Course Description

Techniques of solving mathematical problems will be reviewed, and the seminar will also prepare the students for college level mathematical competitions, like Putnam Exam, and Virginia Tech competition. Parallel to a systematic review of knowledge on algebra, combinatorics, number theory, calculus, geometry and other topics, students will also solve problems from selected problem sets, present and discuss their solutions in seminar.

Course syllabus and presentation schedule

Fall 2005 William and Mary Mathematical Competition 1 (due Oct 12, Wednesday) (all W&M students are welcomed to take it!)

Fall 2005 William and Mary Mathematical Competition 2 (due Nov 30, Wednesday)

Week 1	Problem set 1	Solution of problem set 1	Pigeon hole principle handout	handout from Berkeley
Week 2	Problem set 2	Solution of problem set 2		handout from Berkeley
Week 3	Problem set 3	Solution of problem set 3	Series, and sum handout	handout from Berkeley
Week 4	Problem set 4	Solution of problem set 4	Congruence handout	handout from Berkeley
Week 5	Problem set 5	Solution of problem set 5	Recurrence handout
Week 6	Problem set 6	Solution of problem set 6 (partial)	Inequalities handout	handout from Berkeley
Week 7	no problem set		Floor function handout	handout from W Australia
Week 8	Problem set 7	Solution of problem set 7 (partial)	Polynomial handout	handout from Berkeley 1 2
Week 9	Problem set 8	Solution of problem set 8 (partial)	Probability handout
Week 10	Problem set 9	Solution of problem set 9 (partial)	Binomial coefficient handout
Week 11	Problem set 10	Solution of problem set 10 (partial)	Games, strategy, puzzle handout
Week 12	Problem set 11	Solution of problem set 11 (partial)	Linear Algebra handout	handout from Berkeley
Week 13			Mathematical trick problems	handout from Berkeley

LaTeX information

MikTeX (TeX system for Windows)    WinEdt (TeX Editor for Windows)

LaTeX in W&M Math network   TeX Users Group (TUG) (information for all level of TeX users)

Inventor of TeX: Donald E. Knuth

LaTeX sample file  the pdf printout of the LaTeX sample file

Quick tutorial for LaTeX
----------------------------------------------------------------------------------------------------------------------------------------------------------------------

William Lowell Putnam Mathematics Competition Archive (University of Nebraska)
                                    A part of American Mathematics Competitions (AMC) website

• John Scholes has a Putnam Problems page giving problems from past years and solutions to most of them.
• David Rusin has compiled a Putnam Exams page containing links to problems and solutions.

Virginia Tech Regional Mathematics Contest
                   2005 Virginia Tech Math competition will be held on Saturday, Oct. 29, 8:30am-11:00am.

If you are interested in participate Putnam Competition and/or Virginia Tech Regional Mathematics Contest,  please contact Prof. Junping Shi by email shij@math.wm.edu

Training material from many other universities around US and Canada

MIT: 18.S34 (Fall 2005): PROBLEM SOLVING SEMINAR

           18.S34 Mathematical Problem Solving (Fall 2002)

UC Berkeley Math. H90 Putnam Problems Practice Seminar (Fall 2003)
                         Math. H90 Putnam Problems Practice Seminar (Fall 2004)

Stanford  Training for Putnam

Northwestern University Math Problem Solving Group

Harvey Mudd College Math 191: Putnam Problem Solving Seminar
Problem Solving References & Resources by Andrew J. Bernoff and Francis E. Su
 
Dalhousie University  Math 2790: A Journey Into The World of Problem-Solving

John Hopkings Putnam Problem Solving (110.225)

Georgia Tech 200 problems selected by Prof Yang Wang

UIUC Math Contests

Harvard Information

University of Waterloo training problems

Queen's University Putnam Practice Sessions

UCSD  pdf files of problem sets (1980-2003)

Basic questions about Putnam Competition

What is the Putnam Competition?

The Putnam Exam is a nationwide competetive exam given yearly to full-time undergraduates (all majors are welcome) in the United States and Canada. It is voluntary, and problems are presented with clever and ingenious solutions.

What is the format of this test?

The Putnam Exam consists of two parts, each containing six problems. Contestants are given 3 hours to work on each part. The first session runs from 10:00 a.m. to 1pm, and the second from 3:00 p.m. to 6:00 p.m.on the same day. You are not allowed to bring notes, books, or calculators.

When is it?

The competition is held on the first Saturday of December every year; this year, it is December 3, 2005.

What topics are covered on the Putnam Competition?

Geometry, algebra, trigonometry, calculus, linear algebra, combinatorics (counting), probability, number theory, complex numbers, differential equations, to name a few. Often, you will have to figure out what topic to use to answer a certain problem. The committee claims that every section contains two problems which only require algebra and cleverness, so you shouldn't be intimidated by this list.

How does the scoring work?

Each problem is worth 10 points, so you can potentially get 120 points. Partial credit is given, but typically this means 0, 1, 9, or 10 points for a problem. The median is usually 0 or 1 points. (That is, at least half of the students taking the test don't get any problems right.)

Created by Junping Shi, September 18th, 2004, Updated Fall 2005.