Early Bird Math Olympiad Program 2016-17

I taught this course from January 2017 to April 2017.

Lecture Hours:

Friday & Saturday (7.30 PM - 9.30 PM)

Grading Scheme (per month)

• Attendance: 5 points per class x 8 classes (usually) = 40 points
• Quizzes: (About) 10 points x (about) 6 quizzes = 60 points
• Assignments: 50 points x 2 = 100 points
• Test: 100 points x 1 = 100 points

TOTAL: 300 points

Note that this grading scheme is approximate and the individual points structure may be tweaked. This is provided to give you an overall idea only.

Other Resources

• 12 different proofs of the Cauchy-Schwarz inequality - PDF.

Syllabus

• Basics: Principle of mathematical induction, set theory, functions, graphs of functions.
• Number Theory: Divisibility, primes, congruences, Diophantine equations, Fermat's theorem, number theoretic functions.
• Combinatorics: Counting principles, permutations, combinations, binomial theorem, pigeonhole principle, inclusion-exclusion principle, recurrence relations, basic probability.
• Algebra: Progressions, quadratic equations, polynomials.
• Inequalities: Order in real numbers, quadratic inequalities, AM-GM-HM inequalities, rearrangement inequality, Cauchy Schwarz inequality, minima principle, substitutions.
• Geometry: Translation, symmetry, rotation, homothety, inversion.
• Additional topics: Pythagorean triples, basics of Graph Theory

Italics => completed