# EPGY Math Olympiad Problem Solving

Tentative schedule of topics and problem sets:

 Class Date Topic Problem Set Contest 1 TuesdayJuly 15 General problem-solving techniquesInvariants: parity, divisibility, and symmetryArithmetic ratiosAlgebraic expressions Problem Set: InvariantsProblem Set: Arithmetic ratiosProblem Set: Algebraic expressions 2000 AMC 122008 AIME IAnswers to the 2008 AIME I2008 USAMO (use this as a challenge for any student that finishes the problem sets, AMC 12 contest, and AIME contest) 2 WednesdayJuly 16 Functions and binary operationsGuest 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 ThursdayJuly 17 PolynomialsGuest lecture: Tatiana Shubin, The Mathematics of Strategy Games Problem Set: Polynomials Continue working on the 2000 AMC 12 and the 2008 AIME I. 4 FridayJuly 18 Introduction to combinatoricsThe product and sum rulesThe inclusion-exclusion principle Problem Set: The product and sum rulesProblem Set: Inclusion-Exclusion Continue working on the 2000 AMC 12 and the 2008 AIME I. 5 MondayJuly 21 Permutations and combinationsThe binomial theorem Problem Set: Permutations and combinationsCombinatorics Olympiad ProblemsProblem Set: The binomial theorem 2003 AMC 12 6 TuesdayJuly 22 The pigeonhole principle Problem Set: The pigeonhole principle Continue working on the 2003 AMC 12. 7 WednesdayJuly 23 Mathematical Induction Problem Set: Mathematical induction 2008 AIME IIAnswers to the 2008 AIME II 8 ThursdayJuly 24 Introduction to number theoryPrime factorization Problem Set: Introduction to number theoryProblem Set: Prime factorization Continue working on the 2003 AMC 12 and the 2008 AIME II. 9 FridayJuly 25 Proof by ContradictionGuest lecture: Persi Diaconis, The Mathematics of Shuffling Cards Problem Set: Proof by contradictionSET Tournament Continue working on the 2003 AMC 12 and the 2008 AIME II. 10 MondayJuly 28 Number Bases Problem Set: Number basesMovie--N is a number: Portrait of Paul Erdos 11 TuesdayJuly 29 Modular arithmeticInteger division results Problem Set: Modular arithmetic 12 WednesdayJuly 30 Number theory and modular arithmetic, continuedGuest lecture: Tom Davis, John Conway's "Rational Tangles" Problem Set: Miscellaneous problems involving integersSupplemental worksheet: the Euler Fermat Theorem 2002 AMC 12PAnswer key for the 2002 AMC 12P 13 ThursdayJuly 31 Probability and statisticsSequences and series Problem Set: ProbabilityProblem Set: StatisticsProblem Set: Sequences and seriesMovie: Hard Problems--The Road to the World's Toughest Math Contest 2005 AMC 12ASolutions for the 2005 AMC 12A 14 FridayAugust 1 Presentations of Olympiad problemsConclusions Math Contest TournamentTriangular NumbersFinal Problems 2005 AMC 12BSolutions for the 2005 AMC 12B

Supplemental Material: