Adventures in Mathematical Reasoning

Sherman Stein's Adventures in Mathematical Reasoning (which also goes by the title How the Other Half Thinks) is a book which can teach you how a mathematician thinks. I'm not claim that it will teach you, just that it can teach you, if you remain open-minded. For that reason, I think it might me one of the most directly useful math book's I've read.

Adventures in Mathematical Reasoning includes eight chapters, each of which pose a different question at the beginning. All of the chapters involves strings of letters of some sort, although I didn't actually notice until I was almost done with the book. The chapters cover a wide range of topics, from statistics to combinatorics (which is like mixing things up). All of the topics are interesting examples of mathematical ideas, made relatively simple.

The great strength in the book is its ability to show hoe mathematical reasoning works, when actually creating new mathematical theorems. The tricks which Stein uses in these chapters—abstraction, generalization, simplification, or just plain getting data manually—are tricks which can be used in math much more advanced than this. And just about any branch of math would be more advanced. Stein chose topics which can be understood with nothing more than arithmetic, basic geometry (like, "what is pi?" basic), and an open mind.

If you've ever seen a mathematical theorem or idea and thought, "how could they possibly have thought of that?" then you might want to read this book. As long as you take your time to understand everything, and keep trying to guess where things are headed, you should finish the book with a better understanding of how all the work is done. If this sounds good to you, give Adventures in Mathematical Reasoning a read.

P.S.: He usually goes about a similar strategy as is shown in this Numberphile video, so check that out if you want to see an example.

The Rest Of Us Just Live Here

The Rest Of Us Just Live Here is about the life of a boy named Mikey during his last few weeks of high school. He hangs out with his sister Mel, his best friend Jared, and his not-girlfriend Henna. He's just trying to live his normal life and come to terms with leaving his friends and family to go to college. And, hopefully, finally ask Henna out on a date.

Then, there's also that whole teen adventure thing going on. Something to do with blue light and immortals and whatnot. But, that's not Mikey's problem. The indie kids can deal with that, like they always have, and eventually one of them will become the chosen one or whatever and save the world. Mikey and his friends? Background characters. Nothing they can do. As long as the indie kids can keep their problems to themselves, Mikey's got bigger things to worry about (like that new kid Nathan? What's his deal??).

I love everything about this book. First of all, I love the premise of it being a story about the background characters in a teen adventure novel. It's amazing how well Patrick Ness gets that theme across without making it seem like a gimmick. Somehow, he makes the presence of the "indie kids" (protagonists) seem like "a fact of life" but not "'just a fact of life." I also love all of the characters, and how relatable they are, and just how alive they feel. Every single one of them. Well, except the immortals, but they don't entirely count. I love the ending so much that I won't say anything more about it. It's just so great.

If you like good books which might make you cry, then read this book. I really can't recommend it enough. This is my new favorite book, and I love it so much that I can't really explain why I love it this much. I have so much to say that I don't want to say anything. Please read it, as a favor to me.

Fluke

Fluke is by Joseph Mazur and it's boring. It starts off with an introduction musing about coincidences. Then, it tells ten disjointed stories about coincidences, which can't really have any impact because they are so short and unrelated, so that's boring. Then, he talks about math, and how everything happens eventually, the world is big, yadda yadda yadda. He hints at some cool concepts, and doesn't really go much in depth into them, and it's boring.

Then, he uses this mathematics of probability to give probabilities for the ten stories you read in the beginning. By this time, you've mostly forgotten the stories, but it doesn't matter because he just picks random numbers for the probabilities. And sometimes, he doesn't even do the math right! Like, analyzing the fourth story, he says a probability would be, "1/30 x 1/30 ≈ 0.001, or odds of 998 to 1." Yes, 1/30 x 1/30 = 1/900, which is about 0.001, but that makes the odds 899 to 1. HE FAILS TO FOLLOW THE RULES HE LITERALLY TELLS YOU ABOUT. So, in summary, that section is trash. Then, he has a few essays on probability, risk, and chance which are interesting. That is the only decent part of the book.

In conclusion, read Fluke only if you are very bored.

Proofiness

You, there! Have you ever seen a statistic used in the media? If so, then you have likely been the victim of proofiness. Proofiness is defined by mister Charles Seife as "the art of using bogus mathematical arguments to prove something that you know in your heart is true - even when it's not." Want to be free of this madness? Then I have just the thing for you! This book, Proofiness, is essentially a field guide to spotting said proofiness, and then to seeing through it.

The first two chapters are an introduction to the rest of the book, listing different types of proofiness and making silly words for them. If you'd like, you can see the silly words in my glossary. Chapters three through eight are then about examples of people using proofiness, mostly in the United States of America. Seife covers proofiness polls, elections, courts, and more.

Proofiness is a gripping book which will keep you interested through the whole ride. I mean, sometimes I chose to read this book instead of The Hike. That should tell you something about how compelling it is.

Seife is doing important work here, trying to help people make decisions which are not based on false numbers or bad arguments. He never gets very technical, and keeps it simple enough that anyone at all should be able to read it. If you feel that you should not be lied to, then you should read this book.

P.S. I got a lot of books in New York and I think I'm gonna review them all in order. Here's a sneak preview of the reviews to come!

Well, except for the ACT prep book. That's just sitting there.

The Hike

The Hike, by Drew Magary, is about a man who gets well and truly lost. The man in question is Ben, a thirty-eight year old with a wife and three kids and a house and an important business meeting to get to. Before he goes to the meeting, he decides to take a walk. The walk turn into a hike. The hike turns into a mad sprint for his life. Then he gets lost.

The hotel is gone, as is the road, and all traces of human civilization. The only thing left is a path, and, seeing no other options, Ben follows this path, in the hopes that it will take him somewhere eventually. Then, strange things start to happen, and they keep getting stranger. Only one thing is clear: If Ben goes off the path, then he will die. As long as he stays on the path, he - well, the point is he should stay on the path.

The Hike is a beautifully written page-turner with memorable characters and one of the best endings I've ever seen. Honestly, I think The Hike is my favorite book now. It's hard to find words to express this fully. There's just nothing about it that I don't like. It has a great little mystery and a few twists which not only genuinely caught me by surprise but also made me completely change the way I framed the whole thing. I love it so much.

If you like good books, then you should read this book.

T. rex and the Crater of Doom

T. rex and the Crater of Doom is a book about science unlike any other I've read. Instead of trying to inform the reader about our current understanding of things, it tells the story about how we got there. In other words, it's not just about science, it's about how science is done. Specifically, it tells the story of how puny humans with short lives were able to figure out that all the dinosaurs were murdered by a massive space rock.

This story is told by Walter Alvarez, one of the geologists who first tried to investigate the strange layer at the K-T boundary, which lies right above where the dinosaurs disappear. Walter noticed that there was something odd about the boundary, and decided he would try to get to the bottom of it. As a result, he finds evidence which might go disprove one of the most basic ideas in geology at the time: the idea that all geologic changes happen gradually.

Although the story is gripping, the real reason I love this book is that it explains how science is actually done, not in the abstract, but with an actual real-world example. Anyone who has ever been doubtful of the claims that geologists or paleontologists make about the past needs to read this book. Anyone who thinks that these areas of science are somehow "lesser" than physics or [insert your favorite field here] needs to read this book. And, of course, anyone wondering how we could have possibly found out about this catastrophic event needs to read this book. T. rex and the Crater of Doom is an experience that everyone should have.

Beware The Wild

Natalie C. Parker's Beware the Wild is about a girl named Sterling, who lives in the small town of Sticks, Louisiana. Everything is pretty great in Sticks, so long as you never, under any circumstances, cross the fence and go into the swamp. When the book opens, Sterling is steadily watching the fence for any signs of her only sibling, Phin, who has of course run into the swamp.

