## Review: Train Your Brain: A Year’s Worth of Puzzles

Some books are hard to review. This one isn't. Train Your Brain: A Year's Worth of Puzzles is the kind of book where you look at a few of its puzzles. If they intrigue you, you'll like the book. Simple enough.

Here's one puzzle.

Knight on the Chess Board. We would like to move a knight across the chess board so that we go from the lower-left corner to the upper right corner, landing in the process on each square exactly once. Is this problem solvable?

This is a great puzzle that I'll use in my Math circles. It's a nice little exploration and it generalizes well to make it harder for folks who solve it very quickly. For those who get stuck there is a hint on a different page so that the hint is not right in front of you.

## Review: The Big Questions: Mathematics

What motivates the study of mathematics? Pure Math and recreational Math may not seem to have any connection to our physical world (although they sometimes do) but much of what we study was once motivated by the need to solve some practical problem. The longer I serve in the role of Math communicator the more important I feel it to be to connect people, mathematicians and non-mathematicians alike, with the stories behind the concepts and calculations. Storytelling is a powerful way to help people to relate to the experience of being a mathematician and thinking like a mathematician. Plus, most of us love stories, if they're well told and if they contain intriguing elements. In The Big Questions: Mathematics, Tony Crilly tells 20 compelling stories of the development of mathematical ideas.

The second chapter, *Where do numbers come from?*, takes us back to the earliest counting methods, some 30,000 years ago. Crilly tells us about the tally sticks and notched bones that our ancestors used to count things. We learn about the Babylonians and Egyptians and their counting system based on the number 60, from which we get 60 seconds in a minute, 60 seconds in an hour, and 360 degrees in a circle. And, there's a nice yet simple exploration of the merit of a number system based on 60 -- think of how easily 60 divides into groups of equal number. The chapter on imaginary numbers not only gives a nice introduction to complex numbers, quaternions, octonions, and Clifford Algebras; it also (briefly) connects us to practical applications of complex analysis. More importantly, though, Crilly paints the picture of the people who pioneered the study of complex numbers. We can put ourselves in the shoes of these mathematical inventors and get a sense of their struggles and of their triumphs.

I like "The Big Questions: Mathematics." If you're looking for challenging Math problems to chew on this isn't the book for you. If you would enjoy a broad brush telling of 20 interesting stories then I'd encourage you to pull up a chair and get a copy of the book. The ideas are fantastic and Crilly's storytelling is superb.

## 13 surprising Fibonacci appearances

One of my great Math heroes, James Tanton, has written a great essay that provides thirteen examples of the Fibonacci sequence appearing in strange and unexpected places.

"I have YouTube videos presenting some surprising appearances of the Fibonacci numbers and I’ve been tweeting little puzzlers about the Fibonacci numbers for some time. Here, at long last, is my list of Fibonacci results, and a clever way to prove them all. Some of these puzzlers are classic, some are new to the world."

## Review: Mathematics Education for a New Era: Video games as a Medium for Learning

How can we rethink the current Math education paradigm to consider the wealth of available technology? Can video games teach basic Math skills or are they just a waste of time? Can video games help students to gain Math proficiency? What are the key elements of a game that promote mastery of mathematics? These are some of the "game changing" questions that Keith Devlin tackles in his new book "Mathematics Education for a New Era: Video Games as a Medium for Learning."

Keith Devlin is well qualified to explore these important questions. He is a researcher focused on using different media to teach mathematics. He is the author of 30 books; a number of them explore how we learn Math. Devlin has published over 80 research articles and he has won numerous prestigious prizes and awards. And, many of know Keith Devlin as "the Math Guy" on National Public Radio, the man who, since 1995, has been taking important mathematical ideas from current events and explaining them so that general audiences can understand them.

## Japanese ladder games

Have you ever heard of Japanese ladder games? I hadn't until I read an article in June's MAA Focus magazine. Here's a piece of the article:

The MAA Focus article gives a link to a page with a couple of very interesting papers.

The second paper, "Ladders, Codes, and Actions," has this as a first paragraph.

Combinatorial games often generate interesting mathematics and can help students understand difficult concepts. In this paper, we shall describe three games which are very visual and can be played by anyone regardless of their level of mathematical sophistication. When you are done playing these highly addictive games you will have a deeper understanding of permutations and group actions and you will learn a very interesting connection to coding theory. We have found that the games are very enjoyable to play and that players end up understanding complex mathematical ideas without realizing they have done so.

