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# The Applied and Computational Mathematics (ACM) Program

The Applied and Computational Mathematics (ACM) Program at the Johns
Hopkins University will offer the graduate courses listed below in the fall
semester (6 September 2006 to 16 December 2006) at locations in the
Baltimore−Washington area (Howard and Montgomery Counties, Maryland).

Subject to meeting admission criteria, a non-degree candidate may register as a special
student to take one or more courses to enhance mathematical and statistical skills. These
courses are scheduled at times convenient for the working adult.
For further information related to academic

625.403 Statistical Methods and Data Analysis
Instructor: Allan McQuarrie
Time and location: Thursdays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
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.

625.405 Introduction to Optimization
Instructor: David Hutchison
Time and location: Tuesdays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
This course is an introduction to the theory and practical techniques needed to solve
deterministic linear and non-linear problems. The linear programming portion of the course
includes a discussion of the simplex method, duality theory, sensitivity analysis, network
flow, and project scheduling. Mathematical models for these and for extensions to integer
programming and to certain nonlinear programs will be developed. Students will become
familiar with the use of spreadsheets and an algebraic modeling language as development
tools. No previous familiarity with the software is assumed. Constrained and unconstrained
nonlinear optimization problems with an emphasis on gradient methods and Kuhn-Tucker
conditions will also be discussed.
Prerequisite: Multivariate calculus.

625.409 Matrix Theory
Instructor: Matthew Koch
Time and location: Wednesdays, 4:30 − 7:10PM, Applied Physics Laboratory (southern
Howard County)
In this course, topics include the methods of solving linear equations, Gaussian elimination,
triangular factors and row exchanges, vector spaces (linear independence, basis,
dimension, and linear transformations), orthogonality (inner products, projections, and
Gram-Schmidt process), determinants, eigenvalues and eigenvectors (diagonal form of a
matrix, similarity transformations, and matrix exponential), singular value decomposition,
and the pseudoinverse. The course also covers applications to statistics (least squares
fitting to linear models, covariance matrices) and to vector calculus (gradient operations and
Jacobian and Hessian matrices). Matlab software will be used in some class exercises.
Prerequisite: Multivariate calculus.

625.423 Introduction to Operations Research: Probabilistic Models
Instructor: Eric Blair
Time and location: Thursdays, 4:30 − 7:10PM, Applied Physics Laboratory (southern
Howard County)
This course provides an introduction to some of the more useful OR models that exploit
basic concepts and principles of probability and statistics. Although the course is organized
around mathematical models and methods, the focus is on practical solutions to real
operational problems; sufficient theory is provided to develop understanding of fundamental
results. Topics may vary, being selected from the fields of Markov chains, queueing theory,
decision theory, Bayesian networks, reliability and maintenance, activity networks, Markov
decision processes, and inventory theory.
Prerequisites: Multivariate calculus and a first course in probability and statistics (such as
625.403).

625.480 Cryptography
Instructor: George Nakos
Time and location: Wednesdays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
An important concern in the information age is the security, protection, and integrity of
electronic information, including communications, electronic funds transfer, power system
control, transportation systems, and military and law enforcement information. Modern
cryptography, in applied mathematics, is concerned not only with the design and exploration
of encryption schemes (classical cryptography) but with the rigorous analysis of any system
that is designed to withstand malicious attempts to tamper with, disturb, or destroy it. This
course introduces and surveys the field of modern cryptography. After mathematical
preliminaries from probability theory, algebra, computational complexity, and number
theory, we will explore the following topics in the field: foundations of cryptography, public
key cryptography, probabilistic proof systems, pseudorandom generators, elliptic curve
cryptography, and fundamental limits to information operations.
Prerequisites: Linear algebra and an introductory course in probability and statistics such as
625.403 Statistical Methods and Data Analysis.

