Projects 2023

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

The live-stream of the projects’ introductory session can be found here

1 - Eavesdropping 101

Mentors : Ravija Chandel (ravija#0041), Rahul Jha(juggernaut.jha#1241), Devansh Jain (Devansh#7048)
Project Area : Cryptography
Description : Most projects on cryptography focus on algorithms but like the great Loup Vailant said, one should never roll their own crypto. We will start with basics of finite fields before diving headfirst into DES and AES. Less time would be spent on the specifics of implementation and more time on the cryptanalysis. Then we will introduce key exchange, and their weaknesses.
Prerequisites: MTH102 (Linear Algebra), ESC101 (Intro To CS)
Intended Audience : Y21-Y22
Expected Duration : 10 weeks
Expected Weekly Commitment : 6 hours

2 - Some Problems in Combinatorics

Mentors : Farzan Byramji (geekotechy#7312)
Project Area : Combinatorics
Description : The main goal will be to try solving some problems in combinatorics that seem interesting. Problems of several kinds like enumerative, algebraic, or extremal can be considered. Some of these may have connections to TCS or discrete probability.
Prerequisites : Some very basic combinatorics (say roughly at the level of Bona’s A Walk through Combinatorics or the course CS201) is desirable. More knowledge related to the kind of problems one is interested in tackling (for instance, from Stanley’s books for enumerative combinatorics or Alon and Spencer’s The Probabilistic Method for some extremal stuff) would be helpful. None of this is strictly necessary (or sufficient) and most things can be picked up as we go along. Some mathematical maturity is perhaps the only essential requirement.
Intended Audience : Open to all
Expected Duration : 2-3 months
Expected Weekly Commitment : 3-6 hours

3 - An Introduction to Geometric Deep Learning

Mentors : Aniruddh Pramod (atrytone#6918),Mehar Goenka (mehar#0870)
Project Area : Geometric Deep Learning, Graph Neural Networks, Artificial Intelligence
Description : Geometric deep learning is a rapidly emerging field at the intersection of deep learning and geometry, which has the potential to revolutionize the way we analyze and understand complex data structures such as 3D shapes and graphs. This project is designed to provide you with a solid foundation in the concepts, methods, and applications of geometric deep learning and show you the power of the Erlangen program for Machine Learning. Prerequisites: A good understanding of Python programming.
You can view our presentation here.
Intended Audience : Y21 and Y22
Expected Duration : 9-10 weeks
Expected Weekly Commitment : 8 hours

4 - Introduction to Measure Theory

Mentors : Suyash Kumar Pathak (SoberTone#0164)
Project Area : Real Analysis
Description : This project aims to unearth the deeper and much more sophisticated aspects of real analysis. This would help the students not only to build up on their knowledge of analysis but also make their platform much more robust. The other component would be the application of the concepts learned in areas like cryptography, random number generation, hash functions, etc.
Prerequisites : MTH301 - attempting this course is important, I want to make links between what they already knwo and then get them to know about measure theory.
Intended Audience : Y20 and Y21
Expected Duration : 2 months
Expected Weekly Commitment : 7-8 hours

5 - Rubik’s Cube meets Group Theory: An Algorithmic Adventure

Mentors : Sai Praneeth D (electric_trash#2834), Tarun Goyal (TarunGoyal#3482)
Project Area : Abstract Algebra
Description : In this project we will study the maths behind the Rubik’s Cube, focussing on the topic of Group Theory. Initially the project will delve into the fundamentals of Group Theory and relevant concepts that will be required. We shall further explore how these concepts can be applied in solving the 3*3 Rubik’s cube. The overall aim of this project is to explore a more theoretical and abstract side of mathematics and how it has real life practical uses using the rubik’s cube as an example.
Intended Audience : Y22 mainly, Y21 also
Expected Duration : 2 months
Expected Weekly Commitment : 4-5 hrs

6 - MathData: Empowering Data Science with Mathematical Tools

Mentors : Siddhant Singhai(SiddhantSinghai#2918), Dishant Jain(dishant 02#6679)
Project Area : Statistics , Data Science ,Time Series Analysis
Description : In the first two weeks we would make the mentees familiar with the basics of python and the libraries we are going to use in the project which are pandas, NumPy , matplotlib , seaborn. Then in the following weeks we will focus on the statistical methods used in the data analysis and machine learning.We will also teach scikit-learn library as we will use this for the topics we are going to study later. We will start with the linear regression, Gradient descent, and cost function then we will move to the logistic regression, decision tree and random forest. Next We will finally move on to the K-means clustering. We will also teach if time remains naïve bayes classifier algorithm. At the end we will give them some glimpse of what extrapolation and interapolation is and introduce them to time series analysis also.We will specially focus on the theory of mathematical tools we are using like the regression analysis.
Prerequisites: Basic python skills , Anyone with enthu is welcome(specially Y22)
Expected Duration : 3 months
Expected Weekly Commitment : 6 hours

