Combinatorics For Math Contests (Amc, Aime & Imo)

Combinatorics For Math Contests (Amc, Aime & Imo)
Published 10/2024
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 2.78 GB | Duration: 17h 25m

All the counting techniques you will ever need!

What you'll learn

Learn counting techniques for Math Olympiad problems.

Practice lots of Olympiad quality problems.

Get an understanding of advanced techniques like recurrences, generating functions and graph theory.

Learn the basics of conditional probability, pigeon-hole principle and invariants.

Requirements

No prior experience is required.

Description

This course has 27 lectures and over 17 hours of content. The course covers both the theoretical and problem-solving aspects of Combinatorics. As such, it will be useful for students who wish to appear in National and International Math Contests like the AMC, AIME, IMO, RMO, INMO etc. The course covers advanced techniques like Principle of Inclusion and Exclusion, Pigeonhole Principle, Mono variants and Invariants, solutions of Recurrence relations, Generating functions and Graph Theory. We also discuss problems based on Conditional Probability, Combinatorial Games and there are a lot of practice problems for you to gain a better understanding of these topics. The course is divided into two sections - Theory and Problem-solving lectures. You can do them in a sequence or you can switch between the two sections and get your hands dirty with some problems. Anyone who wishes to get started with Olympiad Combinatorics can use this course fruitfully and will learn a lot of new ideas and concepts. I will be adding more problem-solving videos to the course as students join in. Feel free to reach out to me on Udemy in case you need help with a particular topic, and I will be happy to add more content around that topic. This course is a collaborative learning experience, and your feedback makes the course better.Happy learning!

Overview

Section 1: Techniques in Combinatorics

Lecture 1 Introduction to Combinatorics

Lecture 2 Invariants & Monovariants

Lecture 3 Combinatorial Games

Lecture 4 Pigeon-Hole Principle

Lecture 5 Combinatorial Identities

Lecture 6 Principle of Inclusion and Exclusion

Lecture 7 Constructive Counting

Lecture 8 Counting through Bijections

Lecture 9 Constructive Expectation

Lecture 10 Distributions

Lecture 11 Fibonacci Numbers

Lecture 12 Fibonacci Sequences Part 2

Lecture 13 Recurrences

Lecture 14 Catalan Numbers Part 1

Lecture 15 Catalan Numbers Part 2

Lecture 16 Generating Functions - I

Lecture 17 Generating Functions - II

Lecture 18 Graph Theory - I

Lecture 19 Graph Theory - II

Section 2: Problem Solving Sessions

Lecture 20 8 Counting Problems from the AIME

Lecture 21 10 more Counting Problems

Lecture 22 12 Problems on Binomial Theorem

Lecture 23 Shortest paths on a Rectangular Board

Lecture 24 The Art of Combinatorial Proof

Lecture 25 Pigeon Hole Principle Problems

Lecture 26 Conditional Probability Problems

This course is directed towards parents of students who are going to appear in National and International Math Contests.