Tentative schedule of topics and problem sets:
Class  Date  Topic  Problem Set  Contest 
1  Tuesday July 15 
General problemsolving techniques Invariants: parity, divisibility, and symmetry Arithmetic ratios Algebraic expressions 
Problem Set: Invariants  2000 AMC 12 2008 USAMO (use this as a challenge for any student that finishes the problem sets, AMC 12 contest, and AIME contest) 
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 inclusionexclusion principle 
Problem Set: The product and sum rules  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  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 
8  Thursday July 24 
Introduction to number theory Prime factorization 
Problem Set: Introduction to number theory  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 MovieN 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  2002 AMC 12P 
13  Thursday July 31 
Probability and statistics Sequences and series 
Problem Set: Probability Problem Set: Sequences and series Movie: Hard ProblemsThe Road to the World's Toughest Math Contest 
2005 AMC 12A 
14  Friday August 1 
Presentations of Olympiad problems Conclusions 
Math Contest Tournament  2005 AMC 12B 