In this session, we learn to apply probability in olympiad questions. We learn how to use probability, expectation, pigeonhole, and more. We apply these methods in many olympiad questions. There are no hard prerequisites.
Incorporating 'rigid' ideas, in this session, we will analyze various number theory sequences that have appeared in problems, and see what properties those sequences have. No hard prerequisites.
January 29, 2022 | 08:30 (EST) 19:00 (IST)YouTube Link
We do some basic constructions and used basic properties to prove the existence of some major triangle centers like circumcentre, orthocentre, etc, and solve a few problems from olympiads and prove some nice results as well. No hard prerequisites.
January 23, 2022 | 08:30 (EST) 19:00 (IST)YouTube Link
Yes, now fairies can be found in olympiad math! We'll discuss some cool properties of farey (fairy) sequences (which are essentially reduced fractions between 0 and 1) and ford circles, followed by a bunch of olympiad problems using them. Prerequisites include knowing what a number is.
January 16, 2022 | 08:30 (EST) 19:00 (IST)YouTube Link
We introduce the notion of a dimension of a vector space, linear transformations, quotient spaces, first isomorphism theorem, eigenvalues, and the characteristic polynomial. If we have time left, we talk about what a general linear map looks like and in particular the Jordan canonical form.
January 15, 2022 | 08:30 (EST) 19:00 (IST)YouTube Link
We take a look at what these are actually doing and build a strong theory. Finally, we see its power by deriving some well-known results in seconds via this technique and solving questions. No hard prerequisites.
December 26, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This talk focuses on giving an intuition of why the result holds true and seeing its real power through examples. The key idea here is in construction-type problems where you "freely do what you want and let CRT do the rest". More handouts in the YT description.
This was a session on graph theory and was conducted by Shourya Pandey. We discuss (Olympiad) problems related to paths, cycles, with a special emphasis on trees and possibly other sparse graphs. No hard prerequisites.
December 05, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
Combinatorial Geometry is the application of geometric concepts to combinatorics. We go over various ideas and concepts in the subject with the help of many questions from the olympiads. There are no hard prerequisites. Prerequisites: Basic Maturity
December 04, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This was a session on the use of "density" in number theory and was conducted by Pranjal Srivastava. We do various size-related things. Our motto is "If it's not false that often, must be true somewhere". Prerequisites: Basic Maturity
November 21, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This was an introductory session on inequalities and was conducted by Luke Robitaille. We cover some basic facts about inequalities and solve some inequality problems from contests. No major pre-requisite except basic maturity is assumed.
November 20, 2021 | 09:30 (EST) 20:00 (IST)YouTube Link
An intro to the fascinating Conic Sections, from the point of Projective Geometry. We first cover some basic projective geometry, and then prove some nice results about conics, including the famous Pascal's Theorem. We also conjure formulae for equations of the tangent, chord of contact, etc
November 14, 2021 | 07:30 (EST) 18:00 (IST)YouTube Link
This is a session on Spectral Graph Theory and was conducted by Rishab Dhiman. We introduce Laplacian and Adjacency matrices of graphs and use their eigenvalues/eigenvectors to get information about the graph's structural properties. Few bounds will be proved relating eigenvalues with graph ...
October 30, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
We apply generating functions to solve linear recurrence relations. Using Exponential Generating Functions, we solve more problems and discuss the roots of unity filter. We look at the superpower of Multivariate Generating Functions. No hard prerequisites.
October 24, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
In this introductory geometry session, we introduce the important but tricky concept of directed angles. We see its definition and uses and then solve olympiad problems involving their use. There are no hard prerequisites.
October 23, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
We go through the basics of modulo arithmetic, residue systems, and linear congruences. We also explore the Chinese remainder theorem and introduce you to quadratic congruences. No hard prerequisites. Apar is a third year computer science undergraduate at IIT Delhi.
October 09, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
If you have ever tried newspaper puzzles, you know that solving a sudoku puzzle is harder than checking if the solution given at the back of the newspaper is correct or not. Why is it so? Enter the complexity zoo, is P = NP?
November 13, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This session is an introduction to groups through symmetries and was conducted by Rajdeep Ghosh. We discuss the subsequent motivation for the classical description of a group. We also go through group actions and a very natural presentation of Cayley's theorem. No hard prerequisites.
November 07, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This is an introductory olympiad class on geometry and was conducted by Kazi Aryan Amin. We will provide a comprehensive introduction to olympiad geometry along with various lemmas, ideas, and concepts. And lots of contest questions. No hard prerequisites.
November 06, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
This was the second session on Max Flow Min Cut and was conducted by Aatman Supkar. We revise the content from the last class, and we proceed to discuss the theorem in a more general context, with a couple of applications.
October 31, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
Which natural numbers can be written as a sum of two integer squares? We are going to be better than Fermat and see how this question naturally takes us to the realm of Gaussian integers, which we discuss in some detail, and witness an effortless proof of Fermat’s theorem weaving itself.
The talk is an introduction to the ideas of invariants and mono variants which are fundamental heuristic tools in mathematics and feature commonly in Olympiads. No hard prerequisites. Apar is a third year computer science undergraduate at IIT Delhi.
This talk introduces the notion of the order of a number modulo a prime. We prove a few related results including the existence of a primitive root and then a few problems involving orders. The prerequisites are basic number theory. Apar is a third year computer science undergraduate at IIT Delhi.
October 10, 2021 | 08:30 (EST) 19:00 (IST)YouTube Link
The talk focused on the divide and conquer technique, specifically with an eye towards fast exponentiation. Time permitting, we look at a few other uses of the idea as well. No hard prerequisites. Niyanth Rao is a college freshman at Carnegie Mellon University studying Math and CS.
