+91-674-249-4082
Most Indian Universities however do not have a rigorous study on probability. The aim of this school is to give a comprehensive training to students in a undergraduate/PhD programme onprobability and stochastic processes. Also to give them a chance to interact with researchers in these topics.
We propose to run three courses – 1) Basic probability theory, 2) Measure free Markov chain, 3)Modules of linear algebra and real analysis. There will be around 40 hours of lectures includingtutorials per topic over a 4 weeks period. In addition, over two weekends we plan to invite activeresearchers in probability to present introductory lectures on a research topic and interact withstudents.
Organizers:
a) Nabin Kumar Jana, Assistant Professor, NISER, Bhubaneswar
b) Rahul Roy, Professor, ISI, Delhi
Target audience: 3rd year of B.Sc.; 1st year of M.Sc. or 3rd & 4th year of Integrated M. Sc. students in Mathematics or Physics, 4th Year B.Tech. students in Electrical Engineering.
Speakers: Any 8 out of the following:
a) B V Rao, CMI, Chennai
b) Rahul Roy, ISI, Delhi
c) Anish Sarkar, ISI, Delhi
d) Antar Bandyapadhyay, ISI, Delhi
e) Krishanu Maulik, ISI, Kolkata
f) Parthanil Roy, ISI, Bangalore
g) Arijit Chakrabarty, ISI, Kolkata
h) Srikanth Iyar, IISc, Bangalore
i) Nabin Kumar Jana, NISER, Bhubaneswar
j) Manjunath Krishnapur, IISc, Bangalore
k) Probal Choudhuri, ISI, Kolkata
l) Alok Goswami, ISI, Kolkata
Syllabus: We plan to cover the following topics in this AIS.
Modules of Linear Algebra and Analysis:
Linear Algebra: Vector Spaces: Denition of Vector Spaces and Subspaces, Basis of a Vector Space, Linear Equations, Vector Spaces with an Inner Product; Theory of Matrices and Determinants: Matrix Operations, Elementary Matrices and Diagonal Reduction of a Matrix, Determinants, Transformations, Generalized Inverse of a Matrix, Matrix Representation of Vector Spaces, Bases, etc., Idempotent Matrices, Special Products of Matrices; Eigenvalues and Reduction of Matrices: Classication and Transformation of Quadratic Forms, Roots of Determinantal Equations, Canonical Reduction of Matrices, Projection Operator, Further Results on g-Inverse, Restricted Eigenvalue Problem; Convex Sets in Vector Spaces: Denitions, Separation Theorems for Convex Sets
Analysis: Metric spaces, open/closed sets, Cauchy-Schwarz Inequality, Holder's Inequality, Hadamard's Inequality, Inequalities Involving Moments, Convex Functions and Jensen's Inequality, Inequalities in Information Theory, Stirling's Approximation sequences, compactness, completeness, continuous functions and homeomorphisms, connectedness, product spaces, completeness of C[0; 1] and Lp spaces, Arzela-Ascoli theorem
Reference Texts:
1. C.R. Rao: Linear Statistical Inference and Its Applications.
2. A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
3. G. F. Simmons: Introduction to Topology and Modern Analysis
4. J. C. Burkill and H. Burkill: A second course in mathematical Analysis
Basic Probability Theory:
Orientation, Elementary concepts: experiments, outcomes, sample space, events. Discrete sample spaces and probability models. Combinatorial probability and urn models; Conditional probability and independence; Random variables { discrete and continuous; Expectations, variance and moments of random variables; Transformations of univariate random variables; Jointly distributed random variables; Conditional expectation; Generating functions; Limit theorems;
Reference Texts:
a) S. M. Ross: A rst course in Probability
b) Jacod & Protter: Probability Essentials
c) W Feller: An Introduction to Probability: Theory and Its Applications, Vol I & II
d) George G. Roussas: Introduction to Probability
Markov Chain:
Random Walk, Discrete Markov chains with countable state space. Classication of states -- recurrence, transience, periodicity. Stationary distributions, limit theorems, positive and null recurrence, ratio limit theorem, reversible chains. Several illustrations including the Gambler's ruin problem, queuing chains, birth and death chains etc. Poisson process, continuous time markov chain with countable state space, continuous time birth and death chains.
Reference Texts:
1. W. Feller: Introduction to the Theory of Probability and its Applications, Vol. 1.
2. P.G. Hoel, S.C. Port and C.J. Stone: Introduction to Stochastic Processes.
3. S.M. Ross: Stochastic Processes.
4. S. Karlin and J. Taylor: Stochastic Processes, Vol. 1.
5. J.G. Kemeny, J.L. Snell and A.W. Knapp: Finite Markov Chains.
Last date of application is 10th May 2019.
Application form is available here.
SID |
Name | Confirmation of Participation |
28170 | Mr. Sadhanandh Vishwanath | Confirmed |
28199 | Mr. Yogesh Kumar | Confirmed |
28270 | Mr. Shivam Kumar | Confirmed |
28275 | Ms. S Angel Auxzaline Mary | No confirmation received |
28290 | Ms. Kanchana M | Pending |
28306 | Mr Shyam Surykant Dhamapurkar | No confirmation received |
28309 | Mr. Sanket Nemichand Teli | Confirmed |
28329 | Mr Subhra Jyoti Nayak | Confirmed |
28333 | Mr Bikram Mahapatra | Confirmed |
28352 | Ms Sathya S | Pending |
28354 | Ms Ashweta Padhan | Confirmed |
28356 | Mrs Subhashini Marappan | Pending |
28365 | Ms. Sonali Pradhan | Confirmed |
28368 | Mr Brajamohan Sahoo | Confirmed |
28369 | Ms. Sabhyata Rout | Confirmed |
28371 | Mr. Ajay Shanmuga Sakthivasan | Confirmed |
28409 | Mr. Krushna Chandra Sahoo | No confirmation received |
28447 | Mr. Sachin Sachdeva | Confirmed |
28449 | Ms. Subhashree Sahu | No confirmation received |
28456 | Mr. Saptarshi Saha | Confirmed |
28464 | Mr. Pallab Kumar Sinha | Pending |
28485 | Ms. Km Sandhya | Duplicate |
28489 | Mr Shantam Gulati | Pending |
28496 | Mr Manas Jana | Confirmed |
28499 | Mr Sougata Jana | Confirmed |
28534 | Mr. Vivek Kumar Singh | Confirmed |
28560 | Mr. Ravi Ashok Satpute | Confirmed |
28563 | Ms. Km Sandhya | Confirmed |
28580 | Mr Praneet Nandan | Confirmed |
28582 | Mr. Hiranmay Das | Confirmed |
Second List:
SID | Full Name | Confirmation of participation |
28123 | Mr. Mayavel P | |
28188 | Mrs. Sangita Das | |
28234 | Mr Mostafizar Khandakar | |
28328 | Ms. Niharika Bhootna | |
28336 | Mr. Kunal Verma | |
28508 | Mr Vrikshavardhana Hebbar N | |
28517 | Ms. Debolena Basak | |
28572 | Ms. Sarita Sarita |
Based on the reply, a Third list of selected candidates may be published on 23rd May 2019.
School of Mathematical Sciences
NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050
Tel: +91-674-249-4081