Projects 2022

- To register, fill the form latest by 21st March, 11:59 PM here

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

The recording of the projects introductory session can be found here

1 - Quantum Algorithms

• Project Area : Linear algebra, Logical Thinking
• Mentors : Fahad Sheikh (Mando#5308)

• Description : I have done a similar project last year, where I have done problems from Quantum Computing Nielson and Chung. Some parts of this project will be the same, but at the end of the project I would like for mentees to present a literature review on a set of topics I will give them. I would mainly focus on Nielson and Chung for understanding the basics, and would like to introduce more algorithms other than Shor’s Algorithm and Grover’s algorithm. The mentees have to present a paper on a topic, so that it can make me sure what have they understood in the project. Having a good grip of python is a requirement, as in the later part of the project we will dive into Qiskit, an open-source python module by IBM.

  Prerequisites: MTH102 (Linear Algebra), ESC101 (Intro To CS)

• Intended Audience : Y20-21s

• Expected Duration : 2-3 months

• Expected Weekly Commitment : 6-8 hours

2 - Mathematical Tools for Data Science

• Mentors : Shreya Bhattacharya (shreyab20#4813), Pranshu Gaur (pran#1011)

• Project Area : Probability and Statistics, Basics of Data Science, Machine Learning

• Description : We will be covering the basics of probability and statistics which are used in machine learning algorithms alongwith some relevant libraries and algorithms. Some of the topics we plan to cover are :
  1. Introduction to Data Science
  2. Discussion on AI vs Data Science vs ML
  3. Categories of Data, Statistical Terminologies, Sampling Techniques, Probability Terminologies
  4. Descriptive Statistics, Inferential Statistics, Probability Distribution, Point Estimation, Interval Estimate, Margin of Error, Hypothesis Testing
  5. We will also cover Python libraries like numpy, pandas, matplotlib and seaborn which help in Data Analysis.

  6. We also plan to cover algorithms like Regression, Decision Tree, Random Forest, Naive Bayes to demonstrate the application of the learned topics. An application based project will also be done.

     Prerequisites : None, it all depends on the enthusiasm of the mentees.

• Intended Audience : Y20 and Y21

• Expected Duration : 2 months

• Expected Weekly Commitment : 6-8 hours
  

3 - Regression Analysis

• Mentors : Sandipan Mitra (Aeti#0020), Rohan Kumar (Meursault#6295)
• Project Area : Statistics

• Description : Students taking this project will get to learn about data analysis and model building through popular statistical tools, the base of which being regression. Initially basics of probability and statistics will be covered after which we move into linear regression, our focus of concern being with multiple analysis. There will be an applied project based on the same and students will be required to build models and interpret the results as a real-life frame. We will move into complex topics like panel-data and time-series regression followed by another applied project. If time permits we can cover non-linear regression too.

• Intended Audience : Y20 and Y21
• Expected Duration : 9-10 weeks
• Expected Weekly Commitment : 2-3 hours
  

4 - Number Theory and Applications

• Mentors : Priya Gole (Priyaa#6917), Abhishek Shree (killBird#5626)
• Project Area : Number Theory and Abstract Algebra

• Description : This project aims to introduce the mentees to the basic concepts of number theory and abstract algebra.

  The first part of the project is theoretical, wherein concepts related to number theory and group theory will be introduced, and we would spend our time scratching our heads while trying out problems.

  The other component would be the application of the concepts learned in areas like cryptography, random number generation, hash functions, etc.

• Intended Audience : Y20 and Y21
• Expected Duration : 2 months
• Expected Weekly Commitment : 6-8 hours

5 - Geometric Mechanics

• Mentors : Mohammad Saad (Saad#9798), Annadur Rahul Kesavan (luharnavasek#5344)
• Project Area : Mathematical Physics

• Description : The reading project aims to serve the classical mechanics in a mathematical fashion, unlike the manner in which it is taught mostly in a semester long course. We would not cover the wider contents of a typical mechanics course (like PHY102 or PHY401), instead focus on the mathematics, specially geometry, of the involved physical framework. For example, it would include how the dynamics of a system takes place on a configuration manifold, the geometries of the Lagrangian and Hamiltonian formalism, so on and so forth. We would not be solving funky pully-cart or rotation problems. The project would also have an underlying theme of appreciating the history and philosophy of mathematics and physics, by occasionally visiting some interesting anecdotes wherever required. (Basically, I would try to serve the project the way I wish classical mechanics should have been taught to me.)

  For the evaluation, a common ground can be decided once the project commences. As of now, a final combined group report (ofcourse in LaTeX) or a short presentation would suffice for evaluation.

