Math 220, Philosophy 220, Law 520
Proof in Mathematics, Philosophy, and Law |
Fall 2012 |
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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 4E15William 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 462Proofs 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.

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 fromWhat 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

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.