The schedule of ICTS courses for Aug - Nov 2018 are given below:
- 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
- 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)
- the probabilistic method;
- first and second moment methods, martingale techniques for concentration inequalities;
- coupling techniques, monotone coupling and censoring techniques;
- correlation inequalities, FKG and BK inequalities;
- isoperimetric inequalities, spectral gap, Poincare inequality;
- Fourier analysis on hypercube, Hypercontractivity, noise sensitivity and sharp threshold phenomenon;
- Stein’s method;
- 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.
- Noga Alon and Joel Spencer, The Probabilistic Method ,Wiley, 2008.
- Geoffrey Grimmett, Probability on Graphs ,Cambridge University Press, 2010.
- Ryan O'Donnell, Analysis of Boolean Functions ,Cambridge University Press, 2014.
|Course No.||Course Title|
|MA 212||Algebra I|
|MA 219||Linear Algebra|
|MA 221||Analysis I: Real Anaysis|
|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
- 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.
- 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.