## I. Symbolic Computation Basics of Symbolic Computation Visualization Symbolic Problem Solving Programming Language Concepts Introduction to Numerical Computation II. Procedural Programming Symbolic Programs Numerical Programs Linking Symbolic Language to C/Fortran Control Structures Data Structures

• III. Numerical Computation

### Methods of Computation, e.g., Root Finding Discrete Mathematics (1st and 2nd order difference equations) Data Fitting Area problems Taylor Series (for more advanced students)

• Sources of (Numerical) Error (APES)

#### Approximation Precision Error Stability

• Practical Considerations and Pitfalls

#### Memory, speed, etc.

Our hope is that each contributed module will be essentially "stand-alone" and will be organized roughly as follows:

• Description of the problem (the "physics" of it)
• Description of the relevant method(s)
• How errors arise (APES)
• Pitfalls and Practical Considerations (tricks of the trade)

The modules will be as interactive as possible, containing code, graphics, etc. (at the introductory level our use of the Maple and Mathematica computing engines should make this straightforward. The format for the more advanced courses is yet to be determined.) As the above makes clear, we feel it is very important that the problem-based-approach stress not only the RIGHT way to do things, but also WHAT CAN GO WRONG, both in terms of sources of error (round-off, improper convergence, etc.) and in terms of "pitfalls" which might be encountered, such as choosing a method which is too slow for the available hardware. This, again, can best be accomplished through the use of an interactive approach which stresses a continual ASSESSMENT of the computational approach through ongoing comparison with the reality of the given problem.

### Buffon's Needle Compound Interest Rates One dimensional crystal Monthly Payment on a Mortgage Simple Pendulum Pond in an acre lot THe area of an Ellipse The Logistic Equation Chemical Rate Constants Diffusion of Heat Time Value of Money Kinematics with Friction

Again, we are interested in any more problems you can suggest, and if you are interested in putting together a "module" or two please contact me and we can discuss the type of format we are looking for.