UIC Program in

Mathematical and Information Sciences for Industry:

High Performance Scientific Computing (HPSC) Track

(Tentative Proposal)


Justification for High Performance Scientific Computing
(Computational Science and Applied Mathematics)

Title:

Establishment of Course Rubric for the Program
in Computational Science and Applied Mathematics.


Sponsor: Program in Computational Science and Applied Mathematics
Description: The Program in Computational Science and Applied Mathematics proposes the establishment of an additional rubric: The rubric CSAM assumes the transfer of a number of courses now under the Math and MCS rubrics to the CSAM rubric.
Justification: The proposed Program in Computational Science and Applied Mathematics needs its own rubric to identify courses in applied mathematics and computational science.
Graduates students in Program in Computational Science and Applied Mathematics will be better able to compete in a tight job market if their transcripts reflect their training in computational science and applied mathematics.
The new rubrics are consistent with the program name.
Budgetary and Staff Implications and Library Support: None
Catalog Statement: No changes other than the replacement of course rubrics and the renumbering of courses.
Proposed Effective Date: Fall Semester 1995

Courses for the Program in Computational Science and Applied Mathematics (CSAM)


CSAM Courses for Graduate Students


  
old        new                                        
number*    CSAM   Title                              Hours  

Math 573   501   Methods of Applied Mathematics.     4 hrs. 
Math 576   503   Boundary Value Problems.            4 hrs. 
Math 577   505   Advanced Applied PDE.               4 hrs. 
Math 575   507   Integral Equations and Applications.4 hrs. 
Math 578   511   Asymptotic Methods.                 4 hrs. 
Math 579   513   Singular Perturbations.             4 hrs. 
--------   514   Bifurcation Theory.                 4 hrs. 
Math 584   515   Applied Stochastic Models.          4 hrs. 
MCS  575   517   Computer Performance Evaluation.    4 hrs. 
Math 574   521   Applied Optimal Control.            4 hrs. 
--------   523   Applied Stochastic Control.         4 hrs. 
--------   525   Computational Control.              4 hrs. 
Math 580   531   Physical Principles of Applied Mathematics I. 4 hrs. 
Math 581   532   Physical Principles of Applied Mathematics II. 4 hrs. 
Math 582   533   Wave Propagation and Scattering I.  4 hrs. 
Math 583   534   Wave Propagation and Scattering II. 4 hrs. 
--------   535   Mathematical Fluid Dynamics.        4 hrs. 
--------   536   Geophysical Fluid Dynamics.         4 hrs. 
--------   537   Magnetohydrodynamics.               4 hrs. 
--------   538   Mathematical Plasma Physics.        4 hrs. 
--------   539   Computational Fluid Dynamics.       4 hrs. 
MCS  561   551   Algebraic Symbolic Computation.     4 hrs. 
MCS  563   553   Analytic Symbolic Computation.      4 hrs.  
MCS  565   561   Mathematical Theory of Databases.   4 hrs. 
--------   563   Object Stores and Scientific Computing I. 4 hrs. 
--------   565   Object Stores and Scientific Computing II. 4 hrs. 
--------   567   Workshop in Database Computation.   4 hrs. 
MCS  472   581   Advanced Numerical Analysis         4 hrs. 
MCS  571   583   Numerical Methods for PDEs.         4 hrs.
MCS  572   585   Introduction to Supercomputing.     4 hrs.
MCS  573   587   Workshop Program on Scientific Supercomputing. 4 hrs. 
Math 590   590   Advanced Topics in Applied Mathematics. 4 hrs. 
--------   591   Advanced Topics in Computational Science. 4 hrs. 
Math 593   593   Graduate Student Seminar            1 hr. 
Math 595   595   Research Seminar                    1 hr. 
Math 598   598   Master's Thesis Research.          0-16 hrs.
Math 599   599   Thesis Research.                   0-16 hrs. 

* "------------" denotes a new course and "(Math XXX)" denotes an analog of
a Math course.

