**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

requirements and course content, please contact Dr. James Spall, Program Chair, 240-228-4960.

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.

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.

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).

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

readings and homework.

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.

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

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.

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.

offered 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.

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.