• Intended Audience : UG Y20 and Y21 with basic familiarity of classical mechanics. As per the Stamatics theme, the project would be somewhat mathematically involved. If you’re motivated enough to read books and learn, do apply.
• Expected Duration : 6 weeks
• Expected Weekly Commitment : 2-4 hrs
  

6 - An Invitation to Functional Analysis

• Mentors : Rahul Sethi (the-last-knight#4011)
• Project Area : Analysis

• Description : The directed reading project serves as an introduction to Functional Analysis. In the first half, we will develop some general techniques in Functional Analysis, and in the latter half, the focus will primarily be on Hilbert Space Theory. If time permits, we may look at selected topics in Operator Theory, including exposure to research-level problems.

  This project will help students develop not only an understanding of Functional Analysis but also inculcate an attitude of mathematical inquiry in general. There will be an emphasis (and no compromise) on mathematical rigor. The pace of the project will be dictated by the mathematical maturity of the group.

  Prerequisites: (i) MTH301A* (A First Course in Real Analysis) or equivalent.

  (ii) General Topology (specifically Ch. 2,3 of Munkres’ Topology).

  (iii) Introductory Measure Theory (including Riesz Representation Theorem, Radon Measures, etc.) Additionally, you will be required to prepare a report in LaTeX, and proficiency in the same is a must.

  (ii) and (iii) are desirable but not necessary. If you are not sure whether you meet the prerequisites for this project, please get in touch with the mentor directly.

  *You may register for this project even if you are taking MTH301A in the 2021-22 II semester.

• Intended Audience : Only UG students. Though anyone fulfilling the prerequisites may request to register, the project will mainly be of interest to Y20 MTH and PHY UGs. Y21s should not apply unless they have sufficient (and provable) mathematical background.
• Expected Duration : 4-5 months
• Expected Weekly Commitment : At least 12 hours per week (involves significant self study and exercises).
  

7 - Statistical Simulation

• Mentors : Ananyae Kumar Bhartari (ananye24#4537), Naveen kumar Mathur (Navi_Kane)

• Project Area : Probability and Statistics

• Description : Simulation of random variables from discrete, continuous, multivariate distributions and stochastic processes, Monte-Carlo methods. Use of RNVP to model complex distribution and special attention GMM algorithms.

• Intended Audience : Open to every one who is interested to learn about simulation .

• Expected Duration : 6-8 weeks

• Expected Weekly Commitment : 4 hours
  

8 - Introduction to Proof Complexity

• Mentors : Farzan Byramji (geekotechy#7312)
• Project Area : Complexity Theory

• Description : The broad aim will be to look at some of the main results in proof complexity and see some of the many connections with other things in complexity theory such as circuit complexity, communication complexity, TFNP problems, etc. starting from the basics.

• Intended Audience : The project is mainly targeted at people interested in logic and/or complexity theory. Some familiarity with propositional logic and very basic complexity theory will be essential. These prerequisites are not too hard to pick up since there are readable introductory texts such as Sipser that are sufficient. A stronger background in logic and/or complexity theory will, of course, be useful. Optionally, if one is interested in algebra and wishes to learn about algebraic proof systems, then knowing stuff about polynomial rings, say at the level of Cox, Little, O’Shea’s excellent text Ideals, Varieties and Algorithms, would be helpful.
• Expected Duration : 2 months
• Expected Weekly Commitment : 2-4 hours
  

9 - Insolvability of Quintic Equations

• Mentors : Ajay Prajapati (Ajay Prajapati#6448)
• Project Area : Abstract Algebra

• Description : The goal of this project is to understand one of the major achievements of early 19th century mathematics: Insolvability of Quintic Equations. That you can’t have a formula to find roots of a degree 5 polynomial like you have for quadratic equations. The ideas that went into solving this problem paved the way to modern mathematics. Along the way, we will see some really cool stuff like construction of a regular 17-gon, impossibility of trisecting a general angle with ruler and compass.

• Intended Audience : This project is intended for 2nd year Mathematics and Computer Science students (and those who are familiar basic abstract algebra).
• Expected Duration : 3 months
• Expected Weekly Commitment : 5-6 hours
  

10 - Rational Points on Elliptic Curves

• Mentors : Dawood Bin Mansoor (rockstar2514#0635), Udit Narayan Pandey (UNP#0155)

• Project Area : Algebra and Geometry

• Description : During the course of the project we will be studying rational points (both coordinates rational) on algebraic curves. We will define a very geometric binary operation on this set. We will show that the binary operations makes the set of rational points a group. More interestingly, we will show how this group is finitely generated. Further, if time permits we will study other specific types of points on elliptic curves. As part of thee end term report, a presentation will be required and weekly assignments may be given which may be of programming in nature.