Fortunately, her sister, Lenora May, reemerges from the swamp, just in time for her mother to call them in to dinner. There is no problem with this situation and everything is fine. Except for the small detail that Sterling doesn't have a sister. Or, well, she didn't. Everyone in town has excepted Lenora May as if she was always there, and nobody can remember Phin. In fact, Sterling herself distinctly remembers having Lenora May as a sister throughout her whole life.

Now, Sterling has to figure out what's happening, get her brother back, and send Lenora May back where she belongs. Or does she? First, she must play the age-old game of figure-out-who-you-can-trust-or-die. Saying any more about the plot would kinda spoil the fun of the game, so let's just leave it at that.

Beware the Wild is apparently Natalie's first book, and I have to say she's off to a really good start. The way she portrays the insidious replacement of memories is better than any other I've ever seen. I do think that the first half of the book, the aforementioned game of figuring things out, is better than the second half, or the game of ACTION. That's not to say that Beware the Wild ends badly, far from it, it's just that the first parts were so strong that the exciting, high-stakes climax seems just mediocre in comparison.

In conclusion, Beware the Wild is fun and exciting and a good way to spend a weekend. When you pick it up, you will find it difficult to put down. If you like fantasy in a modern setting with a pinch of the surreal, Beware the Wild is the book for you. Well, it's a book for you. You can also read other books. What I'm saying is you'll like it and you should read it.

Witch & Wizard

Witch and Wizard, by James Patterson and a second author in smaller print, is about a witch and a wizard. Their names are Wisteria and Whitford Allgood, but they usually go by Wisty and Whit. Yes, they are really the All-good family.

Unfortunately for them, "the country" has elected some fellows called the New Order into power, and in "a few months" the New Order has completely destroyed "the old government" and instituted a council to rule over the new authoritarian state and also they've convinced everyone that not only does magic exist but also that it's evil and that it's okay to do terrible things to children and also the Allgoods are the last nice parents on Earth and everyone else is just sorta fine with it except for kids so the New Order just kills children by the hundreds and did I mention EVERYONE IS FINE WITH IT and also there are apparently no countries other than "the country" because everyone is either in the New Order or in the resistance as clearly marked in the map and also the world is flat I guess and there are no oceans but there's also four other levels of reality because why not?

So, yeah, it's set in an alternate reality where that somehow makes sense.

Anyways, Wisty and Whit have somehow missed the fact that the GOVERNMENT IS GONE AND EVERYONE IS EVIL sorry I need a little time to adjust to this premise.

[time passes]

So, Wisty and Whit were not informed about the new government, nor about the existence of magic, nor about the fact that magic is illegal and morally reprehensible. They are then completely surprised when they are arrested by the New Order for the charge of being a witch and a wizard, respectively. They are even more surprised when they start developing magical powers, such as seeing ghosts and being on fire. Slightly less surprising is that they are sentenced to death. Now, Wisty and Whit have to use their magic to escape the torture-prison and find their parents.

The review so far has been a bit ranty, so I feel like I should clarify: I really liked Witch & Wizard. It is fun, and easy to read, and it moves at an incredibly fast pace. The good characters are all likable, and the evil characters are all cartoonishly evil. I'm also okay with the ridiculous setting, because it just emphasizes the whole silly good-vs-bad fun of the story.

So, read this book if you like fast-paced action and fun. Try to ignore my little rant. Honestly, I just made it for fun.

World War Z

The year is like 2026-ish. The world is slowly being rebuilt from the devastating 10-year zombie apocalypse. Max Brooks, of the United Nations Postwar Commission Report, has spent the last few years flying around the world and gathering stories from the survivors. Now, some of their stories have been compiled into World War Z, an oral history of the zombie war.

This is one of my favorite books. It is, as I said, a collection of stories, all in the form of interviews, which together tell the overall story of humanity and it's struggle to overcome this deadly force. It was apparently inspired by a real history book, The Good War, which was told in the same format. I am quickly running out of things to say.

