Rice Course Schedule, Spring 2000
Computational and Applied Math (CAAM)

NOTE: Course web pages are available for some CAAM courses.

CAAM 211   INTRO TO ENG COMPUTATION                 Credits 3.00  Spring 00
* DISTRIBUTION COURSE: GROUP III
Introduction to engineering and scientific computation:  Engineering
workstations, programming software systems, and numerical methods.  Laboratory
to illustrate the application of computational and visualization methods to
problem analysis.  Matlab serves as the primary computational and display tool
with supplementary programs written in FORTRAN. Only one of the two courses
Caam 210, 211 may be taken for credit.
Prereq- Math 101, Phys 101
001 TBA                                 Zhang, Yin                Enr: 0 Max: NA

CAAM 310   LINEAR ALGEBRA                           Credits 3.00  Spring 00
* DISTRIBUTION COURSE: GROUP III
Concepts and results of linear algebra useful in a variety of fields of
application.
001 TBA                                 TBA                       Enr: 0 Max:

CAAM 322   INTRO TO REAL ANAYSIS II                 Credits 3.00  Spring 00
Continuation of Caam 321.  Linear maps and matrices, matrix norms, convergence
of sequences, continuity and differentiability of functions on Rn, the
derivative as a linear map, normed linear spaces, completeness, the contraction
mapping principle, inverse and implicit function theorems, fundamental theorems
on ODEs, compactness, multivariate integration.
Prereq- Caam 321.
001 TBA                                 Heinkenschloss, Matthias  Enr: 0 Max: NA

CAAM 335   MATRIX ANALYSIS                          Credits 3.00  Spring 00
Equilibria and the solution of linear and linear least squares problems.
Dynamical systems and the eigenvalue problem with the Jordan form and Laplace
transform via complex integration.
Prereq- Math 212 and Caam 210 or 211.
001 TBA                                 Cox, Steven J.            Enr: 0 Max: NA

CAAM 336   DIFFERENTIAL EQUATIONS IN SCIENCE AND EN Credits 3.00  Spring 00
Green's functions, exponential and series solutions, and numerical methods for
initial and boundary value problems of mathematical physics. Dynamics of
mass-spring systems and circuits, equilibria of solids, fluids and
electromagnetic fields, heat flow and wave motion.  Emphasis on scientific and
engineering motivation and consequences and on modern computational methods.
Prereq- Math 212 and Caam 210 or 211.
001 TBA                                 Symes, William W.         Enr: 0 Max: NA

CAAM 353   COMPUTATIONAL NUM ANAL                   Credits 3.00  Spring 00
An introductory course in numerical analysis with computer applications.
Prereq- Math 211.
001 TBA                                 Borcea, Liliana           Enr: 0 Max: NA

CAAM 378   INTRO TO OPERATIONS RESEARCH             Credits 3.00  Spring 00
An alternative to Caam 376 for students with a year of calculus.  Some
knowledge of linear algebra and of probability is desirable.
001 TBA                                 Dean, Nathaniel           Enr: 0 Max: NA

CAAM 381   INTRO TO APPLIED PROBABILITY             Credits 3.00  Spring 00
Concepts, interpretations, elementary techniques, and applications of modern
probability theory,
Prereq- Math 102.
001 TBA                                 TBA                       Enr: 0 Max:

CAAM 420   INTRO COMPUTATIONAL SCIENCE              Credits 3.00  Spring 00
Basic principles of computational science, including vector and parallel
computer architectures, parallel numerical algorithms, scientific
visualization, analysis and enhancement of performance, and use of programming
tools and environments.  Programming assignments will involve hands-on
experience with supercomputers and parallel computers.
Prereq- Comp 210 and Caam 353.
001 TBA                                 Moore, Douglas W.         Enr: 0 Max: NA

CAAM 435   ORDINARY DIFFERENTIAL EQUATION           Credits 3.00  Spring 00
Existence, Uniqueness and stability of solutions to systems of nonlinear
ordinary differential equations with applications to control theory.
Also offered as ELEC 508
001 TBA                                 Ghorbel, Fathi            Enr: 0 Max: NA