CSAM Course Descriptions of Courses for Graduate Students


CSAM 501. Methods of Applied Mathematics. 4 Hours. Catalog Description: Applications of applied mathematics, integral equations, eigenfunction expansions, calculus of variations, fluid flow and conformal mapping, special functions, Laplace, Mellin, and Hankel transforms, approximations. Prerequisites: Graduate standing and CSAM 405 Applied Partial Differential Equations and CSAM 402 Applied Complex Analysis; or consent of the instructor.
CSAM 503. Boundary Value Problems. 4 Hours. Catalog Description: Distributions, Green's functions, alternative theorem, regular and singular Sturm-Liouville problems, spectral theory, potential theory, method of images, complex variable methods, equations of evolution. Prerequisites: Graduate standing and Math 320 Linear Algebra I and CSAM 402 Applied Complex Analysis and CSAM 405 Applied Partial Differential Equations; or consent of instructor
CSAM 505. Advanced Applied Partial Differential Equations. 4 Hours. Catalog Description: Quasilinear and nonlinear first order PDE's, shock solutions, second order equations, cylinder and sphere problems, Wave, Laplace and diffusion equations, maximum principles, nonlinear wave motion. Prerequisites: Graduate standing and CSAM 400 Advanced Calculus I and CSAM 402 Applied Complex Analysis and CSAM 405 Applied Partial Differential Equations.
CSAM 507. Integral Equations and Applications. 4 Hours. Catalog Description: Fredholm and Volterra equations, Fredholm determinants, separable and symmetric kernels, Neumann series, transform methods, Wiener-Hopf method, Cauchy kernels, nonlinear equations, perturbation methods Prerequisites: Graduate standing and CSAM 401 Advanced Calculus II and CSAM 402 Applied Complex Analysis and CSAM 405 Applied Partial Differential Equations; or consent of instructor.
CSAM 511. Asymptotic Methods. 4 Hours. Asymptotic series, Laplace's method, stationary phase, steepest descent method, Stokes phenomena, uniform expansions, multi-dimensional Laplace integrals, Euler-MacLaurin formula, irregular singular points, WKBJ method. Prerequisites: Graduate standing and CSAM 405 Applied Partial Differential Equations and CSAM 402 Applied Complex Analysis; or consent of instructor.
CSAM 513. Singular Perturbations. 4 Hours. Catalog Description: Algebraic and transcendental equations, regular perturbation expansions of differential equations, matched asymptotic expansions, boundary layer theory, Poincare'-Lindstedt, multiple scales, bifurcation theory, homogenization. Prerequisites: Graduate standing and CSAM 405 Applied Partial Differential Equations or consent of the instructor
CSAM 514. Bifurcation Theory. 4 Hours. Catalog Description: Hopf bifurcations, multiple bifurcations, singular bifurcations, applications. Prerequisites: Graduate standing and CSAM 513 Singular Perturbations or consent of the instructor
CSAM 515. Applied Stochastic Models. 4 Hours. Catalog Description: Applications of stochastic models in chemistry, physics, biology, queueing, filtering, and stochastic control, diffusion approximations, Brownian motion, stochastic calculus, stochastically perturbed dynamical systems, first passage times. Prerequisites: Graduate standing and Math 450 Introduction to Probability and CSAM 402 Applied Complex Analysis and CSAM 405 Applied Partial Differential Equations; or consent of instructor.
CSAM 517. Computer Performance Evaluation. 4 Hours. Catalog Description: Modeling of computer systems, basic queues, central server models, Little's Law, operational analysis, Markovian networks, Jackson and BCMP networks, product form solutions, computational algorithms, mean value analysis, approximation methods. Prerequisites: Graduate standing and Stat 401 Introduction to Probability and MCS 412 Computer Operating Systems or consent of instructor.
CSAM 521. Applied Optimal Control. 4 Hours. Catalog Description: Introduction to optimal control theory; calculus of variations, maximum principle, dynamic programming, feedback control, linear systems with quadratic criteria, singular control, optimal filtering, stochastic control. Prerequisites: Graduate standing and CSAM 401 Advanced Calculus II or consent of the instructor.
