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Undergraduate Studies Catalog 2001-2003

Department of Computational Science

249 Faculty Office Building
(585) 395-2021
www.cps.brockport.edu

Professor/Chair: Osman Yasar. Assistant Professors: Leigh J. Little, Robert E. Tuzun.

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Along with traditional experimental and theoretical methodologies, advanced work in all areas of science and engineering has come to rely critically on computation. Computer modeling combined with visualization represents a new paradigm for scientific exploration and technological research and development. It permits a new approach to problems that were previously inaccessible.

The computational approach is used in nearly all areas of science and engineering. For example, it is used by the automotive and aerospace industries to design safe and efficient vehicles, by the pharmaceutical industry to design new drugs, by meteorologists to predict the weather and long-term climactic changes, by biologists and ecologists to study the environment and population dynamics, by economists to predict the behavior of financial systems such as the stock market, and so on. Computer modeling is used to help direct research and to study systems before they are put into production; this has saved billions of dollars and years of development time.

The Department of Computational Science has received equipment support from Intel and Silicon Graphics and works closely with local industry, particularly Xerox and Kodak. Students learn computational and mathematical skills that can be applied to a wide variety of problems. The program is flexible so as to allow students to follow their particular interests and continue, if desired, with advanced degrees. Graduates can expect employment in industry, government, business, academia, and at major research and development laboratories.

Major in Computational Science
The CPS undergraduate major requires 36 credits of the following courses from the Departments of Computational Science, Computer Science, and Mathematics and from the department of an application area of interest. Six additional credits of elective courses are required.

(a) Required Courses
Credits
  MTH 203 Calculus III
3
  MTH 243 Elementary Statistics
3
  MTH 424 Linear Algebra
3
  CSC 205 Fundamentals of Computer Science II
4
  CPS 201 Computational Tools I
3
  CPS 202 Computational Tools II
3
  CPS 303 High Performance Computing
3
  CPS 304 Simulation and Modeling
3
  CPS 404 Applied and Computational Mathematics
3
   
(b) Application Sciences (8 credits)
  200-level and higher non-CPS courses from an area of application chosen under advisement
8
   
(c) Elective Courses (6 credits)
  upper-division courses
6
  TOTAL Credits (including electives)
42
   
(d) Prerequisites:
  Calculus I and II (MTH 201 and 2026 credits)
  Discrete Mathematics I (MTH 2813 credits)
  Introduction to Computer Science (CSC 1203 credits)
  Fundamentals of Computer Science I (CSC 2034 credits)
   
Minor in Computational Science
(a) Required Courses (12 credits):
Credits
  CPS 201 Computational Tools I
3
  CPS 202 Computational Tools II
3
  CPS 303 High Performance Computing
3
  CPS 304 Simulation and Modeling
3
   
(b) Elective Courses (8 credits)
  200 and higher-level non-CPS courses
8
  TOTAL Credits (including electives)
20
   
(c) Prerequisites:
  Introduction to Computational Science (CPS 1013 credits)
  Calculus III (MTH 2033 credits)

Note: For additional and updated information on the Department of Computational Science, see the Computational Science Handbook, which is available in the Department office, 112 Faculty Office Building.

Computational Science Courses

CPS 101 Introduction to Computational Science (A,N,E). Prerequisite: MTH 121. Provides an introduction to computation as used in science and engineering. Emphasis on practical applications of formulas to real-life problems and on tools for their solution. Course content includes three distinct areas: 1) techniques (linear regression for data-fitting, determination of areas and volumes, rate changes (differentiation), use of graphical calculator), 2) programming in FORTRAN and C, 3) UNIX operating system (basic commands, editors, input/output). 3 Cr. Fall.

CPS 102 Functions and Their Uses (A). Technology-based course to serve general education to the elementary college algebra level. Modeling, using graphing calculators and software presented for non-math majors to initiate them in problem-solving processes that are an integral part of nature and society. Provides entry-level students with college algebra skills; namely to acquire facility with graphs, tables of values, linear algebraic manipulations, and a qualitative understanding of rates of change. General Education course. 3 Cr.

CPS 201 Computational Science Tools I (A). Prerequisites: CPS 101 or 120. Provides an introduction to the use of computers in science, engineering and business applications for prospective computational science, computer science, mathematics and other majors. Includes an introduction of the impact computers have on our lives; examples that help us understand how computation is recognized as a third way of doing science besides theory and experiment; examples of common applications and related industry and job market; brief introduction to high performance computing; common computation techniques in a variety of science, engineering, and business fields; examples and brief introduction to visualization as it relates to applications and the job market. Also includes topics 1) computer performance (speed), architecture and supercomputers, 2) data representation, algorithms, programming, and compiler directives (all in FORTRAN 77), 3) visualization basics. 3 Cr. Fall.

