Notes for MAT 331

Mathematical Problem Solving with Computers

Summer 2002

Santiago R. Simanca & Scott Sutherland

The University at Stony Brook

Mathematical Problem Solving with Computers

Summer 2002

Santiago R. Simanca & Scott Sutherland

The University at Stony Brook

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- Preliminaries about Maple
- Starting a Maple Session
- Basic Maple
- The Maple worksheet
- Assignments, Functions and Constants
- The limit command
- The diff (and Diff) command
- The int (and Int) command
- The subs command
- Plotting with Maple
- Exercises

- If the Curve Fits, Wear It
- Interpolation
- When the data is approximate
- Fitting a line to data
- Fitting a cubic to data
- Fitting other types of funtions
- Fitting a circle
- Robust fitting
- A nod toward statistics

- The Art of Phugoid
- The Phugoid model
- What do solutions look like?
- Existence of Solutions
- Numerical Methods
- Seeing the flight path
- Fixed Point Analysis
- Qualitative Classification of Solutions
- Dealing with the Singularity

- Bibliography
- fsqFsHn sGGousG
- Introduction to Cryptography
- Simple Ciphers
- Defining functions with proc; Local and global variables
- Caesar cipher redux
- Improved Caesar-like ciphers
- Reading and Writing from a file
- Affine enciphering
- Enciphering matrices
- Modern cryptography
- Some Number Theory
- The RSA Public key cryptosystem
- RSA encoding a file

- Bibliography
- A turtle in a fractal garden
- Turtle Graphics
- A fractal
- Recursion and making a Koch Snowflake with Maple
- Making a tree
- Fractal Dimension
- Cantor sets
- The Sierpinski gasket
- Inside the turtle's shell
- Extending the turtle's commands

- About this document ...

2002-08-29