INDIAN STATISTICAL INSTITUTE
(Headquarters at Kolkata)
203 B. To Road, Kolkata 700 108
Optional Course for B. Stat. IIIrd Year
Academic Year 2019 - 2020: Semester II
Instructor: Antar Bandyopadhyay
Email: antar (at) isid (dot) ac (dot) in
Office: Room # 3.4 on the Third Floor of the A. N. Kolmogorov Bhavan (when in Kolkata)
Class Time: Tuesday and Friday 11:00 AM -- 01:00 PM
(Note: TWO hours on every day of lecture)
Lecture Hall: CSSC VC Room on Fourth Floor of the S. N. Bose Bhavan, or
Class Room # 504 on the Fifth Floor of the S. N. Bose Bhavan.
Course Duration (including examinations): January 13 - May 15, 2020
[Total of 18 Weeks = 7 Weeks of Classes + 1 Week of Break (February 24 - February 28, 2020) + 1 Midterm Examination Week + 7 Weeks of Classes + 2 Final Examination Weeks].
Date: March 03, 2020
Duration: 14:30 hours - 16:30 hours
Venue: Class Room # 520 on the Fifth Floor of the S. N. Bose Bhavan
Date: In the week July 20 - 24, 2020
Duration: 5 days (TAKE HOME)
- General Probability Topics:
- Revision of the First and Second Moment Methods.
- Weak convergence by method of moments.
- Basic Concentration inequalities for sum of independent Bernoulli
variables, binomial and general case.
- Basic theory of discrete time Galton-Watson branching processes;
extinction probability. Poisson Galton-Watson Tree.
- Classical Random Graphs:
- Two basic models of random graphs, also known as,
Erdős-Rényi random graphs: binomial random graphs
and uniform random graphs.
- Concept of Monotonic properties.
Asymptotic equivalence of the two models.
- Concept of thresholds and proof of every monotone
property has a threshold.
Connectivity threshold. Basic idea of sharp thresholds.
- Dense and sparse random graphs.The evolution of the sparse random
graph, the emergence of the giant component, phase transition.
Sub-critical, critical and super-critical phases.
Practice Problems for the Midterm (all are from Random Graphs and Complex Networks: Volume I by R. van der Hofstad):
- Exercises: 2.5, 2.6, 2.7, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19;
- Exercises: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.24;
- Exercises: 4.1, 4.2, 4.4, 4.5, 4.6, 4.22;
- Exercises: 5.6, 5.7, 5.8, 5.16.
- Real Analysis (at the level of Principles of Mathematical Analysis,
- Liner Algebra (at the level of Finite Dimensional Vector Spaces,
P. R. Halmos).
- Basic Probability (at the level of Introduction to Probability Theory,
P. G. Hoel, S. C. Port and C. J. Stone).
- Midterm Exam: 30% of the total credit.
- Final Exam: 70% of the total credit
(including 40% for the Project and Class Presentation).
- The Midterm and the Final Examinations will be
open notes examinations. That means, students will be allowed
to bring his/her own hand written notes, study materials, list of
theorems etc. But no printed or photocopied materials will be allowed.
- Any unfair means used by any students in the examinations will be dealt with the strictest
possible measures, as per the Institute rules. In particular, if any student is found to be
using any kind of unfair practice during any of the examinations (including the quizzes) then
he/she will be awarded ZERO in that examination.
- Regrading of homeworks or exams will only be undertaken in cases where, you believe there has been a
genuine error or misunderstanding. Please note that our primary aim in grading is consistency,
so that all students are treated the same; for this reason, we will not adjust the score of one student
on an issue of partial credit, unless the score allocated clearly deviates from the grading policy
we adopted for that problem.
- If you wish to request a regrading of a homework or exam, you must return it to the instructor
with a written note on a separate piece of paper explaining the problem.
- The entire assignment or the exam may be regraded, so be sure to check the solutions to ensure that your
overall score will go up after regrading.
- All such requests must be received within one week from the date on which the homework or exam was made
available for return.
Last modified June 26, 2020.