Computational science is an emerging interdisciplinary field that integrates computation with traditional scientific models in such a way as to constitute a whole new scientific technique. The field should not be confused with computer science, where the computer itself is the object of study. In computational science, the computer is used only as a tool. Where computer science deals with the science of computation, computational science deals with the application of computational models computer hardware, and software, to the advancement of science.

It is now widely acknowledged that, along with traditional experimental and theoretical methodologies, advanced work in all areas of science and technology has come to rely critically on computation. The technique of computational science represents a new paradigm for scientific exploration and visualization of scientific phenomena. It permits a new approach to problems that were previously inaccessible.

Nearly all areas of science and engineering now use computers for modeling and problem solving. For example, the aerospace industry uses this approach to design safe and economical air craft, to track the trajectories of satellites, and to simulate air flow around aircraft and aerospace vehicles passing through the atmosphere. The automobile industry uses similar techniques to design motor vehicles. Computational science is used in the medical and pharmaceutical industries to develop new drugs, process medical records, and assist in medical procedures. Meteorologists use computational techniques to predict the weather and long-term climactic change. Ecologists and biologists use computer models to study the environment, population dynamics, and the influence of pollutants on the body, the air, and the oceans. Cognitive scientists model brain function using the methods of computational science.

The Computational Science program at Brockport recognizes this growing need for computational scientists and engineers. The program is a multidisciplinary effort including faculty from the Departments of Biological Sciences, Chemistry and Physics, Computer Science, Earth Sciences, and Mathematics. Through the program in computational science, students will learn computational techniques, and will gain firsthand experience with state-of-the-art supercomputers (such as the Intel Paragon, recently donated to our program by Intel, and other visual supercomputer hardware). Graduates can expect employment in industry, government, business, academia, and at major research and development laboratories.

Computational Science Major

For a major in Computational Science, a student must complete the following 43 credit hour program.

(a) Required Courses (37 credits) Credits
MTH 203 Calculus III 3
MTH 442 Statistical Methods II 3
MTH 424 Linear Algebra 3
MTH 471 Numerical Analysis 3
MTH 481 Discrete Mathematics II 3
CSC 205 Fundamentals of Computer Science II 4
CSC 406 Advanced Data Structures 4
CSC 444 Parallel Computing 3
CPS 404 Applied & Computational Mathematics 3
PHS 302 Dynamical Systems 3
CPS 488/489 Interfacing Laboratory I & II (1 credit each) 2
CPS 433 Scientific Visualization 3

(b) Elective Courses (6 credit hours)
From upper division courses in the sciences (Sample upper division courses: Population Biology, Physical Chemistry I & II, Fluid Mechanics, Statistical Mechanics, Dynamic Meteorology, Ecology).

(c) Prerequisites
Calculus I & II (MTH 201 and 202-6 credits)
Discrete Mathematics I (MTH 281-3 credits)
Fundamentals of Computer Science I (CSC 203-4 credits)
College Physics I & II (PHS 201 and 202-8 credits)
Statistical Methods I (MTH 441-3 credits)

Minor in Computational Science
(a) Required Courses (19 credit hours) Credits
MTH 203 Calculus III 3
MTH 424 Linear Algebra 3
CSC 203 Fundamentals of Computer Science I 4
CSC 205 Fundamentals of Computer Science II 4
PHS 302 Dynamical Systems 3
CPS 408/409 Instrument Interfacing Lab I & II (1 credit each) 2

(b) Elective Courses (3 credit hours)
CPS 433 Scientific Visualization 3

(c) Prerequisites (9 credit hours)
MTH 202 Calculus II 3
MTH 281 Discrete Mathematics I 3
MTH 451 Advanced Calculus and Math Methods 3
Note: For additional and updated information on the Computational Science program, see the Computational Science Handbook which is available in the Computational Science Program office, 249 Faculty Office Building.

Computational Science Courses

CSC 203 Fundamentals of Computer Science I. Prerequisites: MTH 122 and CSC 120, or equivalent by permission of instructor. Fundamental computer science concepts and programming in C++. Computing system concepts, problem solving, algorithm design, top-down development, program testing and documentation, data types (built-in and enumerated), data manipulation, sequencing, selection, loops, modules, parameters, arrays, records, sets, strings, files, introduction to sorting and searching techniques and other basic algorithms. Extensive programming and supervised laboratory sessions. 4 Cr. Every Semester.

