Teaching | Ishaan Bhadoo

Mentors: Ishaan Bhadoo, Sarvesh Ravichandran Iyer (Ph.D.)
Outline: We will cover basics of stochastic processes. More specifically, we will focus on Martingales and Markov Chains. Towards the end we will see some applications of these concepts in mathematics and finance.
References: Knowing the odds - John B. Walsh, Mixing times of Markov Chains - David Levin and Yuval Peres
The following people, have completed the reading project by going through, in detail, all the assigned parts and participating in the discussions: Malav Dhaval Doshi (B2), Ria Agarwal (B2), Rishi Somani (B3)

Mentors: Ishaan Bhadoo, Varun Balasubramaniam
Abstract: In the nineteenth century, two very young mathematicians, Neils Abel and Evariste Galois, answered a question about which the mathematical world had been curious for centuries. It is a question about the central activity of algebra, solving equations, particularly the question: Is there a formula for solving fifth degree polynomial equations? In this reading project, we will provide a modernized approach towards solving this question and discover the many uses of this approach and how it plays a central role in Algebra.
Primary References: Galois Theory - Ian Stewart, Galois Theory - Joseph J. Rotman, Field and Galois Theory – Pattrick Morandi
Brief Sketch of Project: Basic Algebra (Groups, Rings), Algebraic extensions: degree, Splitting fields and normal extensions, Algebraic closure.Ruler and Compass constructions. Separability and Galois Correspondence. Notion of Solvable Groups. Solvability by radicals. The Fundamental Theorem of Algebra. Transcendence of (\pi).
The following people, have completed the reading project by going through, in detail, all the assigned parts and participating in the discussions: Amit Kumar Basistha (B1) Aditya Garg (B1). The project is officially completed.