7 - Formal logic and Automata Theory

Mentors : Abir Rajbongshi (Abir #4687), Dhruv Garg (Dhruv Garg#2699), Bhavaj Singla(210265_bhavaj#3414)
Project Area : Mathematical logic
Description : The project will mainly consist of 2 parts - first the basics of formal logic and the second part would be basics of automata theory and computation. In formal logic we will cover propositional logic syntax and semantics, natural deduction, soundness and completeness, axiomatisation and its soundness and completeness, first order logic, examples of some simple SAT solvers and finally modal logic. For the second phase we will mainly cover the basic overview of formal defination of finite automata, regular/non-regular languages, nondeterminism, context free grammars and pushdown automata. We will mainly use our course notes and the book by Michael Sipser for automata and Logic in CS by Huth and Ryan for formal logic.
Intended Audience : This project will mainly be directed towards the Y22 especially those who are going to take up a formal logic course in their upcoming semesters. No prerequisite knowledge is required for this project.
Expected Duration : 6 weeks
Expected Weekly Commitment : 6-7 hours

8 - From the Discrete to the Continuous and Back

Mentors : Nupur Jain (NupurJ#8918)
Project Area : Topology and Combinatorics
Description : The study of topology explores continuous transformations, while combinatorics studies the discrete. The two interact and enrich each other in intriguing ways. In this project, we will take a look at how translating a problem from one of these domains to the other often makes for a more elegant and intuitive treatment. In particular, we will cover a topological proof of Kuratowski’s theorem, a combinatorial proof of Brouwer’s fixed point theorem, and see how triangulations are powerful tools to understand surfaces. Further topics can be decided based on which direction the interests of the mentees develop.
Intended Audience : All batches are welcome. No prerequisites are required. Elementary knowledge of topology would be useful but can easily be covered in the initial part of the project.
Expected Duration : 8 weeks or more
Expected Weekly Commitment : atleast 5 hours

9 - An Introduction to Theoretical Computer Science

Mentors : Rohun Easwar (KnightWatch#7071),Pranjal Singh(pranjal#0532)
Project Area : Theory of Computation, Abstract Algebra
Description : This project is intended as an introduction to theoretical computer science. (i) We will cover finite state machines (DFAs), Turing machines and some variants thereof, complexity classes, direct access (the random access in RAM) and circuits. (ii) We will also cover topics in algebra such as finite groups, rings and fields. Other related topics can be explored as per the interests of the mentees, for example, quantum computing (how the elementary operations differ from classical operations) and one-way functions (and their relation to nondeterminism). Mentees are welcome to present topics that interest them.
Intended Audience : As the project is intended to introduce mentees to theoretical computer science, Y22 UGs stand to benefit the most.
Expected Duration : 8 weeks
Expected Weekly Commitment : 3 hours

10 - Build Your own Computer Vision Library

Mentors : Pratham Sahu(PRATHAMSAHU#6615),Aditya Bangar (AdityaBangar#5236),Dwija Kakkad(moonchronicle#5330)
Project Area : Computer Vision
Description : Build a simple computer vision library in C(like Pytorch) to carry out operations like resize, filter, other processing functions. Will build an intuition into how computer vision actually works
Intended Audience : Open to all
Expected Duration : 5-6 weeks
Expected Weekly Commitment : 6 hours

11 -Probabilistic Thinking

Mentors : Aryaman Singhal (Putra#5030), Kumar Saurav ,Lavesh Mangal
Project Area : Probabilty Theory, Stochastic Processes, Bayesian Analysis
Description : Cover the applications of probability theory to various areas covering axiomatic probability theory, Monte Carlo Simulation methods, stochastic processes and Bayesian analysis applications to Machine learning.
Intended Audience : Y21 (preferred), Y22
Expected Duration : 8 weeks
Expected Weekly Commitment : 6-9 hrs

12 - ClassifyMeister

Mentors : Sandipan Mitra (Aeti#0020), Nitin Gupta (Reganite#7619), Alok Kumar, Shashank Wankhade (shanks#0696)
Project Area : Supervised Machine Learning
Description : Covering the classification algorithms in the Supervised machine learning domain. Will include Logistic regression, naive bayes, k-nearest neighbors, SVM, Decision trees. Tentatively include two programming-based applications as evaluation metrics to gauge the understanding of mentees in the project.
Prerequisites : Basic level linear algebra(operations on matrices). Recommended : Familiarity with arrays, libraries, functions in python (for assignments)
Intended Audience : Open for all batches
Expected Duration : 10 weeks
Expected Weekly Commitment : 4-6 Hrs

