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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.
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