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 LinkThis 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.

We explored the use of induction in combinatorics questions among other important ideas. We also go over instructive olympiad questions related to these. 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 LinkWe 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 LinkWe 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.

This was a revision session on group theory for a problem-solving session. It is a 30 min preclass session.

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 LinkWe 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 covered some properties of Miquel points, Simson and Steiner lines and solve some problems along the way. 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.

It focused on an introduction to projective geometry where we will discuss maps on the projective plane that sends lines to lines. Knowledge of basic linear algebra is suggested but not required

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 LinkThis 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 LinkHall'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.

It covers the basics of angle chasing and power of point to solve olympiad geometry problems and prove various theorems. No prerequisites.

We will prove Lagrange's theorem and introduce the notion of normal subgroups and end with isomorphism theorems. There is no Youtube recording for this session, but one may use the handout.

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 introduces complex bashing and using complex numbers in geometry. There are no prerequisites.

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 video discusses tools and techniques for working with combinatorial games. There are no prerequisites.

The session introduces groups through many examples. It goes over various theorems like Lagrange and FLT.

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 LinkThis session was an introduction to graph theory for math olympiads. The session introduces graph theory from scratch and goes on to harder problems.

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.