Advanced Training for Olympiad Mathematics

Advanced Training for Olympiad Mathematics is a Bangladesh National Camp level course. Familiarity with all the basic topics and theories is required to benefit the most from this course. A student should expect to spend at least 10 hours per week behind the problem sets.

This course is structured in a weekly basis spanning over twelve weeks. Each week will center around a certain topic or a certain group of problems that regularly appear on math olympiads. There will be two classes every week: one Theory class, and one Discussion class. Handouts will be delivered to the students after the theory class. The students are expected to try the problems before attending the discussion class, where the problems will be discussed in details.

One can choose not to register for the classes but receive the weekly handouts. In that option, the cost of the course would be half of the original.

Sample Algorithms Problem Set

Schedule:

	Date	Time
Theory Class	Sunday	12:00pm - 2:00pm
Discussion Class	Thursday	12:00pm - 2:00pm
Weekly problem set submission	Wednesday	11:59pm

Pre-requirements:

• Good grasp on problem solving
• Familiarity with all basic topics

Course Content:

• Week 1 Induction and other strategies

  Using the induction, contradiction, extremal and pigeonhole principal to solve combinatorial problems. This week's focus is to set the necessary foundation for the later topics of this course.

• Week 2 Triangle Centers

  Explore the configurations of important triangle centers like orthocenter, circumcenter, nine-point center, incenter-excenters and mixtilinear centers.

• Week 3 Primes and Orders

  Modular arithmetic modulo primes. Orders modulo prime. Lifting the exponent lemma. Prime factorization.

• Week 4 Graph Theory

  Basic introduction to graph theory. Using extremal principal and induction in graphs. Graph algorithms and bounding.

• Week 5 Projective Geometry

  Basic concepts of cross ratio, harmonic bundle. Pascal, Brianchon and Puppus' Theorem.

• Week 6 NT Functions and Constructions

  Number theoretic functions and integer polynomials, polynomial divisibility. Ad-Hoc number theory construction problems using primes, divisors and modular arithmetic.

• Week 7 Algorithms

  Divide and conquer, greedy algorithms. Other graph algorithms and configuration building strategies.

• Week 8 Polynomials

  Basic concepts of polynomials. Polynomial root finding, polynomial equations, and integer polynomials.

• Week 9 Sequences and Recursion

  Techniques of solving sequence related problems. Solving linear recursive sequences.

• Week 10 Complete Quadrilaterals and Circles

  Explore the configurations of cyclic quadrilateral and complete quadrilaterals in general. Spiral similarity and pole-polar transformation.

• Week 11 Coloring and Invariance

  Using the properties of invariants and monovariants in miscellaneous problems, including grid coloring and algorithmic analysis.

• Week 12 Combinatorial Games

  Basic introduction to combinatorial games. Copying strategies, impartial games.

• Week 13 Poler Polar and Duality

  Polarity transformation and the concept of duality in projective geometry.

• Week 14 Ad Hoc Algebra

  Algebraic manipulation, factorization, telescoping, smoothing and convexity.

• Week 15 Inverstion

  General method of using inversion in solving problems, root bc and other special inversions. Mixtilinear incircle facts.

• Week 16 Cyclotomic polynomial and Zsigmondy's theorem

  Roots of unity, cyclotomic polynomial, and theorems required to prove the powerful Zsigmondy's theorem.

Payment Details:

At the time of registration, you need to make and confirm the payment. You can register for as many or as few courses as you wish. The fee is 1500 BDT per week. So for each month, the fee is 6000 BDT.

The payment should be made via BKash to the number 01928987074. Take note of the BKash number from which the payment was made with and the transaction id, as you will require them to fill up the registration form.

There are also scholarships available to campers. If you want to apply for a scholarship, please contact me personally.