13 - Mathematical Trading Strategies

Mentors: Muditt Khurana(Muditt Khurana#8767), Shivam Pandey(Rogue_Al_Capone#3815)
Project Area : Mathematical Finance
Description :
1. Learn the basics of trading related finance 2. Get a good grasp over technical tools and patterns used for formulating trading strategies and mathematics behind them 3. Understand existing basic algorithmic strategies for profit making in this domain 4. Develop your own unique trading strategy/hypothesis using tools learnt during the project (obviously, backtest it) 5. Statistically test its significance
Intended Audience : Y20/Y21s and Selected Y22s
Expected Duration : 8-9 weeks
Expected Weekly Commitment: 5-6 hours

14 - Knot Theory and its Applications

Mentors: Kalash Talati(Kalash#8641), Srivishnu Rajagopal(Maari#8617)
Project Area : Topology, Group Theory
Description : The project will start with a quick discussion on topological spaces and move onto knot theory, knot invariants, braids and braid group and later part we will discuss the application on knot theory in various domains.
Prerequisites: No pre req, No specific batch
Intended Audience : Y22, Y21, Y20
Expected Duration : 6-8 weeks
Expected Weekly Commitment: 4-6 hrs/week

15 - DataScience with R

Mentors: Sanat Goel(Sanat#0736), Siddharth Pathak(Siddharth Pathak#5745), Rohit Jangid(rohitJangid#2985)
Project Area : Probability, Statistics and DataScience
Description : The project aims to introduce you to the nodes of “Data Science”, the elegant art of finding information from any raw dataset. This raw dataset can be an excel sheet, comma-separated files, self-simulated dataset, extracted data from a website or even an image etc. By the end of the project, you will be equipped with an experience in all of these fields and all the preliminaries to start the machine learning in R.
Prerequisites : ESC101/Familiarity with C/C++
Intended Audience : Y22 mainly, and Y21 interested in SDS related topics, mainly people who do not have much exposure to Data Science, and wants to know more about it
Expected Duration : 8 weeks
Expected Weekly Commitment: 6-8 hours

16 - Forecasting using Time Series Analysis

Mentors: Lavesh Gupta(luhhvesh#6466), Medha Srivastava(Medha#3468), Shubham Kumar(Shubham#8231)
Project Area : Time Series Analysis, Stationary Processes, Machine Learning
Description : This project will cover in detail the concept of Time Series Analysis, which is a specific way of analyzing a sequence of data points collected over an interval of time. Time series analysis helps us understand the underlying causes of trends or systemic patterns over time. Using data visualizations, we can see seasonal trends and dig deeper into why these trends occur. Some of the topics we plan to cover : Time Series Data: Firstly, we’ll look at the types of data and study how to make visualizations of those data, and how do we deal with missing values in our dataset. We also study how to find outliers in the data through some statistical methods. Characteristics and Components: Next, we’ll study the characteristics of time series (smoothening, decomposition, correlation) and also study about the components of time series (trends, seasonality, cyclic variations, residuals) Time Series Models: Next up, we’ll study each time series model in detail and implement them in python using statsmodel library. We will study basic models such as white noise and random walk, and move to more complex models such as AR, MA, ARIMA, SARIMAX and then study models that predict volatility such as ARCH, GARCH models. Space State Models: In the end, we’ll spend a week studying about State Space Models, particularly MSTL Decomposition, and make forecasting using Unobserved Components Models (UCM)
Prerequisites : Basics of Python, and Statistics (can be learnt quickly)
Intended Audience : Y21 and Y22 with an interest in forecast modelling, finance, machine learning.
Expected Duration : 2-3 months
Expected Weekly Commitment: 6-7 hours

17 - Intro to Machine and Deep Learning

Mentors: Anwesh Saha(Anwesh#6428), Arindom Bora(AB10#7658), Aakarsh Mishra(Aakarsh Mishra#5686)
Project Area : Linear Algebra, Machine Learning, Calculus
Description : In this project, we will be going through the math and code of popular machine and deep learning algorithms. We will also learn to implement such algorithms from scratch. The project will end with a small hands-on project applying whatever we learnt.
Intended Audience : Y21 & Y22
Expected Duration : 10 - 12 weeks
Expected Weekly Commitment: 8 - 10 hrs

18 - Mathematical Predictor: Machine Learning

Mentors: Siddharth Garg(Siddharth Garg#9537), Rudransh Goel(Rudransh #1712)
Project Area : Mathematical analysis in machine learning
Description : The idea of this project is to explore the mathematical aspects of machine learning algorithms, optimization techniques, and regularization methods. The project will include mathematical concepts used in linear regression, gradient descent, regularization, optimization techniques that improve model performance. The project can also include more topics such as ensemble learning, Bayesian methods, and dimensionality reduction.
Intended Audience : Y21, Y22
Expected Duration : 2.5 months
Expected Weekly Commitment: 4-5 hours

