Directed Reading Program

I’m helping organize the directed reading program! This is a mentorship program that pairs undergraduates with graduate mentors for a semester long reading group. It’s a great way for undergraduate students to get a taste of some interesting forms of mathematics outside the classroom. You can find more information here about the program. I really recommend this to both graduate and undergraduate students!

If you have any questions about this, don’t hesitate to get in touch!

Here are some projects / project ideas that I am interested in:

Fall 2021

Title: The Mathematics of Machine Learning

Description: In this project, we will survey three core mathematical ideas that are the foundation of machine learning (ML): linear algebra and how it is a great way of understanding data, multivariable and vector calculus and why it is the language of optimization, and analytic geometry. We will work through the first half of the book Mathematics for Machine Learning. By the end, the aim will be for you to understand the language of ML, its moving parts, some historically important ideas, and enough mathematics to take a first course in ML. Time permitting, we will look at selected topics in the second half of the book and/or code a basic ML model that ‘learns’ a function from scratch!

Prerequisites: Students should be comfortable with linear algebra and calc 3. No coding background required - if we get to coding parts of the project, the required python can be picked up along the way.

Possible Future Ideas

  1. Title: An introduction to algebraic curves

Description: Algebraic geometry (AG) is the study of geometric objects using the language of rings and modules. In this project, we will understand the algebra of the simplest (and very rich) case - dimension 1 geometric objects or curves. In the process, you will learn about an interesting topology, affine and projective varieties, some important classification questions in AG, and enough mathematics to take a first course in AG or to do a continued reading in it. The main reference for this project will be Fulton’s Algebraic Curves, with some detours to other books.

Prerequisites: You should be familiar with some ring theory.

These are just some project ideas. If you have some ideas you would like me to mentor, send me an email with your project idea! It doesn’t need to be specific - I look forward to hearing about whatever you have in mind!

Karan Srivastava
Karan Srivastava
PhD Student, Mathematics

My research interests include algebraic geometry, number theory, and machine learning