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OMC Handouts

Algebra

Topic                      : Functional equations
Instructor                   : Aayam Mathur
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Functional Equations
Instructor                   : Ananya Ranande
Lecture Link
Handout Link
Pre-requisites             : Just a basic idea if what functional equations are
Difficulty of session    : Easy - Medium


Topic                      : Recursion and Generating Functions
Instructor                   : Krishna Agaram
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Introduction to Inequalities
Instructor                   : Luke Robitaille
Lecture Link
Handout Link             : N/A
Pre-requisites             : Basic Mathematical maturity
Difficulty of session    : Easy - Medium


Topic                      : Polynomials on $\mathbb{R}[x]$
Instructor                   : Kazi Aryan Amin
Lecture 1 LinkLecture 2 Link
Handout Link
Pre-requisites             : Basic comfort with complex numbers and definition of polynomials. Knowing the statement of the fundamental theorem of algebra is recommended.
Difficulty of session    : Medium - Hard

Combinatorics

Topic                      : Algorithms and Processes
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link , Problem Set
Pre-requisites             : Nothing hard
Difficulty of session    : Easy


Topic                      : The Pigeon, the Mathematician and the Hole
Instructor                   : Rohan Goyal
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : An Introduction to Graph Theory
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link
Pre-requisites             : Nothing hard, everything is covered in session from basics.
Difficulty of session    : Easy - Medium


Topic                      : Introduction to Graph Theory
Instructor                   : Pranjal Srivastava
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Hall's Theorem
Instructor                   : Pranjal Srivastava
Lecture Link
Handout Link
Pre-requisites             : Basic graph theory knowledge will be helpful
Difficulty of session    : Easy - Medium


Topic                      : Graph Theory Paths, Cycles, and Trees
Instructor                   : Shourya Pandey
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Induction and other ideas
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Change is not the only Constant
Instructor                   : Rajdeep Ghosh
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : The Probabilistic Method
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Probability and Expectation 
Instructor                   : Tejas Mittal
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Combinatorics Problem Solving Session
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Problem solving session 
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Combinatorics PSS 
Instructor                   : Vedant Saini
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : How to Count
Instructor                   : Rohan Goyal
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy-medium


Topic                      : Russian Problems
Instructor                   : Kazi Aryan Amin
Lecture Link
Problem set , Walkthroughs and solutions to Prob set
Pre-requisites             : Nothing
Difficulty of session    : Medium - Hard


Topic                      : Fairy Sequences
Instructor                   : Atul Shatavart Nadig
Lecture Link
Handout Link             : N/A
Pre-requisites             : Knowing what a number is and how division works.
Difficulty of session    : Easy - Medium


Topic                      : Extremal Ideas in Combinatorics
Instructor                   : Shourya Pandey
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Extremal Graph Theory Part 1
Instructor                   : Kazi Aryan Amin
Lecture Link
Problem Set , Lecture Notes
Pre-requisites             : Basic Mathematical Maturity
Difficulty of session    : Medium - Hard


Topic                      : Extremal Graph Theory Part 2
Instructor                   : Kazi Aryan Amin
Lecture Link
Problem Set , Lecture Notes
Pre-requisites             : The Previous class
Difficulty of session    : Hard


Topic                      : Intro to Combinatorial Geometry
Instructor                   : Rohan Goyal
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Hard


Topic                      : Divide and Conquer
Instructor                   : Niyanth Rao
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : Combinatorial game theory
Instructor                   : Ritam Nag
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Hard


Topic                      : Combinatorial Game Theory 2.0
Instructor                   : Ritam Nag
Lecture Link
Handout Link
Pre-requisites             : Definition of ordinals
Difficulty of session    : Hard


Topic                      Combinatorial Number Theory
Instructor                   : Milica Vugdelić 
Lecture Link
Handout Link
Pre-requisites             : General Problem Solving experience, nothing too hard.
Difficulty of session    : Hard

Geometry

Topic                      : Angle Chasing
Instructor                   : Rohan Goyal
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : Elementary Geometry
Instructor                   : Rohan Goyal
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Configurations in Olympiad Geometry
Instructor                   : Abhay Bestrapalli
Lecture Link
Handout Link             : N/A
Pre-requisites             : Basic Angle Chasing
Difficulty of session    : Easy


Topic                      : Directed Angles
Instructor                   : Anish Kulkarni
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : Elementary Olympiad Geometry
Instructor                   : Kazi Aryan Amin
Lecture Link
Problem set
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : Inversion
Instructor                   : Atharva Parulekar
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Miquel, Simson and Steiner
Instructor                   : Sudharshan KV
Lecture Link
Lecture notes
Pre-requisites             : Basic angle chasing
Difficulty of session    : Medium


Topic                      : When a Plane met a Cone
Instructor                   : Aditi Muthkhod
Lecture Link
Handout Link             : N/A
Pre-requisites             : Knowing what a cone is
Difficulty of session    : Easy - Medium


Topic                      : Angle chasing with conics
Instructor                   : Rohan Goyal
Lecture Link
Handout Link             : N/A, but you can refer to first chapter of Book or Blog post
Pre-requisites             : Basic knowledge of angles
Difficulty of session    : Medium


Topic                      : Angle chasing with conics (2.0)
Instructor                   : Pranjal Srivastava
Lecture Link
Handout Link             : N/A, but you can refer to Blog Post
Pre-requisites             : Blog Post or  "Angle chasing with conics" session 1.
Difficulty of session    : Medium - Hard


Topic                      : Projective Geometry
Instructor                   : Ojas Mittal
Lecture Link
Lecture notes
Pre-requisites             : Knowledge of basic linear algebra is suggested but not required.
Difficulty of session    : Medium


