Each of the following project is a group project to be done by around 5 students each. Each
project will be done by multiple
groups. Each group does one project. Groups shown with ✓ are already confirmed. The other groups are created arbitrarily
by me (and open to negotiation until 20th Sep, 2026).
Box-Muller transform and other related simulation techniques
Topics to be covered: Box-Muller transform with proof, inverse CDF method, rejection sampling.
You must actually write some code to implement these techniques and show the code and run it to
produce output during the presentation. Resource: Just Google search would give you enough material.
Face recognition using eigenanalysis (computational aspect, moderate).
Topics to be covered: Explain how eigenvalues and eigenvectors help to find the
directions and amounts of scatter. Explain image data.
You must actually write some code to implement these techniques and show the code and run it to
produce output during your presentation. Resource:See this youtube playlist. Also you
can download a relevant data set from here.
✓Pinak, Kaustuv, Rabi: (Date: Nov 06, first slot)
✓Saptarshi, Neerav(Date: Oct 12, first slot)
✓ Lakshya, Leela Sai Krishna(Date: Oct 09, first slot)
✓Gagan (B), Garg, Manish, Parnika, Abinaya(Date: Nov 11, first slot)
✓ Samriddha, Sandip, Mayank, Sourish, Tenzing(Dates: Nov 09, third slot and Nov 13,
second slot)
✓Chinmay(Date: Nov 09, second slot)
Count-min sketch to approximate frequencies from an input stream.
Topics to be covered: Explain hash functions as blackboxes mentioning just the statistical properties you will
use. Explain the problem scenario. Explain the technique with an example. Show how Markov inequality is used. No need to
code anything.
Resource:This page contains
expository articles on the topic.
✓Shinjan M, Anmol, Ankesh, Danish, Pardha Sarathi(Date: Oct 12, second slot)
✓Aarav, Diksha, Disha, Divyansh, Sejal(Date: Nov 06, second slot)
✓ Daksh, Shaurya, Swapnil, Tridham, Akshay, Shinjan G(Date: Oct 07, first slot)
✓ Rishikesh, Siva Lakshmi, Saurav, Manogna, Priyansh(Date: Nov 02, first slot)
BJKST algorithm for counting distinct elements from an input stream.
Topics to be covered: Explain hash functions as blackboxes mentioning just the statistical properties you will
use. Explain the problem scenario. Explain the technique with an example. Show how Markov inequality is used. No need to
code anything.
Resource:This github page
contains some python code using this algo for counting words in a file.
Here is a more mathematical exposition.
✓Aditya, Raunak, Siddhant, Antareep(Date: Nov 09, first slot)
✓ Arka, Ashish, Pritham, Sagnik(Date: Oct 07, second slot)
✓ Jeevantej, Satya Prakash, Lakshmi Narayana Naidu, Varshini(Date: Nov 04, second slot)
✓Nehal, Manvi(Date: Nov 11, second slot)
Showing almost every number is a normal number.
Topics to be covered: Define normal numbers. Give an example. State the result. Prove it.
Resource:This paper provides useful information.
✓Priyanshu, Shreyas, Mahima, Pawan, Abhinav Janga(Date: Nov 13)
✓Omhari, Utkarsh, Kavadi Shyam, Harsh, Abhinav(Date: Oct 09, second slot)
Showing that a random walk in 3D may not return.
Topics to be covered: Define 3D random walk. Clearly define the result to be proved. Prove it. Contrast with
lower dimensional cases (which need not be proved).
Resource:This video
will give a flavour of random walk. But don't get carried away by all the information provided there. Keep your focus on
a rigourous proof.
✓ Vinay, Siva Ganesh(Date: Nov 02, second slot)
✓Vansh, Ketan, Maharshi(Date: Nov 04, first slot)
These are more like elaborate assignments than projects demanding original research. You are
welcome to discuss the projects among yourselves. All the projects will be introduced during the lectures at appropriate
time points.
Instructor: Arnab Chakraborty (arnabc74 at gmail)
TA for Kolkata: Debanjan Bhattacharjee (debanjanbhattacharjee2002 at gmail)
TA for Delhi: Sumangal Bhattacharya (sumangalbisi82 at gmail)
TA for Bangalore: Sayan Roy (rs_math2404 at isibang)
The class notes constitute the main reference. It is based on many sources including the following books:
Ross: A First Course in Probability Theory
Hoel, Port and Stone: Probability Theory
Resnick: A Probability Path
Rosenthal: A First Look at Rigorous Probability Theory
Unfortunately, to my knowledge, there is no textbook just suitable for this course. The first two books mentioned above are
the closest from the easier side. They, however, do not mention many of the advanced topics included in our syllabus. The
last two books do mention them, but contain way too much discussion and are written at a level much higher than the present
course.
In short: the class notes are your best reference!