CAAM 437   PARTIAL DIFFERENTIAL EQUATIONS II        Credits 3.00  Spring 00
Continuation of Caam 436.  Newtonian heat flow, the Gaussian kernel, Fourier
transform in L2, analysis of smoothing property, Maxwell's equations, weak
solutions, distributions, propagation of discontinuity in 1D, Green's function
in 3D, Fourier analysis, additional topics at discretion of instructor.
Prereq- Caam 436.
001 TBA                                 Symes, William W.         Enr: 0 Max: NA

CAAM 452   COMP METH-DIFF EQUATION                  Credits 4.00  Spring 00
Finite difference, variational, and collocation methods for approximating
numerically the solutions of ordinary and partial differential equations.
Computer implementation to verify convergence to the solution.
Prereq- Caam 335 and 336 or permission of instructor.
001 TBA                                 Kloucek, Petr             Enr: 0 Max: NA

CAAM 454   OPTIMIZATION PROBLEMS IN COMPUTATIONAL E Credits 3.00  Spring 00
An introduction to the formulation of optimization problems, with practical
applications.  Topics include appropriate algorithms for systems of nonlinear
equations, parameter identification for differential equations, basic reduction
methods, and examples from computational engineering and science.  A complement
to CAAM 460.
Prerequisites:  Proficiency in Fortran or C, and understanding of numerical
linear algebra and calculus.
001 TBA                                 Heinkenschloss, Matthias  Enr: 0 Max: NA

CAAM 475   INTEGER & COMBINATORIAL OPTIMIZATION     Credits 3.00  Spring 00
Modeling and solving optimization problems with discrete components, graphs and
networks; network flow problems; minimum spanning trees; basic polyhedral
theory; the knapsack problem; the plant location problem; the set packing
problem; computational complexity; branch and bound; cutting planes; Lagrangian
relaxation and Bender's decomposition.
Prereq- Caam 471.
Also offered as ECON 475
001 TBA                                 Cook, William J.          Enr: 0 Max: NA

CAAM 476   OPERATIONS RESEARCH- STOCHASTIC MODELS   Credits 3.00  Spring 00
Probability and decisions; random selection; Markov chains and decision
processes; waiting lines; martingale models.
Prereq- Caam 381 or Stat 310.
Also offered as ECON 476
001 TBA                                 TBA                       Enr: 0 Max:

CAAM 491   INDEPENDENT STUDY                        Credits   Spring 00
No description
001 TBA                                 Staff                     Enr: 0 Max: NA

CAAM 502   UNIX FOR SCIENTIFIC & ENGINEERING APPLIC Credits 1.00  Spring 00
Continuation of Caam 501.
001 TBA                                 Pearlman, Michael D.      Enr: 0 Max: NA

CAAM 513   CONSULTING                               Credits 3.00  Spring 00
Learn about various research topics in applied mathematics.  Lectures in
consulting, presentation skills and various topics, as needed for the
consulting projects.
Prereq- Permission of instructor.
001 TBA                                 TBA                       Enr: 0 Max:

CAAM 522   PROGRAMMING FOR COMPUTATIONAL MATHEMATIC Credits 3.00  Spring 00
Programming techniques, style, data structures, and algorithms for efficient
computational mathematics.
Prereq- Caam 210 or Caam 211; Caam 501 or permission of instructor.
001 TBA                                 Applegate, David Lee      Enr: 0 Max: NA

CAAM 540   APPLIED FUNCT. ANALYSIS                  Credits 3.00  Spring 00
Hilbert spaces, Banach spaces, spectral theory, and weak topologies with
applications to signal processing, control, and partial differential equations.
Prereq- Math 425 of permission of instructor.
001 TBA                                 Cox, Steven J.            Enr: 0 Max: NA