Topic                      Projective Geometry 2.0
Instructor                   : Ojas Mittal
Lecture Link
Lecture notes
Pre-requisites             : Previous session or Section 1.1 of the linked handout
Difficulty of session    : Medium - Hard


Topic                      : The Magic of Conics
Instructor                   : Krishna Agaram
Lecture Link
Handout Link             : N/A
Pre-requisites             : Basic familiarity with Vectors, Definition of Conics, Projective Geo lecture by Ojas Mittal
Difficulty of session    : Medium - Hard


Topic                      : An Introduction to Barycentric Coordinates
Instructor                   : Krishna Agaram
Lecture Link
Handout Link             : N/A
Pre-requisites             : Some basic familiarity with visualizing vectors in three dimensions.
Difficulty of session    : Medium


Topic                      : Complex Numbers
Instructor                   : Arnav Pati
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy

Number Theory

Topic                      : An Introduction to Number Theory
Instructor                   : Apar Ahuja
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : The Chinese Remainder Theorem
Instructor                   : Aditya Khurmi
Lecture Link
Handwritten Notes , Annotated Presentation , Non-Annotated Presentation
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : Order Modulo a Prime
Instructor                   : Pranjal Srivastava
Lecture Link
Handout Link             : N/A
Pre-requisites             : "An Introduction to Number Theory" session by Apar Ahuja
Difficulty of session    : Easy


Topic                      : Exponents in Number Theory
Instructor                   : Tejas Mittal
Lecture Link
Lecture notesHandout link
Pre-requisites             : Introductory modular arithmetic and a few basic results
Difficulty of session    : Easy - Medium


Topic                      : Pell's Equation
Instructor                   : Ojas Mittal
Lecture Link
Handout Link
Pre-requisites             : Basic Number Theory knowledge
Difficulty of session    : Medium - Hard


Topic                      Construction and Architecture
Instructor                   : Rohan Goyal
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Medium - Hard


Topic                      : Density in NT
Instructor                   : Pranjal Srivastava
Lecture Link
Handout Link             : N/A
Pre-requisites             : Basic Mathematical maturity
Difficulty of session    : Medium - Hard


Topic                      Gaussian integers come home for Christmas
Instructor                   : Writika Sarkar
Lecture Link
Handout Link
Pre-requisites             : Basic notions of number theory (congruences and divisibility, orders, primitive roots), notion of the square root of -1 (denoted i), experience with understanding proofs
Difficulty of session    : Easy - Medium

College Maths

Topic                      The Hydra, Cyber Crime, and What We Know We Don't Know
Instructor                   : Dia Basak
Lecture Link
Handout Link
Pre-requisites             : Formal Proof and induction
Difficulty of session    : Easy - Medium


Topic                      The Max-flow Min-cut theorem
Instructor                   : Aatman Supkar
Lecture Link
Handout Link             : N/A
Pre-requisites             : The first section of Handout
Difficulty of session    : Medium


Topic                      : Max Flow Min Cut Part 2
Instructor                   : Aatman Supkar
Lecture Link
Handout Link             : N/A
Pre-requisites             : Part 1
Difficulty of session    : Medium


Topic                      : Groups Through A Symmetrical Lens
Instructor                   : Rajdeep Ghosh
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Easy


Topic                      : An Introduction to Group theory
Instructor                   : Arindam Bhattacharyya
Lecture Link
Handout Link
Pre-requisites             : Nothing
Difficulty of session    : Easy - Medium


Topic                      : Group Theory 2.0
Instructor                   : Arindam Bhattacharyya
Lecture Link               : N/A
Handout Link
Pre-requisites             : Group Theory session 1
Difficulty of session    : Hard


Topic                      : Group theory PSS/Revision
Instructor                   : Arindam Bhattacharyya
Lecture Link(Revision) , Lecture Link (PSS)
Handout Link
Pre-requisites             : First three sections of Handout or the respective recordings.
Difficulty of session    : Hard


Topic                      : Intro to Commutative Rings and Ideals
Instructor                   : Rohan Goyal
Lecture Link
Handout Link
Pre-requisites             : Definitions of fields and rings.
Difficulty of session    : Easy - Medium


Topic                      : Spectral Graph Theory
Instructor                   : Rishabh Dhiman
Lecture Link
Handout Link             : N/A
Pre-requisites             : Basic graph and linear algebra terminology (just knowing how matrices multiply is enough)
Difficulty of session    : Hard


Topic                      Length at Length
Instructor                   : Aniruddhan Ganesaraman
Lecture Link
Handout Link
Pre-requisites             : Working definition of countability and uncountability of sets
Difficulty of session    : Medium


Topic                      : The (Second) Easiest Million Dollar Question
Instructor                   : Shourya Pandey
Lecture Link
Handout Link             : N/A
Pre-requisites             : Nothing
Difficulty of session    : Medium


Topic                      : Vector Spaces and Linear Transformations
Instructor                   : Arindam Bhattacharyya
Lecture Link
Handout Link             : N/A
Pre-requisites             : Knowing what a vector is, and how to add them. Basic Matrix algebra will be helpful too.
Difficulty of session    : Easy


Topic                      : Introduction to Algebraic Number Theory
Instructor                   : Arindam Bhattacharyya
Lecture Link
Handout Link             : N/A; but the first part of the talk will mostly be equivalent to the first chapter of Elias Caerio's algebraic number theory handout.
Pre-requisites             : Elementary number theory and some familiarity with complex numbers. Some knowledge of abstract algebra (namely field extensions and the notion of dimension of vector spaces and free Z-modules) will be helpful for the second part of the talk but won't be required.
Difficulty of session    : Medium

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