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 math.upenn.edu     Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15

William B. Ewald   Law     Telephone: (215)     email: wewald AT law.upenn.edu     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 cis.upenn.edu     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.

Syllabus

Schedule

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:

Mathematics
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.
Voting
Markov Chains (how Google searches).

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

Philosophy
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

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Math Homework Assignments:

• Homework Set 1 Due in class Thursday, Sept. 20. Papers will be accepted until 1:00 PM Friday.   [Hint for #4b].
• Bayesian Probability Problems These will not be collected.