CAAM 541   APPLIED FUNCTIONAL ANALYSIS II           Credits 3.00  Spring 00
Boundary value problems of mathematical physics; function spaces and
distributions; direct method in the calculus of variations; Green's functions
and integral equations; compact operators, spectral theory, regular and
singular Sturm-Liouville problems.
001 TBA - TBA                           Cox, Steven J.            Enr: 0 Max: NA

CAAM 551   ADV NUMERICAL LIN ALGEBRA                Credits 3.00  Spring 00
Iterative and/or direct methods for large scale problems.
001 TBA                                 Sorensen, Danny C.        Enr: 0 Max: NA

CAAM 554   NUM NONLINEAR PROGRAMMING                Credits 3.00  Spring 00
Analysis of modern numerical methods for constrained problems, including
variable metric methods, successive quadratic programming, and trust region
methods.
001 TBA                                 Tapia, Richard A.         Enr: 0 Max: NA

CAAM 564   MINIMIZATION OF FUNC                     Credits 3.00  Spring 00
Optimal control theory and calculus of variations.  Minimization of functionals
depending on variable subject to differential constraints,  nondifferential
constraints, initial constraints, and final constraints. Analytical and
computational methods.  Engineering applications.
Also offered as MECH 564
001 TBA                                 Miele, Angelo             Enr: 0 Max: NA

CAAM 570   ADVANCED TOPICS IN GRAPH THEORY          Credits 3.00  Spring 00
This course provides an overview of the main research topics in Graph Theory.
Each student will report regularly  on some selected area, progress reports
will be supplemented by lectures given by the instructor, and each student will
complete an extensive survey of their area.
Prereq- CAAM 470
001 TBA - TBA                           Dean, Nathaniel           Enr: 0 Max: NA

CAAM 571   ADVANCED INTEGER & COMBINATORIAL OPTIMIZ Credits 3.00  Spring 00
Material will vary from year to year.  Emphasis will be on methods for solving
optimization problems with discrete components.  Possible topics include:
polyhedral structure of fundamental problem classes; matrix properties of
integral polyhedra; cardinality and weighted matching; matroids and
polymatroids; submodular functions; the ellipsoid algorithm and its
consequences; integer lattices; advanced integer programming techniques.
Prereq- Caam 475.
001 TBA                                 Dean, Nathaniel           Enr: 0 Max: NA

CAAM 575   TOPICS IN INTEGER PROGRAMMING            Credits 2.00  Spring 00
Seminar on selected topics in integer programming.  Topics will vary from year
to year.  May be repeated for credit.
001 TBA                                 Applegate, David Lee      Enr: 0 Max: NA

CAAM 582   MATHEMATICAL PROBABILITY II              Credits 3.00  Spring 00
Continuation of Caam 581.
001 TBA                                 Olofsson, Peter           Enr: 0 Max: NA

CAAM 584   ESTIMATION THEORY                        Credits   Spring 00
Maximum likelihood and Bayesian vector parameter estimation.  Minimum mean
square error estimation.  Time series analysis.  Algorithms based on state
variable and ARMA models for signal estimation, model identification, and
spectral estimation.
Prereq- Caam 381 (Caam 583 recommended).
001 TBA                                 Staff                     Enr: 0 Max: NA

CAAM 591   OPERATIONS RESEARCH                      Credits   Spring 00
No description
001 TBA                                 Staff                     Enr: 0 Max: NA

CAAM 592   WAVES IN HETEROGENEOUS MEDIA             Credits 3.00  Spring 00
No description
Also offered as GEOL 520
001 TBA                                 Borcea, Liliana           Enr: 0 Max: NA

CAAM 652   TOPS IN NUMERICAL DE                     Credits 3.00  Spring 00
Content varies from year to year.
001 TBA                                 Staff                     Enr: 0 Max: NA

CAAM 654   TOPICS IN OPTIMIZATION                   Credits 3.00  Spring 00
Content varies from year to year.
001 TBA                                 Tapia, Richard A.         Enr: 0 Max: NA

CAAM 800   THESIS                                   Credits   Spring 00
No description
001 TBA                                 Staff                     Enr: 0 Max: NA