Welcome to Experimental Mathemat

Welcome to Experimental Mathematics (Math 350). This course is a lab based mathematics course intended to highlight the art and science

problem solving. It is expected that you come to this course with some knowledge of programming. We will be using the computer to generate

examples, run simulations, and do complicated calculations that will enable us to conjecture what the solution to a given problem may be.

This will be an introduction to how mathematicians and scientists pose and solve problems.

The course will run as follows

During the first part of the course we will explore some mathematical software such as Geometer's Sketchpad, Matlab, and Maple.
You will work on the projects found below.
You will work on your own problems (both posed and solved by you).
Several times during the semester you will present your solutions to the class.

In this course you should not confuse the written project with "showing your work". Instead your written work should indicate to the reader how well you understand

the mathematical concepts you have used in your solution. A list of calculations without the reasoning is not mathematics. When writing up each project your goal will be to

communicate mathematical ideas to another person rather than show you've completed the assignment.

With this in mind each mathematical write up must include the following:

Introduction: A brief description of the central problem. Do not simply recopy the problem. Rather, describe the problem in enough detail that another math student could understand the problem and its importance. Also include (when appropriate) a "gut-feeling" solution with reasoning.
Results: Answer each question carefully, define each mathematical term and variable in the problem , include the statement of any theorems that were needed to solve the problem, and include a complete solution. If you used computer software to help solve the problem, be sure to cite where and how it was used and attach a copy of your code at the end.
Conclusion: Include brief summary of the problem, highlighting the parts that you felt were most interesting or surprising. Compare you "gut-feeling" solution to your actual solution explaining any differences. State at least 3 new problems that are related to the original that you would like to work on in the future.

Also in this course we will be reading about real-world problems (links to several of the articles are found below). You will also be asked to propose solutions to these (possibly) non-mathematical problems. Your write up for these problems should include:

Introduction: A statement of the problem in your own words and a brief discussion of the problem.
Results: "Solutions" on three different settings: a. What you can do as an individual. b. What we can do as a campus. c. What we can do as a society. These solutions must be plausible. That is you can't say, "Just stop doing it".
Conclusion: Discuss what might happen if any (or all you solutions were implemented) and what might happen if the problem is ignored or gets worse.

PROJECTS:

Geometer's Sketchpad
Click here to download a Maple worksheet to be opened in Maple 10 ONLY. You may need to right click and choose "Save Target"
Maple Fun
Matlab
Dueling Morons
Elliptical gaps
Galileo Sequences
Digit Games *
Gambler's Ruin
Sierpenski's Triangle
Treasure Hunt *
Arc Length of an Eight *
Airport Problem
Bend-o-matic

15. Final Project

Above there are 3 projects that are followed by asterisks, these are projects that can be replaced by a project of your own invention. It must be approved in advance by the class. Your "project" proposal should have the following:

A clear statement of an interesting (judged by the class) problem in mathematics whose solution is unknown to you.
A description of a way to experiment with, model, or simulate, the problem so that you may support your conjecture with examples and possibly acquire insight into a mathematical solution.

Other projects may be modified (with prior approval) to suit your interests.

Reading links: