Announcements:
Problem Sets:
PS #1 (9/21/98) Solutions
PS #2 (9/29/98) Solutions
PS #3 (10/8/98) Solutions
PS #4 (10/14/98, 17:00) Solutions
PS #5 (10/22/98, 17:00) Solutions
PS #6 (11/4/98, 17:33) Solutions
PS #7 (11/13/98, 16:15) Solutions
PS #8 (12/9/98, 17:30) Solutions
Paper:
assignment evaluation/peer review guide mathematical writing Writing Resources on the WWW (MIT) The Craft of Scientific Writing: A WWW Companion Guide. This Web page by Michael Alley is meant as a companion to his book. Among other things, it has lots of exercises that help re-inforce the rules of grammar and punctuation expounded in his book. Writing a Math Phase Two Paper (MIT) This paper is a primer on mathematical writing, especially the writing of a short math paper. This paper is intended to be a model of the format, language, and style of such a paper. First, it reviews the general purpose of the MIT writing requirement and the specific way it must be completed for the math department. Then it explains how to write a short math paper: the organization into sections, the use of language, and the presentation of mathematics. Finally, it gives an example of mathematical writing. (Postscript version of this article by Steven L. Kleiman) Checklist for "Writing a Math Phase Two Paper" This Checklist is an index to the primer above. Use this Checklist to find material in the primer and as a checklist of points to consider. The section on handling mathematical symbols is particularly helpful. Goss' Hints on good mathematical writing (David Goss) (postscript file) evaluation of internet based information(MSU)
Syllabus
This schedule is tentative. Follow links to individual weeks for details and assignments.
Week 0: Course Organization,
Fundamentals of Counting
Week 1: Permuations,
Combinations, Logic
Week
2: Logic cont., Methods of Proof
Week 3: Methods of
Proof, Sets
Week 4: Sets, Inclusion/Exclusion,
Induction (no class during NOBEL CONFERENCE)
Week 5: Induction
Find
the flaw (Exam 1, 10/16)
Week 6: Recursive
Definitions, Properties of Integers (Fall Break 10/23)
Week 7: Division,
Euclidean Algorithm, Modular Arithmetic (Fall Break 10/26)
Large Primes
Week 8: Modular Arithmetic,
Elementary Cryptography, Relations and Functions RSA
FAQ Jabberwocky
Week 9: Properties
of Relations, Posets, Equivalence Relations
Week 10: Posets,
Lattices, Equivalence Relations (Exam 2, 11/20)
Week 11: Graphs
Week 12: Graphs,
Trees
Week 13: Trees
Can computers prove theorems?
Computer Math Proof Shows Reasoning Power (NYT 12/1/96)Corrections and Comments on above article
Summary of results obtained with Argonne's Automated Deduction Software
What is the best way to stack oranges? (NYT 8/25/98)