October 03, 2021 | 07:00 (EST) 17:30 (IST)YouTube Link
We cover various well-known results and theorems like Cauchy-Davenport and Van der Waerden with their applications. We also solve a ton of relevant and interesting problems. No hard prerequisites except general problem-solving experience.
We start by building intuition about a nontrivial well-known result in conics and watch as things fall naturally in place. We then return to the result in question with Dandelin's magic and watch how things unfold to give a beautiful proof. The prerequisites are knowing what a cone is.
September 26, 2021 | 09:30 (EST) 19:00 (IST)YouTube Link
This is an expository talk on Measure Theory- the art of assigning sizes to sets in a no-nonsense fashion, generalizing well-known concepts like length and area. We also explore how interpretations of length have evolved from time immemorial to what it is now.
This will be a problem-solving session with combinatorics questions. We will try to find and motivate the solutions using intuition and develop the thought process behind them. No hard prerequisites.
The talk discusses the "Hydra" theorem of Kirby and Paris and its unprovability from Peano arithmetic (which will be explained). It'll be helpful if people have seen things like formal proof and induction before, but there aren't any hard prerequisites.
We discussed various techniques of solving functional equations and a few interesting problems. Techniques like substitution, equating, and canceling things to make equations easier will be discussed. We solve olympiad questions alongside
We discussed properties and results relating to polynomials with real coefficients alongside interesting olympiad problems. We venture into polynomials with complex coefficients. There are no hard prerequisites except basic comfort with complex numbers and the definition of polynomials.
We discussed properties and results relating to polynomials with real coefficients along with interesting olympiad problems. We venture into polynomials with complex coefficients. There are no hard prerequisites except basic comfort with complex numbers and the definition of polynomials.
This session was a brief introduction to graph theory in math olympiads. There are no hard prerequisites.
August 29, 2021 | 09:30 (EST) 19:00 (IST)YouTube Link
We introduced commutative rings and ideals and further discussed special types of ideals such as prime ideals, maximal ideals, and domains like EDs, and PIDs, UFDs. Bonus points for knowing full forms. The prerequisites are the definitions of fields and rings.
August 28, 2021 | 09:30 (EST) 19:00 (IST)YouTube Link
We solve some problems (only up to section 4 in the handout) involving Lagrange theorem and number theoretic ideas and if time allows, motivate normal subgroups. The prerequisites are the first 3 sections of the handout or the respective recordings where the same content was covered.
The session introduced inversion from the basics and goes over a few important lemmas and facts that will help us solve olympiad questions. We also solved olympiad problems where inversion is helpful. No hard prerequisites.
August 14, 2021 | 09:30 (EST) 19:00 (IST)YouTube Link
We look at common ideas in construction-related problems in NT and Combinatorics. We also try to understand how to think of various types of constructions philosophically. No hard prerequisites.
We will help you solve various problems that we think are instructive. Specifically, IMO 2021 Q1, IMO 2021 Q5, and a problem from Russia 2004 are solved. No prerequisites. The whiteboard can be found in the youtube description
We go through some basic techniques in solving olympiad problems, mostly concerning exponents of primes, like orders and the Lifting the Exponent lemma. The prerequisites roughly include Modular arithmetic and (up to) Euler's theorem. The used notes can be found in the Youtube description.
We defined and characterized maps called projective transformations, and proved that maps sending lines to lines preserve cross ratio. This is a continuation of the previous session but section 1.1 of https://math.mit.edu/~notzeb/cross.pdf can be read as alternative prerequisites.
This is a ELMO Day 1 Livesolve by Kazi Aryan Amin and Abhay Bestrapalli. We tried to solve the questions from the olympiad(and got q4 and q5). You can find more about ELMO on aops.
July 01, 2021 | 08:30 (EST) 18:00 (IST)YouTube Link
This is a ELMO Day 1 Livesolve by Kazi Aryan Amin and Abhay Bestrapalli. We tried to solve the questions from the olympiad(and got all 3). You can find more about ELMO on aops.
June 29, 2021 | 08:30 (EST) 18:00 (IST)YouTube Link
Hall's perfect matching theorem, a graph theoretic result about perfect matchings, often appears unexpectedly in a lot of olympiad problems. In this session, we'll first prove Hall's theorem, and then solve a few questions using it. No hard prerequisites.
A continuation of the discussion on combinatorial games from the prequel. We talk about games as a formal construct, the Sprague-Grundy theorem, Hackenbush and surreal numbers. The session shows you how to create ordinal numbers as games.
This session will cover combinatorics questions often called "Russian problems", which are characterized by low-tech, slick solutions, elegant statements, and seemingly random constants. There are no prerequisites. Extra pset in Youtube description.
The session will be an introduction to methods and ideas in solving classic functional equations. Things will be covered from the basics with heavier emphasis on ideas and motivation rather than details.
The session goes over a bunch of olympiad questions that are instructive along with many ideas and techniques alongside. Specifically, ISL 2015 C1, TSTST 2016/5 and USAMO 2020/2 are solved.
The session mainly focuses on properties of inconics of quadrilaterals, and will also contain some olympiad geometry that can be solved using conics. This is a continuation of the session by Rohan Goyal
The lecture introduced conics and various properties they exhibit. The lecture aimed to be accessible to everyone and thus no prerequisites except basic angle chasing are assumed but the results should be of interest to the experienced viewers as well.
This session was about the Max-flow Min-cut theorem and a discussion about flow in general.
May 16, 2021 | 09:30 (EST) 19:00 (IST)YouTube Link
The session is on analyzing algorithms in math olympiads and went through multiple ideas that lets us do this. It also covers further uses of algorithms. A Pset can be found in the Youtube description.