Mathematics 2024 Reading List

My list:

1. "Algebra" by Serge Lang

Algebra is a classic text for graduate treatment of topics in advanced algebra. In particular I will be using this book for further study on homological algebra.

2. "Partial Differential Equations" by Evans

In all likelihood I will be starting a PhD in analysis at King's this year, and hence since most of the analysts in the research group have some interaction with PDEs I would like to make sure my basic knowledge on the topic is up to scratch.

3. "Algebraic Topology" by Hatcher

Algebraic topology is something I studied last year through the lens of knot theory and associated Siefert surfaces. I would like to learn more about homotopy this year and so I will follow the treatment of it in Hatcher's book.

4. "Algebraic Geometry" by Hartshorne

I have an algebraic geometry course this year which will focus on the classical theory of the subject, however I would like to learn more about the modern treatment using schemes and sheaves, hence Hartshorne is a good choice (albeit a difficult text).

5. "Techniques of Modern Analysis" by Folland

Following on from the fact that my PhD topic will likely at least include analysis, I will continue to read through Folland's book in order to best prepare for my research.

6. "Counterexamples in Analysis" by Gelbaum and Olmsted

This small book has a lot of interesting gems of wisdom that show that real analysis is often more about the exceptions to the rule than the rule itself.