Penn Math Math 220, Philosophy 220, Law 520
Proof in Mathematics, Philosophy, and Law
Fall 2012

Jerry L. Kazdan   Mathematics
    Telephone: (215) 898-5109
    email: kazdan AT
    Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15
William B. Ewald   Law
    Telephone: (215)
    email: wewald AT
    Office Hours: Tues. & Thurs, 4:30-5:15, and by appointment in Gittis 108 (Law School).
Scott Weinstein   Philosophy
    Telephone: (215) 898-1728
    email: weinstein AT
    Office Hours: Tue. & Thu. 12:00-1:20 (and by appointment) in COHN 462

Proofs are vital to many parts of life. They arise typically in formal logic, mathematics, the testing of medication, and convincing a jury. How do you prove that the earth is essentially a sphere (in particular, not flat)? In reality, proofs arise anywhere one attempts to convince others. However, the nature of what constitutes a proof varies wildly depending on the situation -- and on whom you are attempting to convince. Convincing your math teacher or a judge is entirely different from convincing your mother or a jury. The course will present diverse views of Proof. On occasion there may be guest lecturers.

The heart of this course is to achieve some real understanding of proofs in many parts of life. The emphesis will be on mathematical and physical insight and ideas, not complicated formulas.

Prerequisites: Math 104 or Philosophy 5 or equivalent.


  Math: Sept. 6 - Oct. 2   Exam 1: Oct. 2
  Law: Oct. 4 - Nov. 1 (no meeting Oct 23)   Exam 2   Answers
  Philosophy:   Nov. 6 - Dec. 6   Exam 3: Dec.6

Course and Homework Grading: Each of the three parts of the course will have an in class exam (80 minute) at the end of that part. There may also be homework assignments. The course grade will weigh each part separately.

Some References: books, articles, web pages
Video from a Symposium on Proof, Nov.9, 2012 [Released: 11/14/12]

Class Outline:

Sept. 6, 2012: Notes,   Video of Lecture
SoD, a Game   Five Men, a puzzle   Rationals are countable
Euler: Polyhedra (This is from What is Mathematics? by Courant and Robbins)   Seven Bridges of Königsberg
Devlin: Bayes (see also the useful tree diagram).   Bayes articles
What is a Biostatistician Trying to Prove? A special lecture by Professor Susan Ellenberg of Penn's Medical School.
Markov Chains (how Google searches).

Email Oct 2
Notes, Oct. 4
Notes, Oct. 9
Email, Oct. 9

Nov. 12: Email
Nov.18 Problem Set Due in class on Tuesday, November 27, or in Prof. Weinstein's mail slot in 433 Cohen Hall by 1:00 p.m. the same day,
Dec. 5: Memoirs 1-7
Dec. 22: Memoir7add

Math Homework Assignments: