Friday, January 20, 2017

What's Math Got Do Do With It?

Jo Boaler's What's Math Got To Do With It? is about math education. It might surprise you to know that I am interested in this subject. Then again, it might not. I think the best audience for this book is mostly people like me, who are interested in teaching, and maybe parents who want to help their kids learn math.

In other words, What's Math Got To Do With It? is exactly what it says on the cover: it's a book about how teachers and parents can transform mathematics learning and inspire success. It mostly focuses on math teaching in the U.S. and the U.K. and it presents actual research studies on what works and what doesn't. It is well-written and clear, and gives strategies with concrete examples.

In conclusion, if you are a how teacher or parent who wants to transform mathematics learning and inspire success, then you should read What's Math Got To Do With It?.

Sunday, January 08, 2017

Prime Obsession

Prime Obsession is written by John Derbyshire, who also wrote Unknown Quantity. Like Unknown Quantity, it is a book about the history of math. Specifically, it's about the Riemann Hypothesis, how it came to be, and what it actually means.

The Riemann Hypothesis is the greatest unsolved problem in mathematics, at least according to the subtitle. It makes a statement about a function (which is described in the book) that has a deep connection with the prime numbers (which is also explained in the book). If you're the kind of person who reads math books, then you've likely already heard of the Riemann Hypothesis. It's one of the six remaining unsolved Millennium Prize puzzles, so proving it to be true or false will make you a million dollars richer.

Prime Obsession is divided into two parts. The odd-numbered chapters are math-heavy, and the even-numbered chapters focus more on history. This is done so that a reader who's just into math can only read the odds, and a reader who's just into history can only read the evens. I don't really like this split; I preferred the structure in Unknown Quantity, where both areas were present throughout the entire book. The split between the chapters removes the interesting math from the interesting stories of the mathematicians. As a more math-leaning person, I found the even chapters a bit slow. Because the people and their stories were not connected with their ideas, a lot of the people become forgettable to me.

All in all, though, I did like the book. Derbyshire explains everything clearly and takes time to ensure that the reader understands what's going on. This is the first source I've found which explains the zeta function's connection to the primes in a way that's clear and satisfying (although it does take a while to get there). I also like that, when Derbyshire does skip a few steps in the math, he takes a moment to explain that and why he is doing so. If you're curious about what this whole "Riemann zeta" business is about, then Prime Obsession is the book to read.

P.S.: You should also watch this video by 3Blue1Brown, which is about visualizing the zeta function. You can consider it a supplement to chapter 13, or you can just watch it because it's pretty.

Thursday, January 05, 2017

Elliptic Tales

You will probably not enjoy Elliptic Tales, by Avner Ash and Robert Gross. I enjoyed it a lot, but I suspect I’m in the minority on that. You see, Elliptic Tales is by far the most math-intense math book I’ve read. In my opinion, this is a good thing. However, the whole thing might be a bit… daunting to someone who is not actually into math.

Let me back up a bit. What is Elliptic Tales about? Well, Elliptic Tales is a book which will explain to you what exactly the Conjecture of Birch and Swinnerton-Dyer (or BSD Conjecture for short) is. This might be of interest because the BSD Conjecture is one of the six remaining unsolved Millennium Prize puzzles, meaning there is a reward of one million dollars for whoever proves it. To me it's of interest because I'm a nerd, and I want to know what kinda stuff is being worked on in math right now.

The thing is that the BSD Conjecture involves a lot of preparation, and although Ash and Gross do a wonderful job at explaining things, there are some patches in which everything is confusing for a bit. My advice for these parts is to just read on for a bit. Sometimes, Ash and Gross mention concepts that they don't actually introduce until the next paragraph, or even later than that. Trust me when I say that it mostly makes sense in the end. Also, use the glossary. It helps.

I think my favorite parts of Elliptic Tales are the ones in which they are teaching about something else. This is the first source I've found which explains projective geometry well, and some of the earlier stuff with generating series is cool enough to create a formula out of. They say you can skip Part 1, which deals with the degree of a polynomial, but I had a lot of fun reading it. Also, they reference that part later in the book, so if you haven't read it you feel a bit cheated and left out. How do I know how this feels, given that I did read Part 1? Because they also reference their previous book, Fearless Symmetry, and that's how it makes me feel.

So, I really enjoyed the book, because it taught me a lot. However, I realize that this isn't that big a selling point for most people. If you don't really like math, then stay away from Elliptic Tales, and instead read Things to Make and Do in the Fourth Dimension. If you do really like math, and are excited about learning math, then read Fearless Symmetry, so that you can later fully enjoy Elliptic Tales. And never, under any circumstances, read Bridges to Infinity. I think that about covers everything. Until next time!

Tuesday, January 03, 2017

Romeo and/or Juliet

Romeo and/or Juliet is a choose-your-own-adventure book by Ryan North. It has not only one, but several plots, as is typical of a choose-your-own-adventure book. Because of this, I can't really do a plot-focused review, and so I have been putting this off for like two months, because I don't really know what to say.

Romeo and/or Juliet is funny. It makes fun of the original Shakespeare work, pointing out the silly parts of the story and usually replacing them with even sillier ones. The narrator is more of a character than most of the characters, and likes to make anachronistic remarks. When reading, I pictured the narrator as a flying red fairy. You can also do this, if you want.

Well, that's all I've got. Next time, remind me to review a book with a stationary topic. If you like dumb laughs and/or Shakespeare, then you should read this book. Or, I guess I mean you should play it. Interact with it. Read sections of it, and then at the end of those sections make a decision between the offered choices and turn to the appropriate section, and then repeat this process until you get an ending.

See, this is why I had trouble.