• Intended Audience : 2nd year or higher, other necessary concepts(like groups etc.) will be taught in duration of the project.

• Expected Duration : 1.5 - 2 months

• Expected Weekly Commitment : May range between 2-20 hours depending on mentee’s other involvements.
  

11 - Algo101x

• Mentors : Satyam Kumar Roy (stack#8156), Shorya Kumar (shoryak#4571), Kunwar Preet Singh (kpS#9551)

• Project Area : Combinatorics, Number Theory, Probability

• Description : We plan to cover following topics (which are frequently used in Competitive Programming) - application of gcd, hashing, constructive problems, chinese remainder theorem, mobius inversion, matrix exponentiation, dynamic programming, graph algorithms, generating functions and fft

• Intended Audience : Intended audience should be familiar with some programming language(preferably C++). They should be able to analyse time complexity of simple codes.

• Expected Duration : 3 months

• Expected Weekly Commitment : 4 hrs

12 - Machine Learning : Behind the Curtain

• Mentors : Hitesh Anand (hitesh#5074), Arnav Gupta (VaderEvader#8554), Sunreet Khanna (skhanna23#9868)

• Project Area : Machine Learning and Neural Networks

• Description : This project will cover in some detail the mathematical aspects of different ML algorithms. We will start with the basics and touch some of the advanced algorithms as we proceed. The topics that would be covered include:
  1. Linear Algebra
  2. Simple, Multiple, Polynomial Linear Regression
  3. Evaluation of Regression models
  4. Logistic Regression
  5. Clustering algorithms
  6. Associate Rule Learning(Apriori, Eclat)
  7. Optimization techniques like gradient descent, adam, RMSProp, etc.
  8. Loss functions like crossentropy, huber loss, etc.
  9. Introduction to Neural Networks
  10. Convolutional Neural Networks
  11. Neural Style Transfer
  12. Recurrent Neural Networks

  The assignments will include implementation of some of these algorithms from scratch(without using any libraries) in python. Hence, familiarity with basic level python is recommended.

  Prerequisites : Basic level linear algebra(operations on matrices) Recommended : Familiarity with arrays, libraries, functions in python (for assignments)

• Intended Audience : The project is preferable for UG Y21, although students from other batches can enroll too, if interested in the topics mentioned above.

• Expected Duration : 2 months

• Expected Weekly Commitment : 5-6 Hrs

13 - Introduction to Deep Learning and Applications

• Mentors: Ashutosh Sharma (ASH#7887), Prateek Sogra (LightSpeed#2728), Vineet Kumar (Vineetk20#3065)

• Project Area : Linear Algebra , Neural Networks , Introduction to Computer Vision

• Description :

  1. Basics of Linear Algebra required for neural networks
  2. Python and its libraries(numpy pandas matplotlib)
  3. Intro to Tensorflow
  4. Topics from Deep learning
  5. Computer Vision basics and applications

  Prerequisites : Programming basics(Basically Python) and Mathematical Aptitude

• Expected Duration : 3-4 months

• Expected Weekly Commitment: 8-10 hrs
  

14 - Decrypting Technical Indicators

• Mentors: Sujal Harkut (DeadTree#9882), Sheetal Gupta (sheetalg20), Sarah Kapoor (psychocrat#3620), Kushagra Sharma (Mr. Defenestrator#2115)

• Project Area : Maths behind Technical Indicators

• Description : Basically we will dive into the mathematical part of technical indicators and will clear the concepts pertaining to the usage of specific values of parameters such as time period, multiplier for standard deviation or bands, RSI Index. In the beginning, we intend to cover some basic and standard technical indicators like SMA(Small Moving Average) ,EMA(Exponential Moving Average),MACD(Moving average convergence divergence), Bollinger Bands and others. Then we will move ahead onto changing parameters in formulae, or using EMA instead of the default SMA in Bollinger.

  Lastly, we would be covering combinations of this and Backtest on standard Stock Exchanges and Crypto Exchanges and give the result with the highest Sharpe ratio.

• Intended Audience : Y21, Y20

• Expected Duration : 8 weeks

• Expected Weekly Commitment: 5-7 hrs

15 - Connecting the First Search

• Mentors: Utkarsh Jain (JB996#5074), Patil Aditya Bharat (aditya_patil#1265), Saaransh Aggarwal (Saaransh Aggarwal#7225)

• Project Area : Graph theory and Algorithms

• Description : Graph traversal algorithms, shortest path algorithms, Tree algorithms, Advanced graph algorithms.

