Mathematical rabbit holes

[Jane in NC]

This morning at a library book sale I acquired a copy of Yasunari Kawabata's novel, The Master of Go. Both my husband and son play this Japanese game. I thought it worth mentioning in case some of you are seeking interesting reading selections for your strategy game players. (Note to self: tell Nan about this!)

 

If your student wants to examine Go or other impartial games from a mathematical perspective, I suggest you look at the two volume combinatorial game theory classic, Winning Ways for your Mathematical Plays, by Conway, Berlekamp and Guy. It is accessible to high school students with the understanding that "accessible" is a relative term.

 

It seems that chess may be the more common game to enter literature (Through the Looking Glass). This might be a good place to list some literary or film connections to strategy games, something fun to consider for the school year ahead.

[Tullia]

Thank you! :lurk5:

[MBM]

Well, not sure this quite fits what you're trying to gather, but I thought the book The Numbers Behind NUMB3RS looked interesting. It's written by Keith Devlin (NPR's "Math Guy") and Gary Lorden (the math consultant on NUMB3RS). My son has yet to watch the show, but I thought the book had some interesting chapters that high schoolers might like.

[Jane in NC]

Well, not sure this quite fits what you're trying to gather, but I thought the book The Numbers Behind NUMB3RS looked interesting. It's written by Keith Devlin (NPR's "Math Guy") and Gary Lorden (the math consultant on NUMB3RS). My son has yet to watch the show, but I thought the book had some interesting chapters that high schoolers might like.

 

I have not seen Numb3rs but Devlin is great. Thanks for mentioning this.

[Jane in NC]

This morning I discovered some well done podcasts on the History of Mathematics which were produced by the BBC. ( Link.) I guess I am moving away from my OP strategy game connection to another interesting rabbit hole.

 

It seems that much of what is written in "popular" math history materials often covers ideas up to Newton and Leibniz's creation of Calculus. No wonder that so many students believe that nothing has happened in math in the last 300 years! This series begins with Newton and Leibniz. The programs are fifteen minutes in length and can be downloaded.

 

What was so wonderfully serendipitous about this is that I have been having a delightful email exchange with a young teen about several mathematical ideas including infinity. This led me to think about Cantor--and there was a program devoted to Cantor. I can't wait to have him listen to the series to give us more things to discuss.

[Moira in MA]

Seconding Jane here, I recently listened to those Mathematics podcasts, too. They're only about 10 minutes each and well worth the time.

 

Hikaru No Go, a manga comic may be worth the time for any Go fan.

 

~Moira

[stripe]

Thanks. I saw he made a video for the BBC too.

 

I will listen to the podcast on Galois immediately!

[Joan in GE]

If the U.S. would have switched to the metrics system in the 70s, this wouldn’t be an issue. How many of you out there had to learn the metric system in school only to never use it…

 

Stripe - I've been meaning to comment about the metric system which has nothing to do with the blog either... (sorry Jane - not at all related to the OP, but since it's mathematics related, I'm thinking you won't mind)

living in a country where they use only the metric system, I have to make a couple of comments about the problems with it...first, grade school children have extremely little experience with fractions! they don't have 1/4 cups, or 2/3 cups only 1/10's. So they approach algebra with little experience with fractions as well.

 

Then there are the problems with temperature...the Fahrenheit scale, has smaller increments of heat between the numbers...the difference between 20 and 21 C is much greater than the difference between 70 and 71 F or so it feels in the winter anyway...

 

I could whine some more but will spare you :001_smile: Just had to complain to someone who is even thinking about the metric system which I deal with every day.

 

Joan

[stripe]

That's interesting about fractions. I wonder if metric users are more rooted in base 12 whereas those who use all these crazy units are less so?

 

(Anyway it is a weird quote I found on the TSA blog; I didn't write it. I thought it was sort of hilarious. Especially calling it the metrics system.)

 

Eta I have given myself a picture at last. Heh

Edited August 14, 2011 by stripe

[Corraleno]

I have been having a delightful email exchange with a young teen about several mathematical ideas including infinity. This led me to think about Cantor--and there was a program devoted to Cantor. I can't wait to have him listen to the series to give us more things to discuss.

