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2008-09 WOOT Class Schedule

Each class will be held on two dates, as shown. The first class will always be on a Monday, and held at 7:30-9:30 PM ET/4:30-6:30 PM PT. The second class will always be on a Thursday, and held at 9:00-11:00 PM ET/6:00-8:00 PM PT. This class schedule is tentative, and is subject to change.

Class	Topic	Date 1	Date 2
0	Orientation	Monday, September 8	Thursday, September 11
1	How to Solve It, Part 1	Monday, September 15	Thursday, September 18
2	How to Solve It, Part 2	Monday, September 29	Thursday, October 2
3	Induction and Pigeonhole Principle	Monday, October 13	Thursday, October 16
4	Invariants	Monday, October 27	Thursday, October 30
5	Basic Geometry	Monday, November 3	Thursday, November 6
6	Advanced Geometry	Monday, November 17	Thursday, November 20
7	Sequences & Series	Monday, December 1	Thursday, December 4
8	Polynomials and Complex Numbers	Monday, December 15	Thursday, December 18
9	Number Theory A	Monday, January 5	Thursday, January 8
10	Number Theory B	Monday, January 19	Thursday, January 22
11	Triangle Geometry	Monday, February 2	Thursday, February 5
12	Analytic Geometry	Monday, February 16	Thursday, February 19
13	Basic Combinatorics	Monday, March 2	Thursday, March 5
14	Advanced Combinatorics	Monday, March 16	Thursday, March 19
15	Inequalities	Monday, March 30	Thursday, April 2
16	Game Theory	Monday, April 13	Thursday, April 16

Several classes have two parts, such as "Basic Combinatorics" and "Advanced Combinatorics". In such classes, the first part will focus on AIME and beginning olympiad-level problems, and the second part will focus on advanced olympiad-level problems.

Otherwise, the first half of the class will consist of problems that introduce the appropriate techniques and principles, and the second half of the class will cover challenging olympiad-level problems that use those techniques and principles.

1. How to Solve It, Part 1
2. How to Solve It, Part 2
These classes will introduce common problem solving heuristics, such as trying small cases, looking for a pattern, and exploiting symmetry.

3. Induction and Pigeonhole Principle
This class will introduce the two fundamental problem solving concepts of mathematical induction and the Pigeonhole principle. We will also discuss variations, such as strong induction.

4. Invariants
In problems that involve a process, an invariant is a quantity that does not change. This class will show how to come up with quick proofs by looking for and recognizing invariants.
Example Problem:
On the Island of Camelot live 13 grey, 15 brown and 17 crimson chameleons. If two chameleons of different colors meet, they both simultaneously change color to the third color (e.g. if a grey and brown chameleon meet each other they both change to crimson). Is it possible that they will eventually all be the same color? (Tournament of the Towns, 1984)

5. Basic Geometry
This class will lead students through solving problems by using concepts in basic Euclidean geometry, such as similar triangles and cyclic quadrilaterals.

6. Advanced Geometry
This class will build on the concepts introduced in the previous class (Basic Geometry), and focus on locus and construction problems.

7. Sequences & Series
Problems involving sequences and series appear frequently on the AIME and USAMO, and this class will introduce techniques to solve such problems, such as telescoping sums.

8. Polynomials and Complex Numbers
This class will introduce fundamental algebraic results about polynomials and complex numbers. The difficulty level of problems will range from AIME to USAMO.

9. Number Theory A
This class will show how key concepts (namely divisibility and modular arithmetic) can be applied to solve problems in number theory. There will be an emphasis on AIME-level problems.

10. Number Theory B
This class will build on the concepts introduced in the previous class (Number Theory A), to tackle more difficult olympiad-style problems.

11. Triangle Geometry
This class will introduce students to the geometry of the triangle, by describing the major points of the triangle and the formulas, lines, and circles that link them.

12. Analytic Geometry
This class will demonstrate analytic methods, such as complex numbers and vectors, to solve problems in geometry.

13. Basic Combinatorics
This class will show how to use counting arguments to solve problems in combinatorics. There will be an emphasis on AIME-level problems.

14. Advanced Combinatorics
This class will build on the concepts introduced in the previous class (Basic Combinatorics), to tackle more difficult olympiad-style problems, by using more advanced techniques, such as bijective arguments and the Principle of Inclusion-Exclusion (PIE).

15. Inequalities
This class will deal with classical inequalities, such as the AM-GM inequality (and its generalization the Power Mean inequality) and the Cauchy-Schwarz inequality.

16. Game Theory
This class will introduce students to combinatorial game theory, and show students how to analyze such games.
Example Problem:
The Y2K Game is played on a 1 x 2000 grid as follows. Two players in turn write either an S or an O in an empty square. The first player who produces three consecutive boxes that spell SOS wins. If all boxes are filled without producing SOS then the game is a draw. Prove that the second player has a winning strategy. (USAMO, 1999)

2008-09 WOOT Assignment Schedule

Assignment	Available	Due
Practice Olympiad 1	Wednesday, October 8	Monday, October 13
Practice Olympiad 2	Wednesday, October 29	Monday, November 3
Practice Olympiad 3	Wednesday, November 19	Monday, November 24
Practice AIME 1	Wednesday, December 10	Monday, December 15
Practice Olympiad 4	Wednesday, Jaunary 14	Monday, January 19
Practice Olympiad 5	Wednesday, Feburary 11	Monday, February 16
Practice AIME 2	Wednesday, March 4	Monday, March 9
Practice Olympiad 6	Wednesday, April 15	Monday, April 20