18.322 Math and Computers

Spring, 2002

Monday, Wednesday 2:00-4:00

26-152 (The TEAL Room)

Prof. Sara Billey

TA: Etienne Rassart

Dates to Remember

Monday March 4-6, 2002: * Oral Presentations: Project I. SUGGESTED PROJECTS .
Monday April 22, 2002 * Due: Written proposal for Project II
Monday May 6-8, 2002 * Oral Presentations: Project II.
Wednesday May 15, 2002 * Due: Written report for Project II
Problem sets due:

Tuesday February 19, 2002
Monday March 18, 2002
Monday April 8, 2002
Monday April 29, 2002

Course Materials

Office hours for lecturer and TA

Sara Billey: Friday, 3:00-4:00pm

Etienne Rassart: Thursday 3:00-5:00pm

Interesting Web Sites

A=B by Petkovsek, Wilf, and Zeilberger. This is the main text for the course.
Free Maple Introduction on Athena
Maple 7 for Free through MIT's site license.
Maple Packages and Programs by Doron Zeilberger to acompany "A=B".
Hyper is a Mathematica program that will find hypergeometric solutions of linear recurrences with polynomial coefficients, if they exist, or will prove that they do not exist, if they don't.
Wolfram Koepf's web page with maple code for the hyper algorithm.
Maple on the Web - Links to almost every Maple related web site.
Sloane's On-Line Encyclopedia of Integer Sequences
Eric Weisstein's World of Mathematics Dictionary of almost all mathematical terminology.
The new proof of the Four Color Theorem
Mathematical mysteries: Kepler's conjecture (an easy to read summary)
Kepler's conjecture and proof. Info on the computer aided proof by Thomas Hales.
JSTOR

Overview

Summary: "Math and Computers" will be an introduction to computational mathematics and computer verified proofs. The course aims to teach students rigorous mathematics which has developed in conjunction with modern computational facilities. It will also serve as an introduction to mathematical programming and symbolic computation through experimentation and programming projects. This years topic will include combinatorial methods in recursion where computers have been very successful at proof verification. Lectures will cover the mathematical theory behind the automation of proofs. In the laboratory, students will construct their own proof verification system in the programming language MAPLE and explore their own conjectures. This course will also serve as an introduction to MAPLE.

Grading: Four Problem Sets each worth 10%, Two projects each worth 25%, Participation worth 10%. Projects will be assigned letter grades based on content and oral presentation. Problem sets will be graded according to the number of problem successfully completed. You may be asked to extend your solution to particular problems if they are not sufficient for full credit. Everyone is expected to participate in lecture, lab discussions, and attend all student project demonstrations. The participation grade will be given according your contribution to the class as a group. High marks will be given to those who attend class regularly, ask good questions, discuss projects will fellow students, or offer advice on Maple programming.

Text books: The main text will be A=B by Petkovsek, Wilf, and Zeilberger. It is availble at Quantum books in hard cover or you can down load it from the web. We also recommend buying a Maple programming book. Quantum Books will be carying "Maple : An Introduction and Reference" by Michael Kofler but there are lots of other books out there to choose from.

Email list: There is a course email list called 18.322-students which will be used from time to time to make course announcements. Please add yourself to the list from an athena account. Here are the Instructions.

Tentative Schedule:

Wednesday February 6, 2002 * Lecture: Introduction to 18.322 and Maple

Monday February 11, 2002 * Lecture: Solving Recurence relations

Wednesday February 13, 2002 * Lecture: Recurence relations and Sumation

Monday February 18, 2002 * Holiday

Tuesday February 19, 2002 * Lecture: Calculus of Summation * Problem Set 1 due.

Wednesday February 20, 2002 * Lecture: Binomial Coefficients

Monday February 25, 2002 * Lecture: Top Ten Binomial Identities

Wednesday February 27, 2002 * Lecture: More on Binomial Coefficient Identities

Monday March 4, 2002 * Project I Demos * Project I due.

Wednesday March 6, 2002 * Project I Demos

Monday March 11, 2002 * Lecture: Hypergeometric Identities

Wednesday March 13, 2002 * Lecture: Outline of WZ Method

Monday March 18, 2002 * Lecture: Sister Celine's Algorithm * Problem Set II due

Wednesday March 20, 2002 * Lecture: Gosper's Algorithm

Monday March 25, 2002 * Spring Break

Wednesday March 27, 2002 * Spring Break

Monday April 1, 2002 * Lecture: Gosper's Algorithm-- Steps 2 and 3

Wednesday April 3, 2002 * Lecture: Gosper's Algorithm-- Examples

Monday April 8, 2002 * Lecture: Zeilberger's Algorithm * Problem Set 3 Due

Wednesday April 10, 2002 * Lecture: Zeilberger's Algorithm with examples

Monday April 15, 2002 * Holiday

Wednesday April 17, 2002 * Lecture: WZ Phenomena

Monday April 22, 2002 * Lecture: Dual Identities * Proposal Due for Project II

Wednesday April 24, 2002 * Lecture: Algorithm Hyper and the Ring Of Sequences

Monday April 29, 2002 * Lecture: Algorithm Hyper * Problem Set 4 Due

Wednesday May 1, 2002 * Lecture: Topics - The Four Color Theorem

Monday May 7, 2002 * Lecture: Project II Demos

Wednesday May 9, 2002 * Lecture: Project II Demos

Monday May 14, 2002 * 1.5 lab hours

Wednesday May 16, 2002 * Guest Lecture on Computational Mathematics * Project II due

Sara Billey

Last modified: Tue Apr 3 16:57:16 IST 2002