CSAM 523. Applied Stochastic Control. 4 Hours. Catalog Description: An introduction to optimal control of stochastic differential equations for applications. Introduction to stochastic differential equations with Gaussian and Poisson random noise. Relationship between the stochastic chain rule for Markov processes and the chain rule for discontinuous functions. Discounted performance models. The applied derivation of the Bellman partial differential equation of stochastic dynamic programming. Applications. Numerical considerations and the curse of dimensionality. Prerequisites: Graduate standing and CSAM 521 Applied Optimal Control or consent of the instructor.
CSAM 525. Computational Control. 4 Hours. Catalog Description: Numerical techniques for solving control problems. Deterministic control, stochastic control. Differential equation solution methods, probabilistic methods and simulations. Prerequisites: Graduate standing and CSAM 481 Numerical Analysis and {CSAM 521 Applied Optimal Control or CSAM 523 Applied Stochastic Control} or consent of the instructor.
CSAM 531. Physical Principles of Applied Mathematics I. 4 Hours. Catalog Description: Development of concepts and techniques basic to key mathematical models of physical phenomena; particularly discrete and continuum mechanics; derivation of the equations of fluid mechanics and elasticity. Prerequisites: Graduate standing and CSAM 400 Advanced Calculus I and CSAM 402 Applied Complex Analysis and CSAM 405 Applied Partial Differential Equations.
CSAM 532. Physical Principles of Applied Mathematics II. Catalog Description: Development of concepts and techniques basic to key mathematical models of physical phenomena; dynamic problems in elasticity, fluids, nonlinear wave propagation, group speed and velocity. Prerequisites: Graduate standing and CSAM 531 Physical Principles of Applied Mathematics I.
CSAM 533. Wave Propagation and Scattering I. 4 Hours. Catalog Description: Solutions of wave equations in multiple dimensions, vector, and dyadic waves; separable and non-separable problems. Representations: Green's function integrals, complex integrals, spectral representations. Approximate solutions. Prerequisites: Graduate standing and CSAM 405 Applied Partial Differential Equations and 417 Complex Analysis with Applications or consent of instructor.
CSAM 534. Wave Propagation and Scattering II. 4 Hours. Catalog Description: Solutions of reduced wave equations for scattering of scalar, vector, and dyadic waves; separable and non-separable problems. Representations: Green's function integrals, complex integrals. Various approximations. Prerequisites: Graduate standing and CSAM 533 Wave Propagation and Scattering I.
CSAM 535. Mathematical Fluid Dynamics. 4 Hours. Catalog Description: Prerequisites:
CSAM 536. Geophysical Fluid Dynamics. 4 Hours. Catalog Description: Prerequisites:
CSAM 537. Magnetohydrodynamics. 4 Hours. Catalog Description: Prerequisites:
CSAM 538. Mathematical Plasma Physics. 4 Hours. Catalog Description: Prerequisites:
CSAM 539. Computational Fluid Dynamics. 4 Hours. Catalog Description: Prerequisites:
CSAM 551. Algebraic Symbolic Computation. 4 Hours. Catalog Description: Algebraic computation, including multi-precession arithmetic, arithmetic of polynomials, rational functions and power series, factorization techniques, and solving systems of equations and other related topics. Prerequisites: Grade of C or better in CSAM 451 Introduction to Symbolic Computation or equivalent, and a grade of C or better in Math 310 Applied Linear Algebra or Math 320 Linear Algebra I, or consent of instructor. Graduate Standing.
CSAM 553. Analytic Symbolic Computation. 4 Hours. Catalog Description: Analytic computation, including integration algorithms, differential equations, perturbation theory, mixed symbolic--numeric algorithms and other related topics. Prerequisites: Grade of C or better in CSAM 451 Introduction to Symbolic Computation or equivalent, and CSAM 403 Applied Differential Equations or consent of instructor. Graduate Standing.
