Mount Holyoke College Math 251

Laboratories in Mathematical Experimentation - Spring 2005

"The Bridge to Higher Mathematics"

Instructor Information: Jim Morrow

Office: #1 Woodbridge (See Map)

E-Mail: jmorrow@mtholyoke.edu

Class Meetings: MW 1:15 -3:00

Office Hours: MW after class, TTh 11AM-Noon, F & other hours by appointment

Technology mentor: Mary Kazandjieva

E-Mail: makazand@mtholyoke.edu

Office Hours: MW 8-9PM, other hours by appointment

GRADING LAB REPORTS

UPDATED 2/28

Texts: Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics, by the MHC Mathematics and Statistics Department, Key College Publishing. ISBN: 0-387-94922-4; Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire. Recommended: LaTeX: A Document Preparation System, by Leslie Lamport, Addison Wesley, 1994.

Computers: We will be using the computer programs that are available on the computers in Clapp 401, 420 and 422.

Grading: Your grade for the course will be based primarily on written lab reports; there will be approximately six of these.

Resources: Your primary resources are your instructor, (Utilize his office hours!) and your textbooks, including the LaTeX reference manual. However, we have an additional resource this semester, tech mentor Mary Kazandjieva, who will be able to assist you with many of the technological details of the course, including document preparation using LaTeX, computer programming for your lab experiments, and presentation software. Office hours and other details to come!

Agenda: The agenda for Math 251 can be explained in large part by examining the lengthy title of the course text, Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics and the course designation, Writing Intensive.

First: Laboratories. A definition of laboratory is "a place equipped for experimental study in a science or for testing and analysis; broadly : a place providing opportunity for experimentation, observation, or practice in a field of study." In your previous study of mathematics, you probably didn't have so much opportunity for experimentation as you will have in this course. The experimentation you do will be collaborative, in the sense that we will share and report on discoveries made by all of us in the course of our experimentats. Labs generally have tools; for our labs we'll have computer software tools: general purpose computer programming languages and such software as Maple, Geometer's Sketchpad, and Excel. Additionally, you'll be able to use/learn to use the presentation tools LaTeX and PowerPoint.

Secondly, Mathematical Experimentation. What makes an experiment mathematical? Well, much of the point of mathematical experimentation is to notice patterns and to ask questions and form conjectures about what is generally true in a mathematical universe. You will investigate just a few topics, each in significant depth. For topics, I plan to include linear iteration, cyclic difference sets, the Euclidean algorithm, and graph coloring. (Chapters 1 - 3 and 5 of the Lab text.) You'll have the opportunity to choose a topic of your own, as well.

Thirdly, Writing Intensive. You will learn to write a technical description of your experiments and of the mathematical objects you use, give justification for what you believe to be true on the basis of experimental evidence and logical inference, and weave these two aspects into a readable (interesting, even!) exposition.

Fourth: Bridge to Higher Mathematics. A key feature of higher mathematics is the devotion to ideas of proof. In this course you will learn to write proofs and, undoubtedly, extend the notions you have now about the nature of proof. There is currently lively controversy in the mathematical community about the concept of proof, so I'll say no more at this point other than that, as a working idea, proof involves justification and, ideally, understanding and explanation.

For more about the course, including some corrections to the text, click on MHC LAB COURSE.