(202) 994-6237
robinson@gwu.edu
http://home.gwu.edu/~robinson
? Week 1: (short week): Introduction to Computational Mathematics.
Overview of Computational Mathematics. Overview of the course. Lab: Basic
Unix, basic HTML.
? Week 2: Introduction to LaTeX and postscript. The LaTeX typesetting
system as the state of the art in technical document preparation. Postscript
and PDF formats. Posting technical documents on the web. Lab: Using LaTeX
and postscript.
? Week 3: Discussion of the mathematical modeling process. Classical
models including algebraic equations, linear models, ordinary and partial
differential equations, optimization, and stochastic models. Lab: Introduction
to Matlab.
? Week 4: Case study in numerical methods: quadrature. Basic
methods of quadrature. Analysis of errors. Adaptive and Monte Carlo methods.
Lab: Programming in Matlab.
? Week 5: Computer arithmetic errors in calculations. Basic
theory of integer and floating point arithmetic. IEEE floating point standard.
Round off errors and loss of significance. Interval arithmetic and arbitrary
precision arithmetic. Lab: Introduction to Maple.
? Week 6: Lab: Computer Algebra systems. The strengths and weaknesses
of computer algebra systems. Exploring the capabilities of Maple.
? Week 7: Comparison of various computing environments. Review
of Fortran and C. Comparison of Maple, Matlab and traditional languages.
Discussion of object oriented programming and Java. Lab: Benchmarking.
? Week 8: Intermediate computer literacy: Compression and encryption
algorithms. The internet and TCP-IP. Operating systems and graphics environments.
Overview of available computational resources. Free software vs commercial
software.
? Project 1: Choose one substantial computing environment (either
general purpose or special purpose) that available for free over the internet.
It must be one you have not used before. Download and install it on some
computer system. Run several substantial test problems. Write a 5 page
review of the software including: what is the software intended for and
who are its likely users? How easy or hard is it to get up and running?
How easy or hard is it to use? Does it seem to serve it’s intended
purpose? Due March 16.
? Week 9: Algorithms and data structures: introduction to basic
computer science. Lab: Implementing basic combinatorial and discrete
geometry algorithms.
? Week 10: The performance of programs. Computational complexity
and computability. Measuring and improving the efficiency of a program
or an algorithm. Computational complexity: the theoretical limits to this
process. Lab: Studying the performance of algorithms.
? Project 2: This will be your final project. It should consist
of an in-depth analysis of a case study from a field of your interest.
You should discuss the scientific phenomena being investigated, the mathematical
model used, the numerical approach, the computational implementation and
the end results. An abstract is due March 30. The project should prepared
with web based content in a form that can be presented to the class at
the end of the semester. The subject of the final project is to be mutually
agreed upon by the student and instructor.
? Week 11: Classical numerical analysis revisited. Numerical
methods for solving ordinary and partial differential equations. Lab: Applications
to physical, biological and social sciences.
? Week 12: Fourier Methods and wavelets. The discrete Fourier
transform and the FFT. The wavelet transform. Lab: Experiments with transforms.
? Week 13: Specialized software. Many specialized computing
environments are available for solving problems in different fields. Lab:
Molecular biology software.
? Week 14: Some newer mathematical models and numerical techniques.
Topics may include fractals and chaos, neural networks, evolutionary algorithms.
Lab: Experiments with some of these models in different environments.
? Week 15: Student presentations.