When I moved to across the country from Portland, OR to Asheville, NC, I didn’t bring anything but what I could fit into a single backpack.
Since then, I’ve slowly had my mom ship me things as I either need them or want them. She has a large barn, so storing my stuff for me hasn’t been a problem. But we’re finally getting down to the end of it… which is mostly books, especially math books: some of the ones I used back in graduate school.
One of the nice things about advancing in mathematics is that the books shrink down in direct proportion to how much longer it’s going to take you to understand what is in each paragraph. And, they often come in a stylish shade of yellow!
It’s nice to see you, old friends. Let’s drink some bourbon and do some math!
Here’s a list of some of my favorites from this batch of books:
- Theory of Games & Economic Behavior, by von Neumann and Morgenstern. I’m a game theorist, so obviously I have this one. This is the 60th Anniversary Edition which includes a ton of extra material. While not a good place for a beginner to start, it’s certainly one of the most great-breaking works of the 20th century, and belongs in the library of every Game Theorist. Side Note: this edition includes a review by Herbert Simon.
Real & Complex Analysis, by Walter Rudin. Rudin is both brutal and just right once you’re ready for him. This is one of his 3 great books on Analysis, the others being Principles of Mathematical Analysis and Functional Analysis.
Calculus on Manifolds, by Michael Spivak. I can’t believe how rarely this book is used in calculus classes! Once you have the basics of calculus, some linear algebra, and a bit of set theory (all of which you can get in high school, or a term or two of college), you can easily dive into this book. It is a great transition from the kind of “plug and chug* style of math you did when you were young to the deeper shit that you’ll need to grasp to move forward.
Tensor Analysis on Manifolds, by Richard Bishop and Samuel Goldberg. I can’t put my finger on it, but I’ve always loved this little bastard. Maybe it’s silly asides like this one: “Vector spaces in which a notion of limit is defined and satisfies certain additional relations (pun intended) is called a topological vector space.”
Topology, by James Munkres. This is my favorite introductory topology book. He’s also got a nice Algebraic Topology book, though once you get there, you may also want to shell out for Hatcher’s book as well, as they compliment each other well.
Advanced Linear Algebra, by Steven Roman. I fucking love linear algebra. And this book takes an approach that really resonates with me. To be sure, make sure you’ve studied “basic” linear algebra first. I’d also suggest some abstract algebra. I won’t say there’s a lot of talkin’ in this book. But it’s full of well-worked-out proofs and it quite methodical. Hell, even the “preliminaries” section is rather large, so if you’re background ain’t quite up to speed, he’s put in there what you need to know.
Algebras of Linear Transformations, by Douglas Farenick. Like Roman’s book (above), this isn’t full of paragraphs of prose. But it is full of great step-by-step proofs and problems. It also has an awesome chapter on Tensor Products of Vector Spaces.
Counter examples in Analysis, by Bernard Gelbaum and John Olmsted. This is another one of those books (along with Counter Examples in Topology) that I wish was more widely known among mathematics students. It’s often just as (if not more) important to know when a theorem does NOT work as when it does. That’s true for more than just math!
Bayesian Theory, by Jose Bernardo and Adrian Smith. I’m a mathematician. I’m not interested in doing Bayesian statistics. I’m interesting in understanding the mathematical structures underpinning Bayesian statistics. If what you want is a “cook book” for how to do some stats in the Bayesian mode, that’s awesome… but this ain’t it! This is much more “mathy”, which is exactly why I like it.
The bourbon is Old Forester, which is one of the oldest bourbons in America. I’m drinking it as I write this. It’s damned tasty.
Now go lift something heavy,