Projects 2024

- Join the Stamatics discord server to interact with the mentors and for any other communication: invite link

You can view the presentations of all the projects in this link here.

1 - A Reconstruction of Analysis

Mentors : Mohd Sufyan
Project Area : Metric Topology, Real Analysis, Measure Theory
Description : “The project aims to be a self-sufficient development of analysis upto Riemann-Stieltjes integration in one variable via metric topology. Mentees will further be introduced to weaknesses in the Riemann integral followed up with introductory Measure Theory (Borel Sets and Lebesgue Measure on R). The project aims to be rigorous until the Riemann Integral, beyond which it will turn more expository.

The project aims at filling that gap between high school calculus and undergraduate analysis, and further, introducing mentees to the backend machinery of analysis that is measure theory. Exposing them to ideas of measure will help form a much more rigid foundation in their minds for any further ventures in the subject.”

Prerequisites: None
Intended Audience : Y23
Expected Duration : 12-14 weeks
Expected Weekly Commitment : 2-4 hours

2 - Discrete Mathematics

Mentors : Ashutosh Agrawal
Project Area : Computer Science
Description : The project will cover Logics, Combinatorics, Graphs, Trees , Language and Grammar and Automata.
Prerequisites : ESC101
Intended Audience : Y22s and later
Expected Duration : 7 weeks
Expected Weekly Commitment : 6-7 hours

3 - Probabilistic Pioneers: Navigating Random Realms from Markov Chains to Hidden Models

Mentors : Raghav Govind
Project Area : Stochastic Processes
Description : “The primary aim of this summer project is to provide participants with a comprehensive understanding of stochastic processes, particularly focusing on Discrete Space Discrete Time Stochastic Processes, and their applications to model various processes such as gambling in a casino, random walk on integers, etc. The final 2 weeks of this project aims to impart knowledge of Hidden Markov Models and how they may be used to catch credit card fraud. “
Prerequisites : MTH114/MTH102
Intended Audience : Y22/23 (UG) & Y23 (PG)
Expected Duration : 8 Weeks
Expected Weekly Commitment : 6-7 Hours

4 - Application of Probabilistic Theory

Mentors : Kaushal Jain, Siddhi Vora, Diksha Agrawal
Project Area : Probability, Statistics and Game Theory
Description : The project aims at studying connection between two domains of Mathematics : Probability and Statistics with Game Theory. This is being derived from a model of Game Theory which has some nice applications of the former one. For that we will setup basic theory required and discuss about models of individual domain too.
Prerequisites : None (Idea of Probability in JEE would be helpful)
Intended Audience : Y23 (preferred) , Y22
Expected Duration : 8-10 weeks
Expected Weekly Commitment : 5-6 hours

5 - DistanceQuest

Mentors : Sruthi Subramanian, Sambuddha Chakrabarti
Project Area : Machine Learning
Description : An introduction to classification using machine learning. We will look into ways to convert the given data into vectors, and will use the norm of the vectors for classification. We will look at LwP (Learning with Prototypes), and the K-Nearest Neighbour methods for classification. We will also look at how we can change the hyperparameters for a more optimal model. Finally we will have a classification task to apply all of the concepts learnt. Prerequisites : Basic knowledge of python, Linear Algebra (MTH113)
Intended Audience : Y23
Expected Duration : 7 weeks
Expected Weekly Commitment : 5 hours

6 - Mathematical Ciphers

Mentors : Naman Gupta, Ishan Dandwani, Sanskar Yaduka
Project Area : Cryptography, Algebra, number theory
Description : Beginning with number theory essentials like Euclid’s algorithm and Fermat’s little theorem, we traverse abstract algebra’s terrain of Group Theory, Rings, and Fields. Transitioning to practical applications, we unravel key exchange algorithms such as RSA, culminating in the study of AES encryption. Join us in decoding the language of numbers to secure digital communication.
Prerequisites:-
Intended Audience : Y23s,Y22s
Expected Duration : 10 weeks
Expected Weekly Commitment :7-8 hours

7 - Options Strategies and Market Analysis

Mentors : Ayush Baghel and Rahul Ahirwar
Project Area : Finance
Description : The project initiates by delving into fundamental terminologies required to understand the subsequent concepts, models and strategies. Then we will be introducing Derivative contracts along with option pricing models like Black Scholes Model and Monte Carlo Simulation and also their mathematical interpretations and formulas behind it. Then basic and complex option strategies like long put, straddle, butterfly, iron condor, etc. Then we will be doing the backtesting on real data by applying these strategies to check their performance. After it we will proceed to stock movement trends analysis using momentum, volume and volatility, impact of market news and events, finding resistance and support levels,etc. Introducing to importance of risk management in option trading and how to hedge portfolio against adverse price movements.
Prerequisites:Basic python knowledge and Interest in Finance
Intended Audience : Y23
Expected Duration : 6 weeks
Expected Weekly Commitment : 7-8 hours

8 - Bayesian Analysis & Inference

Mentors : Lavesh Gupta
Project Area : Probabilistic Modelling
Description : “Dive into the world of probabilistic thinking! This project will uncover the secrets of probability and statistics, through programming. We’ll begin by exploring the fundamentals of Bayesian statistics, a framework that incorporates prior knowledge, and see how it unlocks new possibilities in data analysis.

