Welcome to the 11th Carnival of Mathematics! 11 is a great number, because it consists of two 1s, and we have two firsts to brag about. First, mathematical readers will note that 11 is the first double-digit prime integer. Second, this is the first time that the Carnival of Mathematics has been hosted 3 times in a single month!

Speaking of 11, a good place to start is the 11th in a series of quotations over at Let's play math. This is a great quote about how students mistakenly see math, and how to solve the problem of how math is viewed.

Just what are the numerous ways to get students interested in math? Laurie at Trivium Pursuit has helped one teacher, who has had a great experience in delaying math.

Over at Math Notes, you can see how a mathematical magic trick was used to get a young girl interested in algebra.

If you haven't explored this site before, you may not realize that I'm a great proponent of making math fun and interesting. Here on Grey Matters, you can watch some amazing math videos, or lean how to perform some amazing feats yourself over in the Mental Gym section (I especially recommend Mental Shopper).

Once students understand that math is more than just disembodied numbers, they can better prepare for more advanced and abstract concepts. At Math Notations, we learn not only how to teach recursive sequences and function to grades 7-12, but how to use the Rule of Four to teach other mathematical concepts, as well. If you're no longer in school, don't think you're getting off easy, because there's a geometry challenge waiting for you at Math Notations, as well.

Mark at the Universe of Discourse uses the example of square and triangular numbers to show how learning from your mistakes can be valuable.

Speaking of learning from experience, JD2718 tries to find the right wording and image for a bonus question for a pre-calc exam and gets some great advice on the problem. As it turns out, few of the students even made it to that question, but provided interesting answers to another question. These last three posts are great lessons in not limiting yourself, and trying to solve problems by changing your point of view.

Even when math is completely abstracted from numbers, it can still provide fascinating and relevant lessons.

The Unapologetic Mathematician discusses categorification and its importance. It's quite interesting, not only because it uses abstraction from numbers, but also employs the abstract notion of the concept of numbers!

When Enigmania examines the notion of finite and infinite collections, leading into a discussing of the concept of potential infinity, and even takes it in new directions.

The 12th Carnival of Mathematics will be held on July 13th over at the Vedic Maths India blog. Send your submissions via the submission tool. Also, contact Alon if you wish to host the Carnival of Mathematics August 24th or later.

The next Carnival of Mathematics will be right here on Friday, June 29th!

Send in your submissions to greymattersblog@gmail.com by Wednesday, June 27th, at 11:59 PDT so you can be added to the Carnival! Please include the phrase Carnival of Mathematics in the subject heading.

Ever since games such as Brain Age and Brain Trainer have become available, there's been a renewed interest in improving the brain.

I mentioned lumosity earlier this month, where you can improve your brain over 30 sessions.

In a more competitive vein, there's BrainSpeeder (also available in German). Once you register for free, there are numerous leagues in which you can pit yourself against people in arithmetic, mnemonic and speedoku competitions. You can even compete to be Brain Of The Day.

Over at BrainBall, you can play all of their games solo without registering. If you want to pit yourself against others, you will have to register.

However, there are two completely registration-free alternatives. First, for those who haven't checked it out already, I'd like to shamelessly plug the Grey Matters Mental Gym. Here, you can learn a wide variety of memory techniques, learn some amazing memory and mental math feats and even practice them!

There are also some obviously kindred souls over at Brain Metrix. There are some excellent articles and activities here. If you enjoy this site, you'll also enjoy Brain Metrix. This is one of those sites you can easily spend several hours exploring.

Since I first mentioned ProProfs' Flashcard and Quizschool sections back in March, they've kept improving the site!

The biggest news would have to be the addition of a very complete free SAT preparation section. The site features a comprehensive collection of SAT preparation material (covering all three major areas of the exam) that includes study guides, flash cards, practice questions, and even simulated exams. Quizzes, videos, blogs, wiki and interactive forums are also provided. I'm more than 2 decades past my SATs, but I still remember some of the expensive SAT classes and software with which I worked, so I must admit to being jealous that such a rich free resource didn't exist at the time.

My one original complaint about ProProfs in the original entry concerned the ability to post quizzes and flashcards on a website or blog:

Unfortunately, there is no simple embed code box, like the ones you find on video sites.

They've not only been working on the site, but listening as well. When you begin flashcards, such as this Spanish 2 set, you are now given an embed code!

The embed code feature isn't yet available in the QuizSchool section, but will be added shortly.

I've listed more than a few flashcard sites here on Grey Matters, but the ProProfs site is quickly becoming a standout site and a very valuable resource.

The 10th Carnival of Mathematics is now up over at MathNotations. Dave opens with an interesting section about splitting the Carnival into two parts, with one part being dedicated to middle and secondary grades, and the other being for college graduate and undergraduate levels.

The next Carnival of Mathematics will be right here on Grey Matters on June 29th! Please send your submissions to me by 11:59 PM PDT on Wednesday, June 27th, at this e-mail address.

Sure, there's plenty of puzzles and challenges over at the Mental Gym, but for those who seek further brain-straining, even more await out on the web!

I'll start with the more familiar puzzles. If you'll fire up your computer's or browser's Java Virtual Machine, we can head over to MazeWorks. This site features many classic puzzles, such as the 15-puzzle and the Towers of Hanoi, along with many new puzzles you may enjoy discovering.

Let us not forget the humble logic puzzle. How about starting by trying to get our hero a kiss from a pretty girl? If that's not enough, and you can keep from peeking at the answers, here's 13 more puzzles for you to solve!

If you're a fan of Sudoku, you can head over to the Mental Gym's Sudoku page. However, if you wish to delve deeper into the nature of the game, see what happens when sudoku and mathematics intersect.

