Carrying on the tradition of the past three years of exemplary work by students who were doing the job of a teaching assistant in the mornings and voracious learners in the afternoon, we had them work with some of the faculty who were visiting Ashoka University during the Lodha Genius - Ashoka University Programme, and this year as well, we had some amazing apprenticeship reports coming out as the outcome of their work.
Many of these projects were inspired by the Apprenticeship Lectures offered throughout the programme-deep, week-long mini-courses on topics such as Modular forms, L-Functions, Generative AI, Complex Analysis, Non-Archimedian Geometry, Cryptography to name a few.
The resulting articles reflect the curiosity, creativity, and initiative of the students, as well as the generosity and mentorship of faculty. These works are intended for an undergraduate audience, and aim to balance motivation, intuition, and mathematical depth.
We hope this collection serves both as a record of the students’ efforts and as an invitation to explore beautiful ideas in mathematics.
Introduction to Bivariable and Multivariable Functions, Aadvik Sameer Jadhav (RUIA College, Mumbai University) under the supervision of Ashish Kumar Pandey
From Random Paths to Deterministic Equations: Brownian Motion, SDEs, and PDEs, Abhinav Baskar (Ashoka University) under the supervision of Sarvesh Iyer
Modes of Cryptography, Ajith kumar Uppala (IIT Delhi) under the supervision of Sourav Mukhopadhyay
A Study of Elementary Methods in Number Theory, Akshat Bhaskar (Harvard University) under the supervision of Shanta Laishram
Surveying the Use of Calibration across Modelling in Medicinal Science and Weather, Ambar Singh Juneja (Ashoka University) under the supervision of Sarvesh Iyer
Two Erdős Problems: A Dual Approach, Anaya Vikrama Singh (Chennai Mathematical Institute) under the supervision of Sneha Chaubey
Theorems of Dedekind and Dirichlet in Algebraic Number Theory, Aniruddha Mishra (IISER Mohali) under the supervision of Shanta Laishram
Graph Search: From Depth-First Search to the N-Queens Problem, Chinmay Barje (Ahemdabad University) under the supervision of Surbhi Rai
Precision and Error Propagation in Matrix Computations, Deepika Gupta (IIT Delhi) under the supervision of Sagar Shrivastava
Solving Degree-Six Equations by Origami, Dharminder Singh (IIT Delhi) under the supervision of Sagar Shrivastava
The Introduction To Probability And Its Applications, Diksha Matta (Delhi University) under the supervision of Kumarjeet Saha
Alternating Sign Matrices and Magog Matrices, Gunamay Dawar (University of Waterloo) under the supervision of Manjil P. Saikia
Fold-and-Cut Theorem, Havisha Chokshi (Ahemdabad University) under the supervision of Sagar Shrivastava
Analysis of Numerical Algorithm, Jaya Patel (IIT Delhi) under the supervision of Sagar Shrivastava
Drifting Fields and One-Step Generative Modelling, Naityik Singh (IISER Pune) under the supervision of Sarvesh Iyer
Privacy-Preserving Federated Learning, Neha Palak (Ashoka University) under the supervision of Sourav Mukhopadhyay
Well Distributed Sequences, Om Chaudhari (Chennai Mathematical Institute) under the supervision of Sneha Chaubey
Uniform Distribution of Zeros of Dirichlet Series, Piyush Kumar Jha (Chennai Mathematical Institute) under the supervision of Sneha Chaubey
Design, Implementation, and Cryptanalytic Study of a Toy Blockchain System, with a Survey of Quantum Computing Threats to Bitcoin, Prem Kumar Yadav (Ashoka University) under the supervision of Sourav Mukhopadhyay
Geometry versus Origami, Pulak Jain (Ahemdabad University) under the supervision of Sagar Shrivastava
Markov Chains, Rohan Roy (Chennai Mathematical Institute) under the supervision of Kumarjit Saha
Algorithm For Finding Cut Vertices Using Tree Search Algorithm, Sivendu Gyaneshwar (IIT Delhi) under the supervision of Surbhi Rai
Fairness in Sponsored Search Auctions, Smritee Thapa (Ashoka University) under the supervision of Sarvesh Iyer
Deep Learning and Portfolio Optimization, Tanav Gupta (Lodha Genius Programme, Ashoka University) under the supervision of Sarvesh Iyer
Algebraic Number Theory: A proof of Dirichlet’s unit theorem, Moirangthem Titan (Chennai Mathematical Institute) under the supervision of Shanta Laishram
Here is the link to the Archives of Math Apprenticeship Programme of the past years.