OUTLINE OF CS 422/522

• I. PROBLEM-SOLVING ENVIRONMENTS
  • 1. Introduction to CS 422/522

    A. Computational science: past, present, future

    B. Mechanics of the course

    C. Languages and problem-solving environments

  • 2. Matlab

    A. Elementary operations

    B. History of Matlab and MathWorks

    C. Graphics

    D. MathWorks marketing statistics

    E. m-files and functions

  • 3. Ordinary Differential Equations (ODEs)

    A. Autonomous initial-value problems (IVPs)

    B. Phase space

    C. Numerical methods

    D. Software

  • 4. Chaos

    A. The Lorenz equations

    B. Other chaotic systems

  • 5. Prof. Steve Strogatz: Interactive Differential Equations
  • 6. Problem-Solving Environments (PSEs)

    A. PSEs in statistics

    B. What is a PSE?

    C. Reasons for the success of Matlab

• II. SYMBOLIC COMPUTING
  • 1. Discrete vs. Continuous

    A. Discrete problems, continuous problems

    B. Floating point arithmetic

    C. Exact arithmetic

  • 2. Maple

    A. History

    B. Elementary operations

    C. Accuracy of physical constants

    D. Variables, expressions, and calculus

  • 3. Finite vs. Infinite Algorithms and Problems

    A. Finite vs. infinite algorithms

    B. Finite vs. infinite problems

    C. Example: Newton's method for a quintic

    D. Infinite algorithms for finite problems

  • 4. Convergent Series

    A. Maple expressions, functions, procedures

    B. Series

    C. Power series

    D. Power series in Maple

  • 5. Asymptotic Series

    A. Definitions

    B. Stirling series for n!

    C. Using files in Maple

    D. Other examples

    E. Asymptotic series and domains of convergence

  • 6. Asymptotic Series, Science, and Symbolic Computing

    A. Asymptotic series in science

    B. Symbolic computing wrap-up

    C. The Inverse Symbolic Calculator (ISC)

• III. SOFTWARE LIBRARIES
  • 1. Overview

    A. NAG, IMSL, and other general-purpose libraries

    B. The long tradition of numerical software

    C. Netlib

  • 2. Linear Algebra Software

    A. 30-year timeline

    B. EISPACK

    C. LINPACK

    D. The BLAS and LAPACK

    E. ScaLAPACK

  • 3. TOMS, NHSE, and Numerical Recipes

    A. TOMS (Transactions of Mathematical Software)

    B. NHSE (National High-Performance Software Exchange)

    C. Numerical Recipes

  • 4. Prof. Saul Teukolsky: Numerical Recipes

• IV. VISUALIZATION
  • 1. Introduction to Scientific Visualization (Prof. Land)
  • 2. Introduction to IBM Data Explorer (Prof. Land)
  • 3. More on Data Explorer (Prof. Land)
  • 4. Fractals and Random Walk

    A. Fractals

    B. Fractal dimension

    C. Random walk

  • 5. Brownian Motion

    A. Random walk in 2D or 3D

    B. Brownian motion -- the physics

    B. Brownian motion -- the fractal

  • 6. A video History of Scientific Visualization (Prof. Land)

• V. PARALLEL COMPUTING
  • 1. Overview

    A. Brains and machines

    B. Some history

    C. References

    D. SIMD, MIMD, SPMD

  • 2. Introduction to MultiMATLAB

    A. History of the MultiMATLAB project

    B. Start, Eval, ID, Nproc, Quit

    C. Send, Recv, Probe

    D. Graphics

  • 3. SPMD Programming in MultiMATLAB
  • 4. Random Numbers and Monte Carle Methods

    A. Why are random numbers useful in computing?

    B. Monte Carlo integration

    C. Parallel random numbers

  • 5. More on Monte Carlo

    A. Huge state spaces

    B. 1/sqrt(N) convergence

    C. MultiMATLAB demo

  • 6. Dr. John Zollweg: Software Tools at the Cornell Theory Center

• VI. PROGRAM TRANSFORMATIONS
  • 1. Introduction

    A. What are "program transformations"?

    B. Automatic differentiation: history

    C. Gradients and Jacobians

    D. An example

  • 2. Using ADIFOR

    A. An example

    B. Derivatives in optimization codes

    C. A Newton's method example

  • 4. Forward vs. Reverse Mode of Automatic Differentiation

    A. Forward mode

    B. Reverse mode

    C. Numerical Experiment

  • 5. MultiMATLAB Demos in the Theory Center Training Facility

• VII. WEB-BASED COMPUTING
  • 1. The Big Picture

    A. The Web

    B. Scientific journals

    C. Science education

    D. Science databases

    E. Web computing

    F. Biological genomes

  • 2. Life on Planet Earth

    A. History

    B. What life is made of

    C. The coding mechanism

    D. The code itself

    E. Reproduction and evolution

  • 3. Genomes and the Web

    A. Genetic codes and computer codes

    B. Organisms whose genomes are known

    C. Genomes on the Web

  • 4. A Case Study

    A. Human hemoglobin A

    B. Sickle-cell anemia

    C. BLAST

  • 5. Whole-Genome Random Sequencing

    A. Haemophilus influenzae

    B. Cloning of random fragments

    C. Assembling the fragments

    D. Closing the gaps

    E. Goodbye

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