CSAM 561. Mathematical Theory of Databases. 4 Hours. Catalog Description: Abstract systems for databases, syntax and semantics of operational languages, dependencies and normal forms, axiomizations, queries and query optimization, null values, algebraic interpretations. Prerequisites: Consent of the instructor. Graduate standing.
CSAM 563. Object Stores and Scientific Computing I. 4 Hours. Catalog Description: Prerequisites: Consent of the instructor. Graduate standing.
CSAM 564. Object Stores and Scientific Computing II. 4 Hours. Catalog Description: Prerequisites: Graduate standing and CSAM 563 Object Stores and Scientific Computing I or consent of the instructor.
CSAM 567. Workshop in Database Computation. 4 Hours. Catalog Description: Prerequisites: Graduate standing and consent of the instructor.
CSAM 581. Advanced Numerical Analysis. 4 Hours. Catalog Description: Advanced numerical methods; eigenvalue problems, power methods, spline interpolation, FFTs, method of least squares, ODE shooting methods, matrix iteration methods, Gaussian Quadrature, computer subroutine packages. Prerequisites: Graduate standing and CSAM 481 Numerical Analysis.
CSAM 583. Numerical Methods for Partial Differential Equations. 4 Hours. Catalog Description: Finite difference methods for parabolic, elliptic and hyperbolic differential equations: explicit, Crank-Nicolson implicit, alternating directions implicit, Jacobi, Gauss-Seidel, successive over-relaxation, conjugate gradient, Lax-Wendroff, Fourier stability. Prerequisites: CSAM 405 Applied Partial Differential Equations and CSAM 481 Numerical Analysis or consent of the instructor. Graduate standing.
CSAM 585. Introduction to Supercomputing. 4 Hours. Catalog Description: Introduction to supercomputing on vector and parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines. Prerequisites: CSAM 481 Numerical Analysis, or CSAM 583 Numerical Methods for PDEs, or consent of the instructor. Graduate standing.
CSAM 587. Workshop Program on Scientific Supercomputing. 4 Hours. Catalog Description: Intensive laboratory immersion in supercomputing; working with existing computer programs to improve their performance by scalar, vector and parallel optimization; techniques of compilation, profiling, debugging under CMS and Unix. Required co-registration of 8 hours thesis research or special projects in participant's department. Prerequisites: Graduate standing. Consent of instructor; Appropriate research project approved by instructor and student's advisor.
CSAM 590. Advanced Topics in Applied Mathematics. 4 Hours. Catalog Description: Topics from areas such as: elastic scattering, nonlinear problems in chemistry and physics, mathematical biology, stochastic optimal control, geophysical fluid dynamics, stability theory, queueing theory. Prerequisites: Graduate Standing. Prerequisite may vary from section to section depending upon topic.
CSAM 591. Advanced Topics in Computational Science . 4 Hours. Catalog Description: Computational topics from areas such as: astrophysics, database methods, biology, chemistry, physics, MHD, network analysis. Prerequisites: Graduate Standing. Prerequisite may vary from section to section depending upon topic.
CSAM 593. Graduate Student Seminar. 1 Hour. For graduate students who wish to receive credit for participating in a learning seminar whose weekly time commitment is not sufficient for a reading course. This seminar must be sponsored by a faculty member. Prerequisites: Graduate Standing.
CSAM 595. Research Seminar. 1 Hour. Current developments in research with presentations by faculty, students, and visitors. Prerequisites: Graduate Standing.
CSAM 598. Master's Thesis. 4 Hours. Catalog Description: Research work under the supervision of a faculty member leading to the completion of a Master's Thesis. Prerequisites: Graduate Standing. Departmental Approval.
CSAM 599. Thesis Research. 0-16 Hours. Catalog Description: May be repeated for credit. Students may register for more than one section per term. Satisfactory/unsatisfactory grade only. Prerequisites: Consent of the department.