625.490 Computational Complexity and Modern Computing
Instructor: Mark Fleischer
Time and location: Tuesdays, 7:15 − 10:00PM, Montgomery County Center (Rockville, MD)
This course will cover the basic issues of computational complexity, with a focus on
applications that require novel computational methods. We will start with a discussion of
algorithm complexity and NP-completeness. Issues related to complex and high-
dimensional data, including the curse of dimensionality, will be studied in some detail. We
will also look at novel computing techniques, such as quantum and molecular computing,
which may be the computational tools of the future. The lectures will be enhanced through
Prerequisites: A graduate course in probability and statistics such as 625.403. Students
should also be familiar with basic linear algebra and have a strong interest in mathematics
and computation.

625.717 Advanced Differential Equations: Partial Differential Equations
Instructor: David Han
Time and location: Thursdays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
This course presents practical methods for solving partial differential equations (PDEs). The
course covers solutions of hyperbolic, parabolic and elliptic equations in two or more
independent variables. Topics include Fourier series, separation of variables, existence and
uniqueness theory for general higher order equations, eigenfunction expansions, finite
difference and finite element numerical methods, Green's functions, and transform
methods. MATLAB, a high level computing language, is used throughout the course to
complement the analytical approach and to introduce numerical methods.
Prerequisites: 625.404 Ordinary Differential Equations or equivalent graduate course in
differential equations. Course in linear algebra would be helpful

625.725 Theory of Statistics I
Time and location: Mondays, 4:30 − 7:10PM, Applied Physics Laboratory (southern Howard
County)
This course covers mathematical statistics and probability. Topics covered include discrete
and continuous probability distributions, expected values, moment-generating functions,
sampling theory, convergence concepts, and the central limit theorem. This course is a
rigorous treatment of statistics that lays the foundation for 625.726 and other advanced
courses in statistics.
Prerequisites: Multivariate calculus and 625.403 Statistical Methods and Data Analysis or
equivalent.

625.775 Data Mining
Instructor: Peter Fitton and Peter Close
Time and location: Mondays, 7:15 − 10:00PM,, Applied Physics Laboratory (southern
Howard County)
Data mining has become very important in corporate decision making, and is becoming
increasingly important in government. With the advent of large data warehouses,
organizations have access to huge quantities of potentially valuable data that they would
like to mine in order to produce business intelligence. This course provides an advanced
introduction to the theory and practice of data mining. The emphasis of the course will be on
the following topics: opportunity identification, estimating the value of a data mining solution,
process standards for data mining, mathematical problem formulation, complexity control
and Vapnik-Chervonenkis theory, optimization algorithms, data and dimensionality
reduction techniques, regression methods, and predictive classification. Techniques
referenced will include classical statistical approaches, neural networks, decision trees, and
local smoothing methods. These concepts will be introduced through lectures, readings,
applied problem solving, and a major project. Most of the examples to illustrate these
applications will come from banking, insurance, and direct marketing.
Prerequisites: Multivariate calculus, familiarity with linear algebra and matrix theory (e.g.,
625.409) and a course in statistics (such as 625.403). This course will also assume basic
familiarity with multiple linear regression and basic ability to program in MATLAB,
FORTRAN, or other programming language. Computer-based homework assignments will
be given. Students are encouraged to contact the instructor for additional information.

The following courses provide mathematical background and review and are not

625.250 Applied Mathematics I (not for graduate credit)
Instructor: James D’Archangelo
Time and location: Wednesdays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
This course covers the fundamental mathematical tools required in applied physics and
engineering. The goal is to present students with the mathematical techniques used in
engineering and scientific analysis and to demonstrate these techniques by the solution of
relevant problems in various disciplines. Areas include vector analysis, linear algebra,
matrix theory, and complex variables.
Prerequisites: Differential and integral calculus.

625.260 Introduction to Linear Systems (not for graduate credit)
Instructor: Janet Effler
Time and location: Mondays, 7:15 − 10:00PM, Applied Physics Laboratory (southern
Howard County)
This course is designed for students who do not have a bachelor’s degree in electrical
engineering. This course provides prerequisite material needed before entering many of the
systems and telecommunications courses offered in the Master of Science in Electrical
Engineering program. Topics include signal representations, linearity, time-invariance,
convolution, and Fourier series and transforms. Coverage includes both continuous and
discrete-time systems. Practical applications in filter design, modulation/demodulation, and
sampling are introduced.
Prerequisites: Differential and integral calculus.