So, I've just read a bunch of other reviews, because I have no ideas of my own. It seems like most of the complaints stem from the strange format, because you cannot connect to the characters and watch their story arcs, because the interview are so short. I can see what they're talking about, but that's not really a problem for me, because I tend to empathize with any character who isn't completely terrible, and most of these characters are likable.

I actually think this format works well, because it emphasizes that the zombie war (and other wars) can't be seen as simply actions of "the masses," and that everyone needs to work together to defeat the zombies. This theme is slightly undercut by the U.S.-centrism which creeps it way into some parts of the book, but it still works overall.

What I like most about World War Z is the fact that Brooks makes so many different kinds of stories. There are quite a few about guilty military personnel, and about how everyone was doing things wrong, but for the most part it was full of diversity. There are some stories about survival, people going insane, a nuclear exchange, the formation of a religious state, plans that pulled humanity back from the brink, people giving their lives to try to cleanse areas from zombies, and gung-ho military operations.

So, If you think you will like it, give it a shot. If not, well, maybe this book is not for you. At least read a few chapters. Oh, and if you liked The Zombie Survival Guide (which uses the same zombies), then you will probably love World War Z, because it is a collection of the kinds of stories you made up while you read the survival guide. That's all I've got.

The Rosie Project

The Rosie Project has a million covers, and it was reccommended to me profusely by my mom. It is supposedly a romance between Don, a professor with a rigid schedule and no social skills, and Rosie, a woman on a quest to find the identity of her biological father. It was okay.

I feel like I just didn't "get" the book. The central romance never really resonated with me, and for almost the entire thing I really wanted Don and Rosie to not get together. Apparently there were subtle hints the entire time that they were perfect for each other, but I just didn't notice. Also, my mom says the book was hilarious (as well as the reviewers on the cover, which is not surprising) but I didn't even laugh once. I also didn't cry once. Maybe it ate my feelings.

So, now I'm in the interesting situation that I didn't like the book, but I'm pretty sure that I'm wrong. I suppose, if someone else reccommends this book to you, you should listen to them. I won't stop you from reading it.

Also, it was written by Graeme Simsion. I couldn't figure out how to integrate that into the review.

The Joy of X

At this point, I think it's just easier to compare Steven Strogatz's The Joy of X to similar math books I've read. Then again, some people might not have read the other reviews. Okay, here's the deal: if you're looking into The Joy of X, then chances are you will also want to consider two other books: Things to Make and Do in the Fourth Dimension and The Magic of Math.

All three books present themselves to a public with not much math background, but they go about it in different ways. One of the most obvious differences is that The Joy of X (which I'll call Joy from now on) is split into a whole bunch of little chapters of about eight pages. These go through the general topics of arithmetic, algebra, geometry, calculus, statistics, and some other newer ideas in mathematics, in that order.

It is also full of personal anecdotes, which makes the reading more memorable. Things to Make and Do in the Fourth Dimension (which I'll call 4D) had a few anecdotes, and a lot of little activities for you to do yourself, which made it very fun to read. The Magic of Math (Magic) did not have many anecdotes or activities. But, it did have proofs, which 4D lacked and Joy only did a few of.

Of the three books, 4D gives the best impression of an actual tour, guiding the reader through whole areas of mathematics and stopping to marvel at each one. In comparison, Magic seems a bit laid back, with only 12 chapters (4D has 21), but you can really take your time to understand the subjects you're given. As I said before, Joy has short chapters. It is therefore more fast-paced, a whirlwind of "Look at that! Isn't that cool? Now, on to the next thing!"

Personally, I think 4D is the best of the three, with Magic as the second and Joy bringing up the rear. This is not to say that Joy is bad. If you like the style of bite-sized tidbits of math, it will probably be your favorite. You can come to your own conclusion, and pick which book (or books) you want to read.