CSAM Courses for Advanced Undergraduate Students and Graduate Students

%
%
old        new                                                  
rubric     CSAM   Title                                   Hours 

Math 410   400   Advanced Calculus I                      3U4G 
Math 410   401   Advanced Calculus II                     3U4G 
Math 417   402   Applied Complex Analysis                 3U4G 
Math 480   403   Applied Differential Equations           3U4G 
Math 481   405   Applied Partial Differential Equations   3U4G 
Math 419   415   Models in Applied Mathematics            3U4G 
Math 484   425   Tensor Analysis                          3U4G 
MCS  460   451   Introduction to Symbolic Computation     3U4G 
MCS  471   481   Numerical Analysis                       3U4G 
--------   491   Special Topics in Applied Mathematics    3U4G
--------   492   Special Topics in Computational Science  3U4G 

* "------------" denotes a new course and "(Math XXX)" denotes an analog of
a Math course.

CSAM Course Descriptions of Courses for Advanced Undergraduate Students and Graduate Students


CSAM 400 Advanced Calculus I 3U4G Hours. Catalog Description: Functions of several variables, differentials, theorems of partial differentiation. Calculus of vector fields, line and surface integrals, conservative fields, Stokes' and divergence theorems. Cartesian tensors. Prerequisite: Grade of C or better in Math 210 Calculus for Mathematics, Engineering, and Science III.
CSAM 401 Advanced Calculus II 3U4G Hours. Catalog Description: Implicit and inverse function theorems, transformations, Jacobians. Point-set theory. Sequences, infinite series, convergence tests, uniform convergence. Improper integrals, gamma and beta functions, Laplace transform. Prerequisites: Grade of C or better in CSAM 400 Advanced Calculus I.
CSAM 402 Applied Complex Analysis 3U4G Hours. Catalog Description: Complex numbers, analytic functions, complex integration, Taylor and Laurent Series, residue calculus, branch cuts, conformal mapping, argument principle, Rouche's theorem, Poisson Integral formula, Analytic continuation. Applications. Prerequisites: Grade C or better in Math 210 Calculus for Mathematics, Engineering, and Science III.
CSAM 403 Applied Differential Equations 3U4G Hours. Catalog Description: Linear first-order systems. Numerical methods. Nonlinear differential equations and stability. Introduction to Partial differential equations. Sturm-Liouville theory. Boundary value problems and Green's functions. Prerequisites: Grade of C or better in CSAM 220 Elementary Differential Equations.
CSAM 405 Applied Partial Differential Equations 3U4G Hours. Catalog Description: Initial value and boundary value problems for second order linear equations. Eiqenfunction expansions and Sturm-Liouville theory. Green's functions. Fourier transform. Characteristics. Laplace transform. Prerequisites: Grade of C or better in CSAM 403 Applied Differential Equations.
CSAM 407 Tensor Analysis 3U4G Hours. Catalog Description: Cartesian tensors, orthogonal transformations. General tensor calculus, Riemannian space, covariant differentiation, Christoffel symbols, curvature tensor, differential geometry. Emphasis on aspects of interest in science and engineering. Prerequisites: Grade of C or better in CSAM 400 Advanced Calculus I and Math 310 Applied Linear Algebra I or Math 320 Linear Algebra I.
CSAM 415 Models in Applied Mathematics 3U4G Hours. Catalog Description: Introduction to mathematical modeling; scaling, graphical methods, optimization, computer simulation, stability, differential equation models, elementary numerical methods, applications in biology, chemistry, engineering and physics. Prerequisites: Grade of C or better in Math 260 Introduction to Computer Science I or Math 190 Introduction to Scientific Computing, and CSAM 403 Applied Differential Equations.
CSAM 425 Tensor Analysis 3U4G Hours. Catalog Description: Cartesian tensors, orthogonal transformations. General tensor calculus, Riemannian space, covariant differentiation, Christoffel symbols, curvature tensor, differential geometry. Emphasis on aspects of interest in science and engineering. Prerequisites: A grade of C or better in Math 410 Advanced Calculus I Math 310 Applied Linear Algebra or Math 320 Linear Algebra I.
CSAM 451. Introduction to Symbolic Computation 3U4G Hours. Catalog Description: Introduction to computer algebra systems (MAPLE), symbolic computation, and the mathematical algorithms employed in such computation, with examples and applications to topics in undergraduate mathematics. Prerequisite: Grade of C or better in MCS 261 Discrete Mathematics and either Math 320 Linear Algebra I or CSAM 310 Applied Linear Algebra or Math 330 Abstract Algebra.
CSAM 481. Numerical Analysis 3U4G Hours. Catalog Description: Floating point arithmetic, computational linear algebra, iterative solution to nonlinear equations, interpolation, numerical integration, numerical solution of ODEs, computer subroutine packages. Prerequisites: Grade of C or better in MCS 360 Introduction to Computer Science II or EECS 270 Introduction to Programming Languages.
CSAM 491. Special Topics in Applied Mathematics 3U4G Hours. Catalog Description: Topics in applied mathematics: such as ordinary differential equations, partial differential equations, complex variables, applications. May be repeated to a maximum of 12 credit hours. Prerequisites: Prerequisites may vary according to topic.
CSAM 492. Special Topics in Computational Science 3U4G Hours. Catalog Description: Topics in computational science: such as symbolic computation, database theory, computational dynamics. May be repeated to a maximum of 12 credit hours. Prerequisites: Prerequisites may vary according to topic.