These games are truly a great find, very simple yet very deep. I'll use these games in my Math gatherings.

## Giveaway: Manga Guide to the Universe

**Contest is over. Ron Green is our random winner. Congratulations, Ron!
**

The nice folks at No Starch Press are giving away a copy of their very new "Manga Guide to the Universe" to one lucky Wild About Math! reader. And, they'll ship it to anyone in the universe, although they used the word "planet." So, here's the deal. Leave a comment telling me you want to win. Be sure to put your email in the comment form. When I get 10 comments I'll disable commenting for this post and I'll have Random.org pick a lucky winner. I'll send your email address to the No Starch folks and they'll ship you the book. If you're one of these people who checks this blog continuously for updates then you might have a 10% chance of winning the book. Sweet!

From the book's web page:

Join Kanna, Kanta, Yamane, and Gloria in The Manga Guide to the Universe as they explore our solar system, the Milky Way, and faraway galaxies in search of the universe’s greatest mysteries: dark matter, cosmic expansion, and the Big Bang itself.

As you rocket across the night sky, you’ll become acquainted with modern astronomy and astrophysics, as well as the classical discoveries and theories on which they’re built. You’ll even learn why some scientists believe finding extraterrestrial life is inevitable!

Note that the ink on the books needs to dry so No Starch Press won't be shipping the book to the winner until the week of June 27.

Good luck!

## Review: Mathematica in Action

[ Editor's note: If you're a Mathematica user you may appreciate a review I just published at my Playing With Mathematica blog. ]

"Stan Wagon and I have exchanged a number of emails about Mathematica. A few messages into the dialogue I realized that I needed to review his latest book: Mathematica® in Action: Problem Solving Through Visualization and Computation. Before I even immersed myself in the book I knew I would like it because I enjoy Stan's playful relationship with Mathematica and I enjoy receiving the simple and elegant little programs that Stan would send me."

## Review: The Number Sense

Oxford University Press sent me a review copy of The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition, by Stanislas Dehaene. The book is an update of the original edition, which was published in 1997.

The author writes in the preface of this new edition that the goal of the first edition of the book was

"to assemble all the available facts on how the brain does elementary arithmetic, and prove that a new and promising field of research, ripe with empirical findings, was dawning."

This new edition updates the reader on findings in the field of numerical cognition. Wikipedia has a nice introduction to the subject, including a list of questions at the heart of the field.

- How do non-human animals process numerosity?
- How do infants acquire an understanding of numbers (and how much is inborn)?
- How do humans associate linguistic symbols with numerical quantities?
- How do these capacities underlie our ability to perform complex calculations?
- What are the neural bases of these abilities, both in humans and in non-humans?
- What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?

## Avoiding the “Summer Math Slide”: tips from TI

Texas Instruments has produced a good article on how to keep kids engaged in Math over the summer break.

**Help Your Teen Avoid the “Summer Math Slide”
Students Lose as Much as Two Months of Learning over the Summer**

DALLAS (June 8, 2011) – Learning math is a lot like learning a sport; you have to practice to improve your skills. If you take three months off, you will get rusty. Students, especially teenagers, want a summer packed with fun, and typically academics aren’t on the list of to-dos for the summer break. But there are things every student can do over the summer (and yes, they can be fun) to prevent losing the days and days of hard work they’ve already put into math during the school year.

According to the National Association for Summer Learning, across the board, all kids lose some math skills over the summer. On average, students lose approximately two months of grade-level math skills in the summer months if they do not participate in educational activities. Additional research, provided on the National Association for Summer Learning website, states losses in math are somewhat greater than those in reading, and teachers often spend four to six weeks re-teaching material. Time lost becomes crucial as students enter more demanding math classes in middle and high school.

But teenagers, with the help of their parents, can prevent the summer math slide.

“Students do not have to lose the math skills they developed during the school year,” says Tom Reardon, a math adviser for Texas Instruments and a retired math teacher with 35 years of experience in the classroom. “Summer is the perfect time for teenagers to focus on tuning up skills, and it can be done in some fun and engaging ways.”

## Mathematica 8 Home Edition for $239 in June 2011

If you're in the U.S. and you've been thinking of getting Mathematica 8 Home Edition (and you're not a student or otherwise eligible for a discount), you can save nearly 20% in June if you buy Mathematica from Wolfram Research via Amazon.com.

See here for more information.