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.
Exact logistics
will be communicated later.
Box-Muller transform and other related simulation techniques
Face recognition using eigenanalysis (computational aspect, moderate).
Count-min sketch to approximate frequencies from an input stream.
BJKST algorithm for counting distinct elements from an input stream.
Showing almost every number is a normal number.
Showing that a random walk in 3D may not return.
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!