Math 410-01, Problem solving techniques, Fall 2006
Instructor: Junping Shi

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 schedule

Week 1 (9/4)
Problem set 1 Pigeon hole principle handout
handout from Berkeley
Week 2 (9/11)
Problem set 2
Mathematical Induction handout
handout from Berkeley
Week 3 (9/18)
Problem set 3
Series, and sum handout
handout from Berkeley
Week 4 (9/25)
Problem set 4
Congruence handout
handout from Berkeley
Week 5 (10/2)
Problem set 5 Recurrence handout

Week 6 (10/9)
no problem set
Games, strategy, puzzle handout midterm practice problems
Week 7 (10/16)
no problem set, fall break

Week 8 (10/23)

Inequalities handout
handout from Berkeley
Va Tech Competition

Week 9 (10/30)
Problem set 6
Discussion of Va Tech problems

Week 10 (11/6)

Polynomial handout handout from Berkeley 1 2
Week 11 (11/13)

Probability handout 2nd midterm practice
Week 12 (11/20)
no class

Week 13 (11/27)

Discussion of 2nd practice problems

Putnam Exam

Week 14(12/4)

Discussion of Putnam problems


William Lowell Putnam Competition Official site
                2006 Putnam competition will be held on Saturday, Dec. 2, 10am-1pm and 3-6pm
William Lowell Putnam Mathematics Competition Archive (University of Nebraska)
                                    A part of American Mathematics Competitions (AMC) website
Virginia Tech Regional Mathematics Contest
                   2006 Virginia Tech Math competition will be held on Saturday, Oct. 28, 9:00am-11:30am.

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

Training material from many other universities around US and Canada


           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 2006.