue-Jane Wang
Time and location: Tuesdays, 4:30 − 7:10PM, Montgomery
County Center (Rockville, MD)
This course introduces commonly used statistical
techniques. The intent of this course is to provide an understanding of
statistical techniques and a tool box of methodologies. Statistical software is
used so students can apply statistical methodology to practical problems in the
workplace. Intuitive developments and practical use of the techniques are
emphasized rather than theorem/proof developments. Topics include the basic laws
of probability and descriptive statistics, conditional probability, random
variables, expectation, discrete and continuous probability models, joint and
sampling distributions, hypothesis testing, point estimation, confidence
intervals, contingency tables, logistic regression, and linear and multiple
regression .
Prerequisite: Multivariate calculus.
Instructor: Ronald Farris
Time and location: Wednesdays, 7:15 − 10:00PM, Applied
Physics Laboratory (southern Howard County)
Topics discussed throughout the course include methods of
solving first -order differential equations, existence and uniqueness theorems,
second-order linear equations, power series solutions, higher-order linear
equations, systems of equations, non-linear equations, Sturm-Liouville theory,
and applications.
Prerequisite: Two or more terms of calculus
Instructor: J. Miller Whisnant
Time and location: Tuesdays, 4:30 − 7:10PM, Applied
Physics Laboratory (southern Howard County)
Combinatorics and discrete mathematics are increasingly
important fields of mathematics because of their extensive applications in
computer science, statistics, operations research, and engineering. The purpose
of this course is to teach students to model, analyze, and solve combinatorial
and discrete mathematical problems. Topics include elements of graph theory,
graph coloring and covering circuits, the pigeonhole principle, counting
methods, generating functions, recurrence relations and their solution, and the
inclusion-exclusion formula. Emphasis is on the application of the methods to
problem solving.
Prerequisite: Two or more terms of calculus.
625.438 Neural Networks
Instructor: J. Miller Whisnant
Time and location: Mondays, 4:30 − 7:10PM, Applied Physics
Laboratory (southern Howard County)
This course provides an introduction to concepts in neural
networks and connectionist models. Topics include parallel distributed
processing , learning algorithms, and applications. Specific networks discussed
include Hopfield networks, bidirectional associative memories, perceptrons,
feedforward networks with back propagation, and competitive learning networks,
including self-organizing and Grossberg networks. Software for some networks is
provided.
Prerequisite: Multivariate calculus.
625.462 Design and Analysis of Experiments
Instructor: Jacqueline K. Telford
Time and location: Tuesdays, 7:15 − 10:00PM, Applied
Physics Laboratory (southern Howard County)
Statistically designed experiments are the efficient
allocation of resources to maximize the amount of information obtained with a
minimum expenditure of time and effort. Design of experiments is applicable to
both physical experimentation and computer simulation models. This course covers
the principles of experimental design, the analysis of variance method, the
difference between fixed and random effects and between nested and crossed
effects, and the concept of confounded effects. The designs covered include
completely random, randomized block, Latin squares , split-plot, factorial,
fractional factorial, nested treatments and variance component analysis,
response surface, optimal, Latin hypercube, and Taguchi. Any experiment can
correctly be analyzed by learning how to construct the applicable design
structure diagram (Hasse diagrams).
Prerequisites: Multivariate calculus, linear algebra, and
one semester of graduate probability and statistics (e.g. 625.403 Statistical
Methods and Data Analysis). Some computer-based homework assignments will be
given.
625.726 Theory of Statistics II
Instructor: Mostafa Aminzadeh
Time and location: Mondays, 4:30 − 7:10PM, Applied Physics
Laboratory (southern Howard County)
This course is the continuation of 625.725. It covers
method of moments estimation, maximum likelihood estimation, the Cramér- Rao
inequality , sufficiency and completeness of statistics, uniformly minimum
variance unbiased estimators, the Neyman-Pearson Lemma, the likelihood ratio
test , goodness-of-fit tests, confidence intervals, selected non-parametric
methods, and decision theory.
Prerequisite: 625.725 Theory of Statistics I or equivalent
625.734 Queuing Theory with Applications to Computer
Science
Instructor: Eric Blair
Time and location: Wednesdays, 4:30 − 7:10PM, Applied
Physics Laboratory (southern Howard County)
Queues are a ubiquitous part of everyday life; common
examples are supermarket checkout stations, help desks call centers,
manufacturing assembly lines, wireless communication networks, and multi-tasking
computers. Queuing theory provides a rich and useful set of mathematical models
for the analysis and design of service process for which there is contention for
shared resources. This course explores both theory and application of
fundamental and advanced models in this field. Fundamental models include single
and multiple server Markov queues, bulk arrival and bulk service processes, and
priority queues. Applications emphasize communication networks and computer
operations , but may include examples from transportation, manufacturing, and the
service industry. Advanced topics may vary.
Prerequisites: Multivariate calculus and knowledge of
probability.
625.743 Stochastic Optimization and Control
Instructor: James C. Spall
Time and location: Thursdays, 4:30 − 7:10PM, Applied
Physics Laboratory (southern Howard County)
Stochastic optimization plays an increasing role in the
analysis and control of modern systems . This course introduces the fundamental
issues in stochastic learning and optimization with special emphasis on cases
where classical deterministic search techniques (steepest descent, Newton-Raphson,
linear and nonlinear programming, etc.) do not readily apply. These cases
include many important practical problems, which will be discussed throughout
the course (e.g. neural network training, nonlinear control, experimental
design, simulation-based optimization, sensor configuration, image processing,
discrete-event systems, etc.). Both global and local optimization problems will
be considered. Techniques such as random search, stochastic approximation,
simulated annealing, evolutionary computation (including genetic algorithms),
and machine learning are discussed.
Prerequisites: Multivariate calculus, linear algebra, and
at least one semester of graduate probability and statistics (e.g. 625.403
Statistical Methods and Data Analysis). Some computer-based homework assignments
will be given. It is recommended that this course be taken in the last half of a
student's degree program for those seeking an M.S. degree.
625.251 Applied Mathematics II (this course is not
offered for graduate credit)
Instructor: James D’Archangelo
Time and location: Wednesdays, 7:15 − 10:00PM, Applied
Physics Laboratory (southern Howard County)
(This course is a companion to 625.250, but 625.250 is not
a prerequisite) Topics include ordinary differential equations , Fourier series
and integrals, the Laplace transformation, Bessel functions and Legendre
polynomials , and an introduction to partial differential equations.
Prerequisites: Differential and integral calculus.
Students with no experience in linear algebra may find it helpful to take
625.250 Applied Mathematics I first.
