Maths Olympiad Master-Class

Training Course for National & International Math Olympiads

What you'll learn

Learn the theory required for Olympiad Maths. The course will cover Algebra, Combinatorics, Geometry and Number Theory.

Practice lots of actual Olympiad problems to test your skills

Learn some common problem-solving strategies that are employed in solving Olympiad problems.

Do mock tests and quizzes to check your understanding.

Requirements

No pre-requisites are required for the course.

Description

The course covers all the topics in Olympiad Maths. The entire course is divided into 25 sections. Each section has multiple videos which cover the theory and applications. Most sections also have assignment with problems from various Olympiads. The theory for the course is covered in a total of 60 video lectures, running for almost 46 hours of high-quality content. We discuss hundreds of problems in these 60 lectures while explaining the ideas. Some of the advanced topics covered in the course include - Functions, Maxima/Minima, Inequalities, Trigonometry, Triangle Geometry, Sets and Partitions, Functional Equations, The extreme principle, Sequences and Series, Advanced Inequalities, Analytic Geometry including Conic Sections, Families of Curves, Mathematical Induction, Complex Numbers and their properties, Recursive and Periodic Sequences, The Construction Method, Combinatorics, Principle of Inclusion and Exclusion, Recursive counting, Number Theory, Congruences, Diophantine Equations, Polynomials, Roots of Polynomials, Irreducibility, Interpolation and Differences of Polynomials etc. The assignment problems have been specially designed to go from beginner to advanced levels. Any students who face difficulties with the assignments can reach out to the instructor and I shall try and provide more content (video solutions) to help clarify your issues. If you have come across a particular idea or theorem in any Olympiad Maths context, we have probably covered it in this course! Happy learning and have fun problem-solving!

Overview

Section 1: Introduction to Sets

Lecture 1 Introduction to Sets

Lecture 2 Problem Solving using Sets Part 1.

Lecture 3 Problem Solving using Sets Part 2.

Lecture 4 Problem Solving using Sets Part 3.

Section 2: Quadratic Functions

Lecture 5 Introduction to Quadratic Functions and Problem Solving

Lecture 6 Quadratic Functions Part 2.

Section 3: Functions and Graphs

Lecture 7 Functions and Properties

Section 4: Basic Inequalities

Lecture 8 Inequalities Part 1

Lecture 9 Inequalities Part 2.

Section 5: Review of Trigonometry

Lecture 10 Trigonometric Problem-Solving

Section 6: Simple Functional Equations

Lecture 11 Functional Equations Part 1

Lecture 12 Fixed Point and Bridge Function Methods in Functional Equations

Lecture 13 Functional Equations Recap.

Section 7: The Construction Method

Lecture 14 Constructing functions to solve inequalities.

Section 8: The 5 Centers of a Triangle

Lecture 15 The five triangle centers

Lecture 16 Problems on Triangle Geometry

Lecture 17 Problems on Triangle Geometry II

Lecture 18 Problems on Triangle Geometry III

Section 9: Lemmas & Theorems for Olympiad Geometry

Lecture 19 Ceva, Menelaus & other theorems

Section 10: The Extreme Principle

Lecture 20 The Extreme Principle for problem-solving

Section 11: Maxima and Minima

Lecture 21 Maxima and Minima using Inequalities

Section 12: Inequalities part 2

Lecture 22 More Inequality Problems

Lecture 23 Substitution method for Inequalities

Section 13: Sequences & Series

Lecture 24 Theory of Sequences

Lecture 25 Problems on Sequences

Section 14: Coordinate Geometry

Lecture 26 Straight Lines

Lecture 27 Circles

Lecture 28 Conic Sections

Lecture 29 Parametric Equations of Curves

Lecture 30 Families of Curves

Section 15: Mathematical Induction

Lecture 31 Induction Part 1.

Lecture 32 Induction Part 2. (Spiral Induction, Reverse Induction & Double Induction)

Section 16: Complex Numbers

Lecture 33 Review of Complex Numbers

Section 17: Advanced Inequalities

Lecture 34 Mean Value Inequalities

Lecture 35 Cauchy Inequality

Lecture 36 Rearrangement Inequality

Lecture 37 Convex functions & Jensen's Inequality

Section 18: Advanced Sequences

Lecture 38 Recursive Sequences

Lecture 39 Periodic Sequences

Section 19: Geometrical Methods

Lecture 40 Polar Coordinates

Lecture 41 Analytical Methods in Plane Geometry

Section 20: Proof Methods

Lecture 42 Proof by Contradiction

Lecture 43 The Construction Method - Part 2

Section 21: Combinatorics I

Lecture 44 Permutations & Combinations

Lecture 45 Binomial Coefficients

Section 22: Combinatorics II

Lecture 46 Correspondence and Recursion

Lecture 47 Inclusion - Exclusion Principle

Lecture 48 Combinatorial Problems

Section 23: Number Theory I

Lecture 49 Exact Division

Lecture 50 Prime Numbers

Lecture 51 Congruence I

Section 24: Number Theory II

Lecture 52 Diophantine Equations I

Lecture 53 Problems in Number Theory

Lecture 54 Chinese Remainder Theorem & Lucas' Theorem

Lecture 55 Indeterminate Equations

Section 25: Polynomials

Lecture 56 Operations & Exact Division of Polynomials

Lecture 57 Zeros of Polynomials

Lecture 58 Polynomials with Integer Coefficients

Lecture 59 Interpolation & Difference of Polynomials

Lecture 60 Roots of Unity & Applications

The course is targeted for Parents and guardians of students in high school who might be appearing for National and International Math Contests.