Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159) Book

Mathmatics and the Unexpected takes a look at three changes in mathmatics and how these affected how people thought about what could be solved through mathmatics. More a cultural study than a math text book, the examples used show the evolution of mathmatic in application. It is written for someone who has a strong grasp on college level mathmatics (calculus and statistics), but is written for easy consumption, not rigorous proofs.

I really liked this book. As I'm behind on my book goal for the year, I thought a short but intense book might be warrented for once, and this one was really quite facinating. I'll be the first to admit I have a good gradp on the mechanics of math, but I fail to understand the possibilities of thier application, so a book dedicated to following the application of these processes I've been studying was really eye opening. With the added element of historical context, it probided a well rounded evolution of certain ideas and how those ideas affected thier societies.

My favorite chaper is probably the first one (calculous and determinism), though the ideas in the second are really interesting(chaos theory and probability). I'm not sure I followed the third chapter particularly well, as catastrophe theory seems too open ended to really mean anything. It's a near idea, but I don't think I understand how it's supposed to be used, beyond a new way to take notes on a phenomenon.

I though short, it is dense with ideas, as it tries to explain the questions past mathmatians faced and the experiments they used to try to solve them. I recommend this to anyone interested in mathmatics, or someone who wants to know the limitations of these tools they learned about in college.