Directed Reading Program
I think most people that pursue a degree in mathematics enjoy the subject and talking about it with any captive audience they can find.
One of my favorite things to do at K-State has been one-on-one reading projects through the KSU Directed Reading Program. During my tenure as the DRP Committee chair, we revamped both Undergraduate recruitment and the recruiting of graduate student mentors. In Spring 2025 we had the largest participation and end-of-semester DRP conference in the history of the program.
If you're thinking of starting a Directed Reading Program in your department, the KSU DRP page has lots of helpful resources.
Some DRP reading projects I've done with undergraduates and my thoughts.
Mathematics of Quantum Physics
We used Kreyszig’s Introductory Functional Analysis with Applications.
In retrospect this was a lot to push an undergraduate through without a stronger analysis background. Something with more background on metric spaces (with function space examples) would be better if I do this again.
Groups, Symmetry and (Hopefully) Physics
We used Pinter's A Book of Abstract Algebra
It is a great little book and it's not too expensive a purchase for the undergrad that wants to buy it for themselves. That said, the presentation isn't the best if the student is more interested in physics or engineering and this student was a physics undergraduate.
KSU Integration and Differentiation Bee
The Kansas State Math club hosts an Integration and Differentiation Bee every year and I've moonlit as a proctor and exam grader several times.
I mention this here for K-state grad students who are interested in participating in the Directed Reading Program but don't know any interested undergraduates. Many of the undergraduates that participate in the Integration and Differentiation Bee go on to declare math minors, participate in the DRP and take additional math classes. It's also a ton of fun and there's usually pizza.