The Magic of Math

The Magic of Math, by Arthur Benjamin, has so many puns. I feel like I should start with that. Some puns, are bad, and some are worse, but they all are puns. Also it's about, like, math, I guess.

This book, I think, is definitely aimed at more of an everyday audience than other math books I've covered (except, of course, for this one, which you should all read). I think that, as long as you have a decent grasp on basic algebra, you will breeze through the book, especially if you skip the asides which are scattered throughout.

The Magic of Math spends a lot more time on proofs than all the other math books I've read, and I think that works to its benefit. Sometimes the other books state things and expect you to just take them as facts, which works for them, because they are just kinda taking you on a sightseeing tour of different areas of mathematics. However, I like the way Arthur Benjamin proves everything in the book (sometimes in asides), because it means you can take the time to understand what he is saying. This is especially effective because The Magic of Math is a book (how insightful of me!), so you can take your time re-reading things and it won't go anywhere.

In conclusion, if you are slightly interested in reading a book about math, read either The Magic of Math or Things to Make and Do in the Fourth Dimension. The first one is more focused and requires more work on the reader's part (at least if you want to understand everything), while the second is a fun tour on mathematical discoveries and concepts. Choose wisely. Or, you know, just read both.

The Extraordinary Secrets of April, May, & June

I liked The Extraordinary Secrets of April, May, & June, and my friends make fun of me for it. Yes, it is about girls, and yes, it has elements of romance, and yes, it is very cheesy, but it was fun to read and had an interesting story.

April, May, and June are three sisters, named in chronological order (April is the oldest and June is the youngest). They have just moved to the town of Somewhere Probably because their parents got divorced. Now, they are living with their mom, and about to start school. Already, this has a lot of stuff going for it, but it gets better: on the first day of school, the three sisters get superpowers.

I know, right? So, April gets the power to catch glimpses of the future, May gets the power to turn invisible, and June gets the power to read minds. Now, in a new town, at a new school, and with crazy secret powers, the three girls have to learn to live with their new lives.

The Extraordinary Secrets of April, May, & June was a fun book to read. I was on board with the characters the whole time, and I wanted to see them triumph, and it feels good to share their struggles. If you like fun, cheesy books which are full of heart, then read this book. No matter what your friends say.

Killer of Enemies

Killer of Enemies is kind of a terrible book and it's great. I initially started reading it because of its ridiculous title, and it lived up to its cover. This is not to say that is was a bad book; I had fun reading it and the world of the story is pretty cool, so I don't feel like I wasted my time or anything. So, what is it about?

Have you ever thought to yourself, "I wonder what it would be like to read about someone playing Monster Hunter or Shadow of the Colossus or a similar game with giant monsters"? Have you ever then immediately thought, "no, wait, that wouldn't be nearly as interesting, I'll just play them myself and that will be more fun"? Well, Joseph Bruchac did not have the second thought, and so Killer of Enemies was born.

The book involves our protagonist, Lozen, who is the best at everything, killing huge genetically modified monsters. This is a post-apocalyptic future, set after the rigidly-divided classist technofuture from so many books. An entity known only as the Cloud has come and turned off all of the electronic devices and engines, but not gunpowder, and also rocket launchers and automatic weapons still work. The rules seem to be kinda fuzzy.

Anyways, all the super rich leaders had electronic implants or nanobots and so they died when the Cloud came. Some survivors who didn't have many implants formed a rigid society with aristocrats as evil dictators. One such society is holding Lozen's parents hostage to make her kill things. She then kills things. Usually huge things. There's more story, but not much.

Killer of Enemies is not high-brow hmmyes fiction, and it doesn't try to be. It really reads like a fanfiction of Shadow of the Colossus, because it mostly involves Lozen outsmarting and then wrecking giants. There is a simple story, which is nice, but it's not the focus. If you like big dumb action, and I certainly do, then you should read Killer of Enemies.

Oh and also there's magic. And zombies. Just thought you should know.