19 - Image Processing and Computer Vision

Mentors: Akshat Agarwal(akku#0940), Subhrajit Mishra(Subhrajit_Mishra#3214)
Project Area : machine learning , probability and statistics.
Description : Sampling and quantization, Image enhancement, Spatial domain analysis, frequency domain analysis, Edge detection, Image segmentation using ML algorithms, Image denoising, important probability distributions and their usage
Prerequisite : MTH102A and ESC101A
Intended Audience : Y20, Y21 and Highly Enthusiastic Y22s
Expected Duration : 6 to 8 weeks
Expected Weekly Commitment: 10 hr/week

20 - You Only Look Once

Mentors: Saugat Kannojia(Saugod#0051), Shrilakshmi S K(maathp#5873), Rohan Virmani(210871_RohanV#9397)
Project Area : Deep Learning and its Applications
Description : Our project mainly focuses on the CNN aspect of Deep Learning with an intensive analysis of Linear Algebra involved in it. We will be talking mainly about what CNNs are and its real world applications, mainly focusing on YOLO algorithm. Firstly, we will be teaching the basics of Deep Learning and Neural networks, proceeding to learning CNNs from scratch and going deep into how YOLO algorithm works along with its implementation on a real-time project. We are providing our action plan as of now in this google doc- https://docs.google.com/document/d/10R2miHyRdpcLgYnc9rrM0WfLqVp9EKw-H8X4C3xsrig/edit .
Intended Audience : Y22(preferably), Y21
Expected Duration : 6-8 weeks
Expected Weekly Commitment: 7-8 hours

21 - PhysiLearn - Learning physics through neural networks

Mentors: Emaad Ahmed(EmaadAhmed#9226), Om Shrivastava(om shrivastava#6974), Jetha Ram(Jetharam#2056), Shivansh Maheshwari(Shivansh Maheshwari#9708)
Project Area : Mathematical Physics
Description : We are going to implement PINN( Physics Informed Neural Network) to solve differential equations. And, eventually coding a Harmonic Oscillator using PINN.
Prerequisite : Familiarity with Python.
Intended Audience : Y22 ( preferred )and Y21
Expected Duration : 8 Weeks
Expected Weekly Commitment: 8-10 Hours

22 - Networking of Nodes

Mentors: Havi Bohra(havi#6078), Vekariya Keval(Keval#1656),Venkaat Balaje(Venkaat Balaje#6196)
Project Area : Graph Theory and Algorithms
Description : Time and Space Complexities , Graph traversals Algorithms , Shortest Path Algorithms, Tree traversals algorithms, Disjoint set union
Prerequisite: ESC101(or ESC111+ESC112)/ Familiarity with C/C++
Intended Audience : Y22 ( preferred )and Y21
Expected Duration : 2 months

23 - Cryptographic Applications of Number Theory and Abstract Algebra

Mentors: Mihir Mittal(none_24#0679),Shwetank Anand(Shwetank Anand#0363), Aditya Kumar(ADITYA KUMAR#4526)
Project Area : Abstract Algebra, Number Theory, Group Theory and Cryptography
Description : We will start with some basics of number theory, including Euclid’s algorithm, Bezout’s Identity, Fermat’s little theorem, Euler’s Totient Function, Chinese Remainder Theorem and Diophantine equations. Then if time permits, we might extend to combinatorial number theory. Then we start with Abstract Algebra covering Group Theory, Rings, Fields, Finite Fields and Algebraic Closure of Fields and their Applications. Finally, we move to the above applications in Cryptography after covering the basics. We will cover key exchange algorithms like RSA. Then we will culminate with the most used encryption algorithm AES(Advanced Encryption Standard).
Intended Audience : Y22 ( preferred )and Y21
Expected Duration : 2-2.5 months
Expected Weekly Commitment: 6-7 hours

24 - Mathematical Foundations of Computer Graphics, Rendering, and Lighting

Mentors: Ishan Bawne(RockStarDaddy#8138), Prakhar Pratap Mall(TheTUFGuy#0138)
Project Area : Computer graphics
Description : In this project, students will explore the mathematical foundations of computer graphics, rendering, and lighting. Over eight weeks, they will cover topics such as ray tracing, lighting, procedural generation, and special topics like curves, tangents, and splines. Students will also learn programming skills in C++/C# and develop problem-solving skills that are valuable in various fields such as game development, computer graphics, and computer vision. Throughout the course, students will gain hands-on experience implementing ray tracing, procedural generation, and mesh generation techniques. By the end of the course, they will have a solid understanding of the mathematical foundations of computer graphics and will be able to apply their skills in real-world situations. This course is perfect for anyone interested in computer graphics or game development and is looking to expand their knowledge and skillset in these areas.
Intended Audience : Y20/Y21, Y22 with decent C++/C# experience
Expected Duration : 8 weeks
Expected Weekly Commitment: 9-10 hours/week