MC36
Relation-Based Structures
Fall 1998
Moira McDermott

Office:  Olin 313
Phone:  x7478
Office Hours:  MTR 2:30-3:30, F 9-10, and always by appointment

Announcements:

Course Information:  html postscript
Send me e-mail

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)

    Four Color Theorem