Harry Potter and the Methods of Rationality

I ragged on Harry Potter and the Methods of Rationality (sometimes awkwardly abbreviated to HPMOR) quite a bit on my other blog. A lot of my points still stand. The characters start out unlikable, at least to me, to the point where I actually quit reading. Eventually, though... well, here I am, done with the book.

So, what is HPMOR? It is a fan-fiction of Harry Potter composed by Eliezer Yudkowski, He Who Is Not Recognized By Spell-Check. It takes place in an alternate-universe type deal in which Harry was raised by scientists and is a boy genius armed with the powers of Rationality. If that makes you really want to read it, then I doubt I could stop you even if I tried. If not, then... eh. It's cool.

That's it. This post is essentially just to say that I've read HPMOR. To reiterate: your first impression is probably indicative of how much you will like this book. I wouldn't recommend it if you don't buy into the premise. Laters!

Masterminds: Criminal Destiny

This is the second Masterminds book. If you want to know what I think about it, read my review of the original, because all of the same things apply. I'm not going to write a new review for this one, because there is a chance some of you will not have read the original Masterminds, and you should read it with no spoilers. That said, this book is amazing, so I'm just gonna gush for a while.

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Thank you. For reference, I started this book at like 11:00 AM today, and read until it was over. It's super good. As a great man once said, "if you like books about people doing things, you will probably love this book." Couldn't have said it better myself. I mean, I guess there should be a "then" in the second clause. But the point still stands.

READ IT!

Unknown Quantity

Do you like math? No? Chances are, I've already scared you off. For those of you who are still here, I've got a treat for you: John Derbyshire's Unknown Quantity. It's a history book, but about algebra.

Well, there go the rest of you. Now nobody is reading this. Ah, well. I thought it was a good book. It's funny, and informative, and did a swell job of keeping me interested throughout the entire thing. There's not that much else to say about it, because it's literally what it says on the cover. It's a history of algebra.

Well, I suppose it would be a good idea to explain what Derbyshire means by "algebra." Algebra isn't just using symbols like X and Y to stand for variables. At it's heart, algebra is using abstraction to make things easier. As you can imagine, this broad definition encompasses a lot. That's what makes it cool, because you can see the logical progression of ideas over hundreds of years into what algebra is today.

I'd say this is more on the math side than the history side, although it's got a lot of both. You spend quite some time learning about the characters behind the equations and ideas, which I like. Basically, if you are interested in the history of math, or in learning how the dingus people ever came up with this crazy math stuff, then this book is for you.

Soon I Will Be Invincible

While reading Soon I Will Be Invincible, by Austin Grossman, I get the feeling that I would enjoy it more if I was into that whole comic book superhero type culture. It feels like the book may be full of tropey-type jokes that I just don't get. This means I don't entirely trust my own opinion, here.

Of course, that's not about to stop me. Soon I Will Be Invincible has a great title and two protagonists. Well, two main characters. The first is Doctor Impossible, the Smartest Man Alive, who aims to bust out of prison and take over the world. The second is Fatale (pronounced fuh-toll) the cyborg with a dark past that isn't really there.

Fatale has just been admitted into the Champions, a league of superheroes investigating the disappearance of Superman Legacy The Tick Core-Fire, a charismatic invulnerable flying tank with more abilities than anyone could ever need. Meanwhile, Doctor Impossible has escaped, and is already scheming to take over the world.

I don't really have much to say about this. It has almost nothing in the way of character growth, for anyone other than Fatale. It is riddled with either poorly-executed foreshadowing or terribly-executed exposition. Honestly, those are the only two problems for me, but they seem like big ones. I really think it might just be because I'm not used to books like this.

Blugh. I don't like writing reviews that aren't positive (I've only got one truly negative review). It leaves a bad taste in my mouth. You know what? Don't listen to me. Give Soon I Will Be Invincible a try. It was fun. I read it in a few days, so that's good for something (like, it grabbed my attention or whatever). And, in the end, it does have a pretty sweet title.