In addition to the Ph.D. and Masters degrees, SCS also offers a separate Certificate in Computational Techniques and Applications which affords students an opportunity to improve their basic computational skills. The Certificate is independent of the doctoral program and is designed primarily for technical professionals, but it also provides prospective and currently enrolled Ph.D. students with a useful intermediate step before undertaking the dissertation.

The Certificate in Computational Techniques and Applications is composed of 15 credit hours of coursework designed to provide an accelerated introduction to concepts in modern computation. Topics covered include operating systems, environments, languages, and applications. The Certificate is designed to provide graduate students (M.S. or Ph.D.) and working professionals with the tools and techniques to solve computational problems in science, mathematics, or engineering. It is intended for:

1. - Scientists and/or Engineers employed by local industry or government who wish to upgrade their knowledge of state-of-the-art computing techniques,

2. - Masters students in any Physical Science, Mathematics and/or Applied Mathematics (Statistics, Operations Research) who seek exposure to the latest computing methodologies,

3. - Masters students in Computer Science, Engineering, and/or Information Technology who wish to incorporate a Scientific Application Domain into their studies,

4. - Doctoral students in either Computational Sciences and Informatics, Environmental and Public Policy, or Information Technology who need to improve their computing abilities.

The Certificate is flexible enough to permit a program tailored to these various audiences.

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1. All applicants to the Certificate Program should have an undergraduate degree in either science, mathematics, or engineering, with a GPA of at least 3.00 in their last 60 credits of study.

2. All applicants to the Certificate program should also have a mathematics background up to and including Differential Equations. All applicants to the Certificate program should also have at least one course in Computer Science that includes programming concepts.

3. Applicants should submit the followings materials:

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The certificate requires a total of 15 credit hours distributed in the following way:

1. The TOOLS courses are practical, skill-based courses covering specific software packages commonly used by scientists and engineers to solve problems. Depending on the student's background, one to six credit hours of TOOLS courses are required. Students are advised to take no more than 4 credits of TOOLS courses in a single semester.

2. The TECHNIQUES courses are designed to cover algorithms and methodologies used to develop software and utilize packages to solve problems. Two 3-credit TECHNIQUES courses are required.

3. The APPLICATIONS courses provide content from a specific scientific domain and demonstrate the utilization of computational techniques within that context. These courses are electives that can be selected from several concentration areas as explained below. One 3-credit APPLICATIONS course is required.

Special course schedules may be designed depending upon the background and qualifications of the student. For example, some (or all) of the tool and techniques courses may be waived if the equivalent knowledge can be adequately demonstrated by the student. The waived credits are to be replaced with applications courses from the list given below.

The recommended course sequence is tools, techniques, applications.

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Note: CSI doctoral students may not apply credits earned in the courses CSI 600-610 towards their 48 hour doctoral course requirement.

TOOLS COURSES (1-6 credit hours as needed)

Courses in this category are one credit mini-courses on the basic tools used in scientific computation. These courses are designed for professionals who are already familiar with other languages, packages, and operating systems, but need a rapid introduction to specific software and mathematical methods used by scientists and engineers. Some of these courses may be offered via the World Wide Web in a distance-learning format. Students are advised to take no more than 4 credits of TOOLS courses in a single semester.

CSI 601 - Computational Science Tools I
Prerequisites: A course in computer science, and knowledge of a programming language, or permission of instructor. Introduction to basic tools in computational science. Covers UNIX, editors, LaTeX, HTML, and graphics. Emphasizes application and use rather than theory. Substantial portion of instruction is delivered via a distance-learning Web interface. (1 credit)

CSI 602 - Computational Science Tools II
Prerequisites: CSI 601 or permission of instructor. Introduction to basic tools in computational science. Covers MATLAB, MAPLE, and GNUPlot. Emphasizes application and use rather than theory. Substantial portion of instruction is delivered via a distance-learning Web interface. (1 credit)

CSI 603 - Introduction to Scientific Programming I
Prerequisites: CSI 601 or permission of instructor. Introduction to programming in C or Fortran. Emphasizes application and languages rather than theory. Features a combination of lecture and lab. Assignments are complete via a distance-learning Web interface. (1 credit)

