EPGY Math Olympiad Problem Solving

• Course schedule, updated July 18, 2008

• Course syllabus

• Lecture notes

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:

• 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 contests, and AIME contests)

  Solutions to the 2008 USAMO

• 2003 AMC 12A

  Answers to the 2003 AMC 12A

• 2008 AIME II

  Answers to the 2008 AIME II

• 2007 AIME I

• 2007 AIME II

• Supplemental problem set: Graph theory

• Supplemental problem set: Complex numbers

• Supplemental problem set: Inequalities problems

• Supplemental problem set: Problem-solving strategies

• Supplemental problem set: Triangular numbers