Online Math Club

Information about OMC

The Online Math Club is an initiative to reach high school students interested in math and give them a platform to learn more and interact with others.

The Club aims to increase exposure to olympiad mathematics and advanced mathematics. The format of the classes shows a great deal of diversity depending on the topic. Usually, they should be about 60-90 minutes in length and will be held over Zoom.

You can find more information and apply via the website here

The Probabilistic Method

Thinking out of the box

My classes

Lectures on Graph Theory

Graph Theory

This was taken as a part of the Unofficial IMOTC 2022.

It is a brief introduction to graph theory, beginning with the basic definitions and learning about trees and cycles, and how they find application in various olympiad problems

Graph theory #2

This too, was taken as part of the Unofficial IMOTC 2022.

It builds on the first lecture, covering bipartite graphs and chromatic numbers, as well as a basic introduction to other key topics in graph theory such as tournaments, cliques and independent sets.

Graph Theory #3

This was taken after the training camp in OMC as a follow up to the first two classes.

This was mostly a problem solving session where several recurring techniques to approach graph theory problems were discussed.

Hall's Theorem

A session on how Hall's theorem - a theorem on perfect matchings in graph theory - can be used to solve a variety of olympiad problems.

Expected Value and the Probabilistic Method

Expected Value

This lecture introduces the concept of Expected Value, and how it can be evaluated smartly using techniques like the Linearity of Expectation

The Probabilistic Method

This lecture builds on the previous one and discusses the Probabilistic Method - a powerful method that allows us to make conclusions based on the result when you do something 'randomly'.

Random walks

A fun lecture discussing random walks, and how it can lead to several counter-intuitive mathematical results.

Other Combinatorial Techniques

Dynamic Programming

A lecture exploring dynamic programming - a method to bruteforce through all possibilities in an efficient manner.

Fun fact: this was the first lecture I took in OMC! You'll also see me write on my own camera here, but it was too much effort to repeat that in next classes :(

Double counting

This lecture explores the method of counting in two ways - which allows us to bound expressions in a powerful way by relating it to a known quantity.

Greedy Algorithms

In this class, we discuss greedy algorithms - which allow us to make decisions by trying to maximize short term goals while not bothering too much about the overall result.

Combinatorial Games

A fun lecture discussing combinatorial games, and methods to find winning strategies for such games.

Processes

This class introduces the concept of soft techniques and shows how we can analyse processes. We also discuss the technique of "superposition", which helps solve a variety of hard olympiad problems.

Thinking out of the box

This class introduces one of the most exciting parts of combinatorics: the art of thinking innovatively. Through various examples and puzzles, we discover the power of a change in perspective and breaking rules, sometimes.

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