CSI 604 - Introduction to Scientific Programming II
Prerequisites: CSI 601 and 603 or permission of instructor. Introduction to programming in an object-oriented language such as C++. Features a combination of lecture and lab. (1 credit)

CSI 605 - Software Construction Tools for Scientists
Prerequisites: CSI 601, 603, 604 or programming experience with C, C++, or Fortran and familiarity with the UNIX operating system; or permission of instructor. Introduction to the tools commonly used for software construction and development. Covers revision control, debuggers, profilers, Makefiles, and regular expressions. Designed for students who wish to develop moderate to large software systems and need an introduction to the basic tools used in construction. (1 credit)

CSI 606 - Scientific Graphics and Visualization Tools
Prerequisites: CSI 601 or permission of instructor. Introduction to the use of scientific visualization tools for data analysis. Use of specific packages will be taught on a rotating basis. Packages include PV-WAVE, S-Plus, SV, XMGR, and the pnm tools. (1 credit)

CSI 607 - Database Tools for Scientists
Prerequisites: CSI 601 and 602 or permission of instructor. Introduction to database tools. Teaches the student how to deal with the relation model, on which database packages like Oracle are based. Under this language, database design concepts, table operations, triggers, sequences, and introduction to simple query language (SQL) will be covered. (1 credit)

TECHNIQUES COURSES (minimum 6 credit hours)

CSI 600 - Quantitative Foundations of Computational Sciences
Prerequisites: MATH 213 and 214. Accelerated review of mathematical tools for scientific applications and analysis. Topics include vectors and matrices; differential and difference equations; linear systems; Fourier, Laplace, and Z-transforms and probability theory. (3 credits)

CSI 610 - Introduction to Computational Sciences
Prerequisites: CSI 601, 602, 603, 604, 605, and 700 or permission of instructor. Covers advanced numerical methods, computer architecture, and scientific software development. Includes software design, construction, and validation techniques commonly used in industry. Also serves as an introduction to high-performance computing. (3 credits) Note: CSI 610 comprises the same lectures as CSI 701, minus the group project. Students who may be considering the CSI Ph.D. program are therefore advised to take CSI 701 because that course counts towards the 48-credit Ph.D. curriculum requirement whereas CSI 610 does not.

CSI 700/MATH 685 - Numerical Methods
Prerequisites: MATH 214, 203, and some programming experience. Covers computational techniques for the solution of problems arising in science and engineering. Algorithms are developed for the treatment of typical problems in applications, with special emphasis on the types of data encountered in practice. The course covers theoretical development, as well as implementation, efficiency, and accuracy issues in using algorithms and interpreting the results. When applicable, computer graphical techniques are used to enhance interpretation of results. (3 credits)

APPLICATIONS COURSES (minimum 3 credit hours)

Students may choose one three-credit CSI course to complete the certificate. The course is selected from one of the three application areas indicated below:

Visualization and Data Mining:

CS 652 - Computer Graphics
CSI 758 - Visualization and Modeling of Complex Systems
CSI 771/STAT 751- Computational Statistics
CSI 773/STAT 663 - Statistical Graphics and Data Exploration
CSI 703/INFT 875 - Scientific Visualization
CSI 710/INFS 714 - Scientific Databases
CSI 904 - Workshop on Molecular Graphics (one credit)

Physical Simulations:

CSI 721/CSI 722 - Computational Fluid Dynamics
CSI 734 - Computational Neurobiology
CSI 753 - Global Change V: Observational Methods
CSI 761/ASTR 761 - N-body Methods and Particle Simulations
CSI 764/ASTR 764 - Computational Astrophysics
CSI 780/PHYS 613 - Computational Physics and Applications
CSI 783/PHYS 736 - Computational Quantum Mechanics
CSI 786 - Molecular Dynamics Modeling
CSI 788/PHYS 728 - Simulation of Large-Scale Physical Systems

Applied Mathematics:

Copyright School of Computational Sciences, George Mason University, Fairfax, VA, USA
Last modified: December 28, 2005

Please send questions or comments to Dr. Peter A. Becker at  pbecker@gmu.edu

Graphic design: Janejira Kalsmith
Programming: Guido Cervone an d Liviu Panait