Wednesday, September 8, 2010

Books and Math: Part 3 & 4

Part 3: For Adults and Older Kids

If you'd like to expand your own understanding of mathematical concepts (in a way that feels different from your experiences in high school math), here are some books you may enjoy looking through. These books are also great for helping older kids see what math can look like beyond a text book.

Here are the highly recommended offerings I've found on other's blogs or on resource lists or through my own explorations.

The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover.

I love this book. It's a beautiful book, lots of graphics, that is a timeline of mathematical history. Each page has a date, a mathematical "milestone", the name of the person who was involved and a brief blurb about both. It's a wonderful book for flipping through or looking things up.

The brilliant Pickover has written other mathematics-based books that we also have on our shelves for future reference, such as Calculus and Pizza: A Cookbook for the Hungry Mind and The Mathematics of Oz. I assert that every home library should have at least one Pickover book on the shelves. The Math Book is a good place to start.

The Joy of Mathematics: Discovering Mathematics All Around You by Theoni Pappas

I've raved about Theoni Pappas in my previous post about math-related books. I've had this particular book for a very long time. This book contains a wonderful assortment of mathematical ideas that will open your mind to the math that surrounds us all the time and you might even get a bit excited about it!

If you find that just the one book won't do it, she's also written a sequel titled More Joy of Mathematics: Exploring Mathematics All Around You.

A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science by Michael S. Schneider.

This book opens with a quote from Albert Einstein "The most incomprehensible thing about the universe is that it is comprehensible." The author goes on to say that "the universe may be a mystery, but it's not a secret." This books informs us about the universe through the mathematical principles found all around us in the natural world. It's a wonderful book full of extremely cool things.

Mathematics from the Birth of Numbers by Jan Gullberg.

"The unstated premise in this book -- a premise that virtually all mathematicians would agree to -- is that mathematics, like music, is worth doing for its own sake." The book is truly a survey course in mathematics and you can read it as an armchair book or you can pour over it, pencil and paper in hand. Or you can, like me, use it as a reference book, to pull out and read up on something that's rusty or that you never knew. It's not a book for beginners, necessarily, as it assumes a certain familiarity with language of mathematics to begin with. It does a fantastic job, though, for individuals truly interested in mathematics, of tying together history and theory and practice.

The Colossal Book of Mathematics by Martin Gardner.

I don't actually have this book. I'd like to have this book, though. The reason is that Martin Gardner was an amazing and prolific author of math and puzzle books (he died this past May at the age of 95). He was also an expert on Lewis Carroll and edited the beautiful The Annotated Alice.

And here's the Amazon blurb to entice you: "The Colossal Book of Mathematics collects together Gardner's most popular pieces from his legendary "Mathematical Games" column, which ran in Scientific American for 25 years. Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the unreachable dream of time travel, this volume comprises a substantial and definitive monument to Gardner's influence on mathematics, science, and culture." Sounds brilliant! His puzzle books are brilliant, too.

Part 4: A Nod to Textbooks

I'm not particularly shy about my dislike of textbooks, so you've probably picked up on that by now. But I'm also not the type of person to, as my mother would say, throw the baby out with the bath water.

If you have been following a math program with your kids for years and it seems to be meeting everyone's needs, I wouldn't rock the boat by changing gears (unless you or your kids are unhappy).

If your older child has not spent time with a formal math program and would like to explore higher mathematics, Harold Jacobs' Mathematics: A Human Endeavor is a brilliant place to start. It's definitely not your typical textbook as it builds on natural events and everyday applications to explain mathematical concepts. Jacobs has also written texts for algebra and geometry, which will someday also grace our shelves "just in case" anyone is interested.

If you are looking for a math program off the beaten track (that is, if your kid is bored of the typical math programs for homeschoolers), I want to give a thumbs-up to Life of Fred. I realize that it's been out long enough now that there are probably people who haven't liked it (so do scope out some reviews) - I have heard mostly wonderful things about it, though, so I feel comfortable mentioning it here. What I like about it is that it is a narrative-based program. It's a story. About Fred. Fred Gauss. And his precocious young life. It's entertaining but also informative. Stanley Schmidt, the author, lists four reasons to choose his program: fun, clear, cheap, and comprehensive.

We're in it for the "fun".