Understanding the principles behind the puzzles may or may not help you solve them, but it will help you understand the nature of the puzzle itself. This can even help you create new puzzles. As a matter of fact, Maki Kaji, the father of Sudoku, has used similar principles to create a new type of puzzle called Masyu (PDF, will open in new window). If you want to try this Masyu puzzle for starters (PDF, will open in new window). Don't worry, there are already plenty of Masyu puzzles available on the web if you get hooked.

Oh, and if you need any help solving any of these puzzles, take some advice from Square One TV's Larry Cedar:

It's time to visit some more sites in the spirit of my Fun With Pi and More Fun With Pi posts.

I'll start off with the digits of Pi being sung. The music and vocals are right out of Hard N Phirm's "Pi" Video, and are much more accurate than Kate Bush's version.

If you would like to try your own hand at making some music based on Pi, check out pi10k, where you can select music notes to represent the digits 0 through 9, and then hear the first 10,000 digits played as those musical notes!

Moving from music to haiku, we have this interesting pi haiku from autoDogmatic:

Can I know a cycle,
according to nature round,
and never complete?

Not only is it an excellent summation of the central question of Pi, but it's also a Pi mnemonic! If you count the number of letters in each word, you have the first 12 digits of Pi!

Of course, pi doesn't have to be treated only as an art form. After all, this entry itself is titled, Even More Fun With Pi. Over at Mighty Wombat, they've shown what happens when Pi and i get together. While at xkcd, they seem to have found a secret message hidden in Pi.

That last cartoon reminds me of an old Pi joke. A computer programmer working on Pi runs up to his supervisor excitedly and yells, "Sir! We've made a major Pi breakthrough! I have good news and bad news to report!" The supervisor asks, "What's the good news?" The programmer replies, "We have definitive proof that there is a message hidden inside Pi, inside the very fabric of the universe!" The supervisor then asks, "What's the bad news?" The programmer responds, "It's in Hebrew, and we have to start reading it from the right."

For Mac OS X 10.4 users, you can download the piclock widget, for use on Dashboard. This widget will show the time and even the date as digit strings from Pi, Theta, Euler's number or the square root of 2.

For now, I'll leave you to explore Mathematician's Pictures, a store devoted to the world of math and mathematicians, including their Pi Department and their Pi Of The Month Club.

Back in May, I briefly mentioned Danica McKellar when discussing mathematically-oriented women. This is one child star who is winding up very well adjusted and successful!

When you probably last saw her, she was portraying Winnie Cooper, and telling Kevin Arnold (Fred Savage) that they should go their own ways and find out who they are. I'll let this clip from 20/20 catch you up on her life since then:

Yes, you heard correctly. She's a math whiz! If you want to read her paper, you can read Percolation and Gibbs states multiplicity for ferromagnetic Ashkin–Teller models on Z² here, as published in the Journal of Physics A: Mathematical and General (Now known as Journal of Physics A: Mathematical and Theoretical). Remember, I said you could read it. How well you understand it will depend on your physics background.

Moving to the more recreational mathematic side, Danica also possesses an Erdös-Bacon number of 6, the lowest of any professional actor or actress. Since your head is probably still spinning from ferromagnetic physics, I should probably explain this number.

Most of you are familiar with the 6 Degrees of Kevin Bacon concept, through which you could determine an actor or actress' Bacon number. Those who collaborate on mathematical papers have a similar concept, but with Paul Erdös instead of Kevin Bacon. When you add these two together, the total is the Erdös-Bacon number. Danica is linked to Erdös through four collaborations (citations 13-16 here) and to Kevin Bacon through 2 steps, giving a total of 6.

Besides her acting projects, she'll also be releasing a book on math in August 2007, called Math Doesn't Suck: How To Survive Middle School Math Without Losing Your Mind or Breaking A Nail. If you scroll down on that page, you'll see that she also answers e-mailed math questions, too. Besides her site, she also has her own math column targeted to help kindergartners through 8th graders called Danica's Corner.

Between being known for her nerd-loving character Winnie Cooper, and being published in a physics journal, you would think she would have a hard time shaking a nerdy, wholesome image. However, her interest in ballroom dancing and her lingerie photo shoot for Stuff Magazine (which may or may not be safe for work, depending on your office standards) will probably help shed that image.

Here are some quick snippets for you:

* Neuroscientists from UCSF and Standford have created a site called Lumosity that is designed to improve your attention, processing speed and memory. This is done over the course of thirty 15-minute sessions which require registration, which is free while the site is still in beta. You can also evaluate your IQ for free without registering.

* Computer clusters from three different institutions have found the prime factors of a 307-digit number after 11 months of computing. while this may not sound like much more than computers solving a boring math problem, it becomes interesting when you realize that this technique can be used to break advanced encryption techniques used by businesses and governments. Granted, 11 months of computing is a long time, but as processors get faster, this will fall.

* Cinema Advanced offers a wonderful alternative to rote script memorization in their post, Don't Memorize Your Lines.

* If you need to do some real-world estimates for varying types of problems, mental math shortcuts provides just what it promises.

* If you enjoyed the Prisoner's Dilemma post, you might also enjoy the Toilet Seat Dilemma, where similar game theory is applied to the age-old question of leaving the toilet seat up.

It took just a little longer than expected, but the 9th Carnival of Mathematics is up over at JD2718!

The next one will be on the 15th at MathNotations. After that, you'll find the 11th Carnival of Mathematics right here on Grey Matters!

The Carnival needs new hosts, too. Currently, the Carnival of Mathematics only has hosts through July 13th, 2007. E-mail alon_levy1@yahoo.com to submit your math blog for consideration as Carnival host.