The schedule of ICTS courses for Aug - Nov 2018 are given below:


  1. Techniques in discrete probability (Elective)

Instructor: Riddhipratim Basu

Venue: Math department LH-5, IISc, Bangalore

Meeting Time: Tuesdays and Thursdays, 2:00-3:30 pm 

First Class: Thursday, 2nd August, 2018


MA 394: Techniques in discrete probability

Credits: 3:0

Pre-requisites:

  1. This course is aimed at Ph.D. students from different fields who expect to use discrete probability in their research. Graduate level measure theoretic probability will be useful, but not a requirement. I expect the course will be accessible to advanced undergraduates who have had sufficient exposure to probability.

We shall illustrate some important techniques in studying discrete random structures through a number of examples. The techniques we shall focus on will include (if time permits)

  1. the probabilistic method;
  2. first and second moment methods, martingale techniques for concentration inequalities;
  3. coupling techniques, monotone coupling and censoring techniques;
  4. correlation inequalities, FKG and BK inequalities;
  5. isoperimetric inequalities, spectral gap, Poincare inequality;
  6. Fourier analysis on hypercube, Hypercontractivity, noise sensitivity and sharp threshold phenomenon;
  7. Stein’s method;
  8. entropy and information theoretic techniques.

We shall discuss applications of these techniques in various fields such as Markov chains, percolation, interacting particle systems and random graphs.


Suggested books:

  1. Noga Alon and Joel Spencer, The Probabilistic Method ,Wiley, 2008.
  2. Geoffrey Grimmett, Probability on Graphs ,Cambridge University Press, 2010.
  3. Ryan O'Donnell, Analysis of Boolean Functions ,Cambridge University Press, 2014.

 

The following is the list of courses offered at IISc. For the current list see:

Core Elective Courses
Course No. Course Title
MA 212 Algebra I
MA 219 Linear Algebra
MA 221 Analysis I: Real Anaysis
MA 231 Topology
MA 261 Probability Models
MA 223 Functional Analysis
MA 232 Introduction to Algebraic Topology
MA 242 Partial Differential Equations
MA 213 Algebra II
MA 222 Analysis II : Measure and Integration
MA 224 Complex Analysis
MA 229 Calculus on Manifolds
MA 241 Ordinary Differential Equations

Advanced Elective Courses
Course No. Course Title
MA 215 Introduction to Modular Forms
MA 277 Advanced PDE and Finite Element Method
MA 361 Probability Theory
MA 368 Topics in Probability and Stochastic Processes
MA 278 Introduction to Dynamical Systems Theory
MA 313 Algebraic Number Theory
MA 314 Introduction to Algebraic Geometry
MA 315 Lie Algebras and their Representations
MA 317 Introduction to Analytic Number Theory
MA 319 Algebraic Combinatorics
MA 320 Representation Theory of Compact Lie Groups
MA 332 Algebraic Topology
MA 364 Linear and Nonlinear Time Series Analysis
MA 369 Quantum Mechanics

The schedule of ICTS courses for Jan - Apr 2018 are given below

  1. Introduction to PDEs (Reading)

    Instructor: Rukmini Dey

    Venue: S N Bose Meeting Room, ICTS Campus, Bangalore

    Meeting Time: Monday and Friday: 11:30 am - 1:00 pm

    First Class:  Monday, 15th January, 2018

    Course contents: First 5 chapters of Ian Sneddon's book: Elements of PDEs.

    Syllabus: Ordinary Differential Equations in more than 2 variables; Partial Differential Equations of the first order; Partial Differential Equations of the Second Order; Laplace Equation; Wave Equation. If time permits we will go through some chapters of "Fourier Series" by Georgi P. Tolstov.​
     

  2. Introduction to Dynamical Systems (Reading)

    Instructor: Vishal Vasan

    Venue: ICTS Campus, Bangalore

    Meeting Time: Friday: 4:30 pm - 6:00 pm

    First Class:  Friday, 19th January, 2018

    Course contents: Nonlinear Dynamics and Chaos by S Strogatz. Selected reading from Differential Equations and Dynamical Systems by L Perko and other suitable texts.

    Syllabus: The course will cover the entire content of Strogatz' book supplemented with more detailed mathematical treatments of selected theorems from other sources.

Courses for Aug - Nov 2017

Courses for Jan - Apr 2017