CSAM Courses for Undergraduate Students Only


old        new                                                     
rubric     CSAM   Title                                     Hours

Math 180   180   Calculus for Appl Math, Engr and Sci I     5 hrs. 
Math 181   181   Calculus for Appl Math, Engr and Sci II    5 hrs. 
Math 210   210   Calculus for Appl Math, Engr and Sci III   5 hrs. 
Math 220   220   Introduction to Differential Equations     3 hrs. 
Math 310   310   Applied Linear Algebra                     3 hrs. 
--------   393   Special Topics in Applied Mathematics      2-4 hrs. 
--------   394   Special Topics in Computational Science    2-4 hrs. 

* "--------" denotes a new course and "(Math XXX)" denotes an analog of
a Math course.

CSAM Course Descriptions of Courses for Undergraduate Students Only


CSAM 180. Calculus for Applied Mathematics, Engineering, and Science I 5 Hours. Catalog Description: Differentiation, curve sketching, maximum-minimum problems, related rates, mean-value theorem, antiderivative, Riemann integral, logarithm, and exponential functions. Computational Techniques. Credit not given for CSAM 180 if the student has credit in Math 166 or Math 180; a student with credit in Math 165 (but not in Math 166) may not take CSAM 180 for credit. Prerequisites: Grade of C or better in Math 121 or C or better in Math 125.
CSAM 181. Calculus for Applied Mathematics, Engineering, and Science II 5 Hours. Catalog Description: Techniques of Integration, arc length, solids of revolution, applications, polar coordinates, parametric equations, infinite sequences and series, power series, complex numbers. Computational Techniques. Prerequisites: Grade C or better in CSAM 180 or Math 180 (Calculus I)
CSAM 210. Calculus for Applied Mathematics, Engineering, and Science III 5 Hours. Catalog Description: Vectors in the plane and space, vector valued functions, functions of several variables, partial differentiation, maximum-minimum problems, double and triple integrals, applications, Green's theorem. Computational Techniques. Prerequisites: Grade of C or better in CSAM 181 or Math 181 (Calculus II).
CSAM 220. Introduction to Differential Equations 3 Hours. Catalog Description: Principal ideas, applications, and techniques of differential equations. First order equations, separable, exact, and linear. Linear equations in general. Frobenius' method. Fourier series, Laplace transforms. Prerequisites: Grade of C or better in Math 210 Calculus for Mathematics, Engineering and Science III.
CSAM 310. Applied Linear Algebra 3 Hours. Catalog Description: Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given in both CSAM 310 and Math 320. Prerequisites: Grade of C or better in Math 210 Calculus for Mathematics, Engineering and Science III.
CSAM 393. Special Topics in Applied Mathematics 2-4 Hours. Catalog Description: Topics in applied mathematics. May be repeated for credit. Students may register for more than one section per term. Course content is announced prior to each term in which it is given. Prerequisites: Prerequisites may vary according to topic.
CSAM 394. Special Topics in Computational Science 2-4 Hours. Topics in computational science. May be repeated for credit. Students may register for more than one section per term. Course content is announced prior to each term in which it is given. Prerequisites: Prerequisites may vary according to topic.

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