EPGY Math Olympiad Problem Solving

Tentative schedule of topics and problem sets:

Class Date Topic Problem Set Contest
1 Tuesday

July 15

General problem-solving techniques

Invariants: parity, divisibility, and symmetry

Arithmetic ratios

Algebraic expressions

Problem Set: Invariants

Problem Set: Arithmetic ratios

Problem Set: Algebraic expressions

2000 AMC 12

Solutions to the 2000 AMC 12

2008 AIME I

Answers to the 2008 AIME I

2008 USAMO (use this as a challenge for any student that finishes the problem sets, AMC 12 contest, and AIME contest)

Solutions to the 2008 USAMO

2 Wednesday

July 16

Functions and binary operations

Guest lecture: Stan Isaacs, Puzzles and Problem Solving

Problem Set: Functions and binary operations Continue working on the 2000 AMC 12 and the 2008 AIME I.
3 Thursday

July 17

Polynomials

Guest lecture: Tatiana Shubin, The Mathematics of Strategy Games

Problem Set: Polynomials Continue working on the 2000 AMC 12 and the 2008 AIME I.
4 Friday

July 18

Introduction to combinatorics

The product and sum rules

The inclusion-exclusion principle

Problem Set: The product and sum rules

Problem Set: Inclusion-Exclusion

Continue working on the 2000 AMC 12 and the 2008 AIME I.
5 Monday

July 21

Permutations and combinations

The binomial theorem

Problem Set: Permutations and combinations

Combinatorics Olympiad Problems

Problem Set: The binomial theorem

2003 AMC 12

Answers to the 2003 AMC 12

6 Tuesday

July 22

The pigeonhole principle Problem Set: The pigeonhole principle Continue working on the 2003 AMC 12.
7 Wednesday

July 23

Mathematical Induction Problem Set: Mathematical induction 2008 AIME II

Answers to the 2008 AIME II

8 Thursday

July 24

Introduction to number theory

Prime factorization

Problem Set: Introduction to number theory

Problem Set: Prime factorization

Continue working on the 2003 AMC 12 and the 2008 AIME II.
9 Friday

July 25

Proof by Contradiction

Guest lecture: Persi Diaconis, The Mathematics of Shuffling Cards

Problem Set: Proof by contradiction

SET Tournament

Continue working on the 2003 AMC 12 and the 2008 AIME II.
10 Monday

July 28

Number Bases Problem Set: Number bases

Movie--N is a number: Portrait of Paul Erdos

11 Tuesday

July 29

Modular arithmetic

Integer division results

Problem Set: Modular arithmetic
12 Wednesday

July 30

Number theory and modular arithmetic, continued

Guest lecture: Tom Davis, John Conway's "Rational Tangles"

Problem Set: Miscellaneous problems involving integers

Supplemental worksheet: Fermat's Little Theorem

Supplemental worksheet: the Euler Fermat Theorem

2002 AMC 12P

Answer key for the 2002 AMC 12P

13 Thursday

July 31

Probability and statistics

Sequences and series

Problem Set: Probability

Problem Set: Statistics

Problem Set: Sequences and series

Movie: Hard Problems--The Road to the World's Toughest Math Contest

2005 AMC 12A

Solutions for the 2005 AMC 12A

14 Friday

August 1

Presentations of Olympiad problems

Conclusions

Math Contest Tournament

Triangular Numbers

Final Problems

2005 AMC 12B

Solutions for the 2005 AMC 12B


Supplemental Material: