CM700 – Introduction to Olympiad Math
Description:This class is intended for students who have been active in math competitions for a few years but are relatively new to Olympiad Math (proofs). Students will learn how to write proofs and learn more in depths topics and techniques to transition from AIME type of problems to USA(J)MO type of problems. In terms of difficulty of problems solved in class we will be focusing on and solving USA(J)MO-level Olympiad problems and various competitions from around the world. CM700 helps students improve their USA(J)MO scores.
Who should take this course? Students who wish to enroll this class are expected to have qualified for the USA(J)MO in the past.
Homework: 2 Olympiad problems are assigned to each student to solve and upload on Canvas each week. Students are expected to spend about 5-6 hours per week outside the class to prepare for the online meeting and to finish the homework after the meeting.
What will be covered:
2018 Fall (Combinatorics):
Week 1. Principle of Inclusion and Exclusion (PIE)
Week 2. Counting in Two Ways
Week 3. Monovariants
Week 4. Algorithms
Week 5. Processes
Week 6. Proof techniques: Pigeonhole Principle; and Induction
Week 7. Recursions
Week 8. Linearity of Expectation
Week 9. Extremal Principle
Week 10. Graph Theory
Week 11. Games
Week 12. Challenge Problems Day
2018 Summer (Geometry)
The main textbook is Evan Chen’s Euclidean Geometry for Mathematical Olympiads. In addition, we will use Lemmas in Euclidean Geometry by Andreescu et al.
Week 1. Angle Chasing and Cyclic Quadrilaterals
Week 2. Orthic Triangle, Incenter Excenter Lemma, Phantom Points
Week 3. Power of a point and radical axes/center
Week 4. Extended Law of Sines, Collinearity/concurrency and Ceva/Menelaus theorems
Week 5. Homothety and the Nine Point Circle
Week 6. Simson Lines, Incircle and Excircles
Week 7. Isogonal Conjugates and Symmedians
Week 8. Curvilinear incircle and mixtilinear incircles
Week 9. Computational Geometry I: Coordinates, Areas, and Trigonometry
Week 10. Computational Geometry II: Coordinates, Areas, and Trigonometry