We’ll then delve into probabilistic programming, a revolutionary approach that lets you code with probability itself! Using cutting-edge libraries like PyMC and ArviZ, we’ll build sophisticated hierarchical models that capture complex relationships within your data. Additionally, we’ll re-visit familiar machine learning models like Linear Regression and Regression Trees from a fresh perspective, viewing them through the lens of probability.”

Prerequisites :Familiarity with Python programming is must. Familiarity with basic python libraries like NumPy, and Matplotlib (optional). High-School Probability Concepts like Bayes Theorem, Conditional Probability (prior, posterior).
Intended Audience : Y22 and Y23 only
Expected Duration : 9-10 weeks
Expected Weekly Commitment : 5-6 hours

9 - Theoretical Machine Learning

Mentors : Viral Chitlangia, Zehaan Naik
Project Area : Machine Learning, Statistics, Linear Algebra
Description : Many of you might be acquitted with Machine Learning, and have used it before, but do you know why Machine Learning works? Throughout the duration of this project, we will go through concepts of Machine Learning, from Linear Regression to Clustering, to NLP, and finish off on a high by using the concepts on a real life example.
Prerequisites :Sufficient Knowledge of Python(Numpy), Linear Algebra, Calculus. Pytorch recommended.
Intended Audience : Y23s with a rudimentary idea of ML
Expected Duration : 8 Weeks
Expected Weekly Commitment : 10-12 Hours

10 - Combinatorics and Computation

Mentors : Dev Gupta, Soham Sen, Vrinda Sharma
Project Area : Combinatorics
Description : “This is an invitation to extremal and additive combinatorics with applica- tions to computer science. We will follow (Jukna, 2001) for the first part of the project and lecture notes by Avi, Boaz and Luca (https://www.math.cmu.edu/ ~af1p/Teaching/AdditiveCombinatorics/allnotes.pdf), (Tao and Vu, 2006), (Lovett, 2017) for the second part. We hope to solve plenty of interesting and challenging problems in the project. Our aim is to illustrate the techniques that enables one to solve certain combinatorial problems elegantly. The emphasis will be more on the methods used to prove theorems than on the theorems themselves.”
Intended Audience : Anyone interested in discrete maths.
Expected Duration : 10-12 weeks
Expected Weekly Commitment : 3 hours

11 -An Introduction To Number Theory

Mentors : Sriram CV, Sahil Goyat
Project Area : Number Theory
Description : It will be a reading group on Ireland and Rosen’s book on Number Theory, we will learn some basic abstract algebra along the way.
Intended Audience : Y22,Y23
Expected Duration : 8 weeks
Expected Weekly Commitment : 6-8 Hours

12 - Forecasting using Time Series and Analysis

Mentors : Gagandeep, Abhinav, Ganesh
Project Area : Machine Learning, Time-Series
Description : We will study about time series model in detail and implement them in pyhton using statsmodel library. We start from basics models like naive, white-noise,random walk and then move to more complex model like ARIMA and SARIMA.
Prerequisites : Basic Python and some py libraries like numpy, pandas, seaborn is plus
Intended Audience :Y23’s
Expected Duration : 8 weeks
Expected Weekly Commitment : 6-7 hrs

13 - Introduction to Type Theory and Functional Programming

Mentors: Apoorv Tandon, Mridul Gupta
Project Area : Type Theory and Functional Programming
Description : The project will have a concurrent focus on Functional Programming with OCaml as well as Type Theory. The first two weeks aim to introduce Functional Programming concepts, while the third week begins to focus on Type Theory. Towards the end of the project, mentees will be expected to write concurrency models using OCaml.
**Prerequisites: **ESC111, ESC112
Intended Audience : no batch preference
Expected Duration : 2 months
Expected Weekly Commitment: 8 hours
13 - An Introduction to Representation Theory
Mentors: Rohun Easwar
Project Area : Algebra
Description : We will be studying the basics of representation theory from ‘Linear Representations of Finite Groups’ by Serre, and then we will move on to other topics as per the interest of the mentees.
**Prerequisites: **Some familiarity with linear algebra and abstract algebra is expected. The background of prospective mentees will be assessed before they are allowed to join.
Intended Audience : Anyone who satisfies the pre-requisites
Expected Duration : 8 weeks
Expected Weekly Commitment: 2-3 hours