CPS 202 Computational Science Tools II (A). Prerequisite: CPS 201. Techniques and software tools commonly used in scientific computing applications. Topics include high-level programming languages such as Fortran 90 and C/C++; the UNIX operating system; general strategies for scientific computing; graphics, symbolic manipulation, and multi-purpose software packages such as MAPLE, MATLAB, and MACSYMA; numerical libraries such as BLAS, ScaLAPACK, problem solving-environments such as NetSolve, industrial benchmarks, grid-generation techniques, and communication libraries such as PVM, MPI. Applications in chemistry, physics and other fields are discussed. Extensive programming in F90 and C is required. 3 Cr. Spring.

CPS 303 High Performance Computing (A). Prerequisites: CPS 202 and MTH 203. Computational methods commonly used in scientific applications. Parallel programming strategies and general principles of scientific computing are illustrated in the context of numerical methods. Use of parallel supercomputers on the campus is covered. Computing topics to include are: modern computer architectures, understanding parallelism, evaluating benchmarks, parallel computing, language support for performance. Mathematical topics to include are: differentiation, integration, and interpolation; solution methods for linear systems; calculation of eigenvalues and eigenvectors; error analysis; data fitting, regression and smoothing. Programming is required. 3 Cr. Fall.

CPS 304 Simulation and Modeling (A). Prerequisite: CPS 303. An introduction to continuous and discrete simulation methods used in scientific applications. Includes steps required to model and simulate a system, including discussion of generic partial differential equations and governing equations, discretization of these equations (finite difference, finite-element, spectral methods), generation of computational grid to solve these governing equations, basic numerical schemes to solve the discretized equations, specification of initial conditions, and the formulation and development of simulation problems, programming strategies, and data analysis. Representative applications include scheduling problems, molecular dynamics, weather prediction, engine combustion modeling, groundwater flow and others. Students will be exposed to recently developed techniques using finite element and particle based modeling approaches in groundwater modeling. In the finite element component, strategies such as Eulerian-Lagrangian Adjoint Schemes, structured and unstructured matrix computation and assembly, element by element approaches, sparse matrix solution methods (e.g. multigrid, PCG, BiCGSTAB, GMRES, QMR) will be introduced. In the particle method component new innovative strategies such as lattice Boltzmann method for porous media flow and reactive transport will be introduced. Use of methods such as genetic algorithms and neural networks for optimization and inverse problem solution will be briefly introduced. Extensive programming is required. 3 Cr. Spring.

CPS 404 Applied and Computational Mathematics (A). Prerequisite: MTH 202. This course will provide the mathematical skills for the development of efficient computational methods for several topics including: elementary numerical methods and their computer implementation, linear and nonlinear equations, ordinary differential equations, initial and boundary value problems, modeling of data, statistical distributions, generation of random numbers, discrete-event simulations, and statistical analysis of the output of simulations; introduction to stochastic processes, Markov decision chains and applications from transportation, inventory control, and health care; Discrete Fourier transforms and its application to digital signal processing. 3 Cr.

CPS 433 Scientific Visualization (A). Prerequisites: MTH 424 and CSC 205. This course provides concepts and techniques for visualization and its implementation. Specifically, use of visualization tools in mathematical simulation modeling such as data entry and data integrity, code debugging and code performance analysis, interpretation and display of final results will be emphasized. Hands-on experience with visualization software packages in X-Windows environment will be provided. Students may be required to develop a new visualization software designed to aid in the analysis of a chosen problem. Knowledge of programming in a high-level language is essential. 3 Cr.

CPS 488 Instrument Interfacing Laboratory I (A). Corequisite: CPS 404. This course provides theoretical and practical knowledge of instrument interfacing techniques. Students will conduct experiments using modern instrument interfacing techniques to collect data. Includes experiments such as A/D-D/A feedback Control, A/D workstation and temperature measurement, measurement of D/A Resolution, IEEE interfacing using a digital multi meter, and IEEE interfacing using a digital electrometer. Three hours of laboratory per week. 1 Cr.

CPS 489 Instrument Interfacing Laboratory II (A). Prerequisite: CPS 406. This course provides theoretical and practical knowledge of instrument interfacing techniques. Students will conduct experiments using modern instrument interfacing techniques to collect data. Includes experiments such as measurement of chemical luminescence, digital acquisition of spectrophotometer and gas chromatography data, digital acquisition of analog CCD (video) signal, Fourier transform infrared spectrometry, modern autosampling technology and robotics. Three hours of laboratory per week. 1 Cr.

PHS 302 Dynamical Systems. Prerequisite: CPS 404 (A). An introduction to dynamical systems. Topics include conservation laws, phase space, Lagrange's and Hamilton's formulation of dynamics. Applications include linear and nonlinear oscillators, perturbation theory, and coupled oscillators. Chaotic dynamics is studied in computational problems, appropriate programming language such as C, C++, and software packages such as Mathematica will be used for problem solving and for determining equations of motion. A solid understanding of differential equations is essential. 3 Cr.