CSC 205 Fundamentals of Computer Science II. Prerequisites: MTH 281 and CSC 203. Abstract data structures and their operations and software engineering concepts. Topics include program development (interpreting specifications, top-down development, information hiding, structured testing), implementation of built-in data types and structures, files, pointers, stacks, queues, linked lists, recursion, trees, searching and sorting algorithms, introduction to complexity analysis of algorithms. Extensive programming and supervised laboratory sessions. 4 Cr. Every Semester.

CSC 406 Advanced Data Structures. Prerequisites: CSC 205 and MTH 481. Covers the design and analysis of data structures and associated algorithms. Includes these topics: arrays, strings, stacks, linear and generalized lists, multi lists, multi rings, queues, sets, hashing, trees, graphs, recursion, searching and sorting, and applications such as text processing, polynomials, space matrices, storage management, and unlimited-precision arithmetic. Requires extensive programming. 4 Cr. Every Semester.

CSC 444 Introduction to Parallel Computing. Prerequisites: MTH 481 and CSC 406. This course deals with design and analysis of parallel algorithms. Topics include parallel models of computation, measures of complexity, parallel algorithms for selection, searching, sorting, merging, matrix algorithms, transitive closure, connected components, shortest path, minimum spanning tree and routing algorithms. Hands-on experience in a parallel programming environment. 3 Cr. Spring.

MTH 201 Calculus I. Prerequisite: Three and a half years of college preparatory mathematics, or MTH 122. Covers limits and continuity; derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions; and applications of the derivative. 3 Cr. Every Semester.

MTH 202 Calculus II. Prerequisite: MTH 201, or one year of calculus in high school. Covers techniques and applications of integration, approximation methods, Taylor polynomials, improper integrals and L'Hospital's rules, and an introduction to infinite series. 3 Cr. Every Semester.

MTH 203 Calculus III. Prerequisite: MTH 202. Infinite series, vectors and 3-space, polar coordinates, functions of several variables, applications of partial derivatives, and multiple integrals. The TI-85 graphics calculator is required for this course. 3 Cr. Every Semester.

MTH 281 Discrete Mathematics I. Prerequisite: Three and a half years of college preparatory mathematics, or MTH 122. Provides an introduction to discrete mathematics. Topics include prepositional and predicate logic, sets, functions, matrix algebra, algorithms, valid arguments, direct and indirect proofs, mathematical induction, permutations and combinations, and discrete probability. 3 Cr. Every Semester.

MTH 424 Linear Algebra. Prerequisite: MTH 202 or either MTH 245 or MTH 281. Matrices and determinants and their uses, vector spaces and sub spaces, dimension, linear transformations, and Euclidean vector spaces. 3 Cr. Every Semester.

MTH 441 Statistical Methods I. Prerequisite: MTH 346 or 243 or an equivalent introductory statistics course. Covers estimation, hypothesis testing, simple regression, multiple regression, categorical data, and non-parametric methods. Uses computer statistical analysis packages such as MINITAB and SPSS. 3 Cr. Fall.

MTH 442 Statistical Methods II. Prerequisite: MTH 441. One- and two-way analysis of variance multiple regression, experimental design, and linear models. Uses computers for data analysis. 3 Cr. Spring.

MTH 471 Numerical Analysis. Prerequisites: MTH 203 and CSC 203. Provides a survey of methods used to numerically approximate the solutions of a variety of mathematical problems. Covers the generation and propagation of roundoff errors, convergence criteria, and efficiency of computation. Includes these topics: roots of nonlinear equations, polynomial approximations, and an introduction to numerical differentiation and integration. 3 Cr. Spring.

MTH 481 Discrete Mathematics II. Prerequisites: MTH 201 and MTH 281. A second course in discrete mathematics. Includes these topics: complexity of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory, trees, Boolean algebra, grammars, formal languages, and finite-state machines. 3 Cr. Every Semester.

PHS 201 College Physics I with Laboratory. Corequisite: MTH 201. This course deals with the fundamentals of mechanics and thermodynamics including kinematics, Newton's Laws, energy, rotational motion, kinetic theory of gases, and the first and second law of thermodynamics. Three hours of laboratory per week. 4 Cr. Fall.

PHS 202 College Physics II with Laboratory. Prerequisite: PHS 201. Corequisite: MTH 202. This course deals with the fundamentals of electricity, magnetism, optics and sound, including the electric field, electric potential, electrical circuits, the magnetic field, Maxwell's equations, and wave propagation. Three hours of laboratory per week. 4 Cr. Spring.

CPS 404 Applied and Computational Mathematics. 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.

PHS 302 Dynamical Systems. Prerequisite: CPS 404. 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.

CPS 488 Instrument Interfacing Laboratory I. 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. 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.

CPS 433 Scientific Visualization. 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.