Here's my senior mathematics students' discussion about the great selection of books they read. No more than four are allowed per book, and they can choose from (or add to) this list. This page is our in class discussion. The links on the students' names go to their reviews.
How to Bake π, Eugenia Cheng: Sarah Park, Nick Karavas, Rob Wilson, Kate Vandenberg
We all liked it, with mixed feelings about the end. Good book for everybody, especially the first half. Games and stuff to do that really increases interest, and you can apply to every class we’ve had to take. Really gave examples that made sense; like about logic, “cookies don’t obey logic.” Made me laugh out loud. She talks about baking while drunk, having her heart broken and then having mathematical thoughts about these kind of things.
Journey through Genius, by William Dunham: Lindsay Czap, Kevin Forster, Adam Keefer, Joe Young
A great read, follows history. All the guys he covered contributed. Newton could focus so hard he wouldn’t sleep for 4 days. Leibniz & Bernoulli sent him a problem they worked on for a year, but he solved in 12 hours. Everyone seemed curmodgeonly, but Euler was well rounded and produced the most. Author does a good job relating unsolved problems, too. Newton exemplified perseverance. A lot of the chapters have historical background and fairly dense proofs, but you can skim the proofs if you want. The last two chapters were Advanced Calculus, basically. But if you don’t like proofs, we might not recommend it. The historical background is accessible and useful to teachers, though.
(This is the default text when other people teach this course, for good reason. Almost always enjoyed and appreciated.)
Euler: The Master of Us All, William Dunham: Brennan Kulfan, Brandon Piotrzkowski
The title might be true. He seemed like a cool guy the Journey through Genius people said, but this book focuses on the breadth of his mathematics. Actual proofs, includes the still open questions. It was a little boring the way it was organized; every chapter was before Euler, Euler, after Euler. But I really appreciated his crazy methods, and his reliance on logarithms and infinite series.
How Not to Be Wrong, Jordan Ellenberg: Holli McAlpine, Natalie Van Dorn, Lauren Noyes, Schmitty
Mathematics can give power to our common sense. The book falls apart from there. The book tries to reach back to that, seemingly not knowing who the audience is. Overexplain simple ideas, use super-complex statistics. Big data has power, and there were cool examples. It was a good read, and parts were captivating, but it will lose you at some point. I liked it a lot more; the examples were really good. Like the connection between reading entrails and advanced statistics. It did include applications to teaching. The second half is the in depth math parts, which could get confusing. But even then you can get the big point of the chapters. There was no single thesis to tie it all together. There were a lot of statistics, and thinking about how they are misused logically. Important, but doesn’t tie together.
Love and Math, Edward Frenkel: Kali Orenstein, Brian Hurner, Khadijah Shaaf
We all enjoyed it. It’s the story of his life, and how he went from physics to math, and the connection between the two. Goes back and forth between his life and mathematics. About halfway through the book the math gets really deep; what are lie algebras? Unified theory of mathematics: number theory and curves over finite fields, etc. using symmetry. He is definitely writing for a general audience, so he simplifies everything he can. If you don’t understand, skip it, and I’ll explain it later. The problem of his Jewish last name in Russia is fascinating and troubling. Amazing to think about that going on so recently. Starts at 17, invited to Harvard at 21 even before his bachelor’s.
The Math Book, Clifford Pickover: Brooke Ramsey, Dakota Doster
Very short one page summaries, great images, great overview of all of math history. Some of them I wished went more in depth or I had time to dig in more deeply. But anyone high school and up with any interest in math or history could benefit from it.
The Number Mysteries, Marcus du Sautoy: Josie Whitsel, Katie Tizedes
Primes, shapes, uncrackable code, the future… I liked how it jumped around. Seemed random, but always fresh. What has not been answered at all is the end. A few were deep enough you might not understand. Like the rock, paper, scissors section with real life lizards that live that way or the world champion RPS player. Strongly recommend it. Primes, for example, we talk about a lot, and we know so much about it, how can we not know these basic things about them; then the David Beckham . Every chapter has something like that.
Visions of Infinity, Ian Stewart: Anthony Pecoraro, This book looks at some of the hardest problems mathematicians have faced and why solving these problems have been so important. Along with a glimpse into what the future has in store for mathematicians. Pretty dense book with a lot of abstract math. Some of the greatest math was discovered along the way to proving something else. The connections were cool. The people who were wrong section was interesting. Pretty hard book to read. Explained sigma summation, but assumes knowledge about elliptical curves.
Joy of X, Steven Strogatz: Paige Melick, Joey Montney, Abby Fatum. Guided
tour from 1 to infinity; it really does go from numbers, to algebra,
uses lots of examples. Do not have to be a math person at all. This
could convince you of why you learn math even if you don’t like it. The
notes at the back give ideas for deeper math content and proof.
Recommended for teachers, negative times negative. Not as much depth
because it was an easy read; reading stuff we already know. Original
examples. Could read some of it to a fifth grader… doesn’t really teach
you math. Mentions the topic and why it’s important.
The Calculus of Friendship, Steven Strogatz: Molly Carter
Tuesdays with Morrie, with a lot of proofs in it. My takeaway was more about the relationship than the proofs. Since the proofs were in correspondence, it was not as precise as it could be. All these years of letters were about math, not about the personal stuff, but the relationship was the important part.
The only assignment beyond the discussion is a one page-ish review and a chance to see their annotations or notes. What follows this is a book swap, supplemented with a few of mine, and I ask them to skim the second book. I love how we get references from different people's books as we progress through the history of math. Next week is Euler week, for example, so there will be lots of connections.