Jane, can you recommend any resources on the concept of infinity that would be accessible to a middle-schooler? My DS has always been fascinated by the concept. When he was in 3rd grade he asked me if you could use infinity like a number — can you multiply something by infinity, or cut it in half? When I asked how he would do that, he said he could imagine a number line divided at zero, so there would be the "negative half" of infinity and the "positive half," and he wondered if you added those together would you get zero or infinity. When I asked how he would divide infinity into more than 2 parts, he said he could imagine a ball that kept getting bigger and bigger and never stopped and you could cut it up into pieces but each piece would go out into space forever. All of which left me kind of :blink: since this was a kid who was flunking 3rd grade math.

 

Jackie

[Guest]

Here are two titles of books that might interest math-oriented high schoolers.

 

Out of the Labyrinth by George and Ellen Kaplan is about the founding and philosophy behind the original Math Circles in Boston, written by the founders of the circles.

 

Solve This is a book inspired by/related to the Math Circle pedagogy. It's a collection not exactly of problems, riddles, thought experiments, and other different ways of approaching mathematical topics.

 

Sorry I have not included links. I tried, and kept getting them really messed up.

Edited August 14, 2011 by Guest

[Dana]

Jane, can you recommend any resources on the concept of infinity that would be accessible to a middle-schooler? My DS has always been fascinated by the concept.

 

The Cat in Numberland by Ivar Ekeland is a picture book, but it's got a neat illustration of countably infinite sets. I think Crimson Wife recommended it. I'd check if your library has it rather than buying it though... :)

[stripe]

Jane, can you recommend any resources on the concept of infinity that would be accessible to a middle-schooler?

 

Aha! Gotcha by Martin Gardner.

http://www.amazon.com/Aha-Gotcha-Paradoxes-Puzzle-Delight/dp/0716713616

[Jane in NC]

Jane, can you recommend any resources on the concept of infinity that would be accessible to a middle-schooler? My DS has always been fascinated by the concept. When he was in 3rd grade he asked me if you could use infinity like a number — can you multiply something by infinity, or cut it in half? When I asked how he would do that, he said he could imagine a number line divided at zero, so there would be the "negative half" of infinity and the "positive half," and he wondered if you added those together would you get zero or infinity. When I asked how he would divide infinity into more than 2 parts, he said he could imagine a ball that kept getting bigger and bigger and never stopped and you could cut it up into pieces but each piece would go out into space forever. All of which left me kind of :blink: since this was a kid who was flunking 3rd grade math.

 

Jackie

 

I see that you have received a couple of recommendations, but I will add that listening to the aforementioned BBC podcast on Cantor might also be thought provoking. It was Cantor who realized that there are different infinite cardnalities (the number of integers compared to the number of reals, for example).

[Jane in NC]

Here are two titles of books that might interest math-oriented high schoolers.

 

Out of the Labyrinth by George and Ellen Kaplan is about the founding and philosophy behind the original Math Circles in Boston, written by the founders of the circles.

 

Solve This is a book inspired by/related to the Math Circle pedagogy. It's a collection not exactly of problems, riddles, thought experiments, and other different ways of approaching mathematical topics.

 

Sorry I have not included links. I tried, and kept getting them really messed up.

 

Both of these books are geared to math educators. Has your highschooler enjoyed them?

 

A question about the second: Do these classroom activities translate well to homeschool situations or is a group needed, i.e. a co-op or math club?

[Colleen in NS]

Here are two titles of books that might interest math-oriented high schoolers.

 

Out of the Labyrinth by George and Ellen Kaplan is about the founding and philosophy behind the original Math Circles in Boston, written by the founders of the circles.

 

Solve This is a book inspired by/related to the Math Circle pedagogy. It's a collection not exactly of problems, riddles, thought experiments, and other different ways of approaching mathematical topics.

 

Sorry I have not included links. I tried, and kept getting them really messed up.

 

Oh, wow, I just heard about Math Circles a few months ago. We went to one of their events to observe (it's where I found the 1960s Dolciani Trigonometry book, Jane! ;)), and are thinking of somehow getting involved in a year or two.

 

Great thread!:lurk5:

[MBM]

The eIMACS blog might be worth a look for more ideas.

 

http://www.eimacs.com/blog/