  Prerequisites : ESC101/Familiarity with C/C++

• Expected Duration : 2 months

• Expected Weekly Commitment: 5-7 hours
  

16 - Number Theory and Cryptography

• Mentors: Piyush Beegala (FranticAlien#7151), Sujal Harkut (DeadTree#9882), Bipplav Kumar Tiwari (Bipplav Tiwari#6662)

• Project Area : Number Theory and Cryptography

• Description : Beginning with Euclid’s algorithm and Bezout’s Identity, we progress to Fermat’s little theorem, Euler’s theorem, Totient Function, Congruences, and Diophantine equations. In the second half, we’d like to concentrate on cryptographic applications such as hashing techniques, primality testing, public key algorithms (such as Diffie–Hellman and RSA), and cryptanalysis. We will also go over the fundamentals of ECC (Elliptic Curve Cryptography).

• Intended Audience : Y21

• Expected Duration : 2-2.5 months

• Expected Weekly Commitment: 4-6 hrs

17 - MCMC Methods in Julia

• Mentors: Vansh Bansal (Vansh#7537), Pramodh Gopalan (Pramodh Gopalan#7422)

• Project Area : Computational Statistics

• Description : This project will mainly focus on Markov Chain Monte Carlo techniques. Markov Chain Monte Carlo sampling provides a class of algorithms for systematic random sampling from high-dimensional probability distributions. MCMC techniques often solve integration and optimization problems in large dimensional spaces. These two types of problems play a fundamental role in machine learning. Just going over the theory is boring. This project will also involve a substantial computational aspect, and you will be asked to implement various algorithms, preferably in Julia. The tentative list of topics that we want to cover is as follows:
  1. Sampling Methods and general Monte Carlo methods
  2. Rejection Sampling and Importance Sampling
  3. Markov Chain and Measure Theory basics
  4. Metropolis-Hastings Algorithm
  5. Accelerating MCMC Algorithms
  6. MCMC Algorithms for Intractable Posteriors

  Prerequisites : This advanced project requires a good grasp of probability and statistics basics.

• Intended Audience : Anyone well-acquainted with the contents of MSO201 / CS203 or any other equivalent course.

• Expected Duration : 14 weeks

• Expected Weekly Commitment: 8-10 hours

18 - Quantum Theories and Applications

• Mentors: Bhoomi Choudhary (Bhoomi#8271)

• Project Area : Mathematics, Quantum Theory Basics, Coding

• Description : Understand the basics of classical computing. Obtain an informal understanding of quantum mechanics. Rigorously understand the basics of quantum computing. Discover and understand some of the most counterintuitive features of quantum computing, like interference and entanglement, through a number of simple and fascinating applications. Understand and be able to code simple quantum computing algorithms using IBM’s Python library, Qiskit.

  We will be referring to Nielsen, M. A., & Chuang, I. (2002). Quantum computation and quantum information.

  And solving some interesting cryptographic applications alongside

• Intended Audience : Anyone with basic understanding of linear algebra and classical computing (Though these aren’t strict pre-requisites and can be covered along the project.)

• Expected Duration : 2-3 months

• Expected Weekly Commitment: 7-10 hours

19 - Introduction to Game Theory and Auctions

• Mentors: Panshul Rastogi (Panshul Rastogi#6165)

• Project Area : Game Theory & Mechanism Design

• Description : The project would be divided into 2 parts. The first half will introduce students to strategic-form games, concepts of Nash Equilibrium & Dominant Strategy Equilibrium. Further, we’ll also explore Mixed Strategy Nash Equilibrium and see related examples and its application in Economics. In the secong half, we’ll explore auctions: First price, Second Price Auctions, the underlying assumptions and the Revenue Equivalence Theorem. For independent private values, we’ll study Myerson Optimal Auction. If time permits, we’ll look at the existing literature on correlated Private values and Ronen Lookahead Auctions. The project would mostly involve reading and evaluation would be done on the basis of 2-3 assignments.

• Intended Audience : Y21 (preferable), Y20

• Expected Duration : 2 months

• Expected Weekly Commitment: 6-8 hours

20 - Introduction to Automata Theory

• Mentors: Nupur Jain (Nupur Jain#8918)

• Project Area : Theory of Computation, Logic

• Description : Automata are mathematical models of computation. We will cover the basics of automata theory, including finite automata, pushdown automata, and Turing machines, and the languages they represent. If time permits, we can also explore cellular automata, basics of complexity theory, or current literature in the field, depending on the interest of the mentees.

• Intended Audience : Y21 and Y20

• Expected Duration : 3 months

• Expected Weekly Commitment: 4-5 hours