Maths Olympiad Master–Class

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.


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