Thursday, June 30, 2011

The Ever-Intriguing Ramanujan

University of Illinois professor explores the work of Ramanujan:

http://www.thehindu.com/life-and-style/society/article2134518.ece

“In some ways, it is fortunate that Ramanujan didn't have formal training in math. If he had had to undergo the European kind of math training, he would have had to spend time proving his results vigorously, and would consequently have discovered far less,” says Prof. Berndt. “Some of Ramanujan's math is simply startling. If he had not discovered them, nobody would ever have. These equations make connections between entities you would never have supposed to have connections.”

Wednesday, June 29, 2011

Travelling Salesmen and Travelling Bees

The "travelling salesman problem" is a classic mathematical conundrum (about how to optimize a salesman's travel route when visiting several different cities), that mathematicians hunt for an algorithmic solution to.
Perhaps they should consult with bees:

http://www.sciencedaily.com/releases/2011/06/110628191339.htm

"Computers solve it by comparing the length of all possible routes and choosing the shortest. However, bees solve simple versions of it without computer assistance using a brain the size of grass seed."

Tuesday, June 28, 2011

Museum of Math

NY Times reports on the New York Museum of Mathematics to open next year:

http://www.nytimes.com/2011/06/28/science/28math.html?_r=1

It will be the only strictly mathematics museum in the entire nation.
“There are all sorts of myths about mathematics out there, math is hard, math is boring, math is for boys, math doesn’t matter in real life. All these are cultural myths that we want to blow apart.”  (from the article)

Monday, June 27, 2011

Paul Samuelson and Risk-Aversion

Interesting stat-type decision-making problem from Psychology Today dealing with "irrational behavior" being "seductive":

http://www.psychologytoday.com/blog/the-decision-tree/201106/can-psychology-solve-classic-paradox

At first glance it doesn't seem terribly profound to me, though it's apparently more nuanced than it looks on the surface. (Be sure and read the comments as well; unfortunately the Samuelson 'proof' alluded to isn't readily available.)

Sunday, June 26, 2011

Revisiting the Most Re-Revisited Problem in Popular Mathematics... Again

A recent 14-minute podcast from Scientific American on... guess what... the Monty Hall Problem:

http://www.scientificamerican.com/podcast/episode.cfm?id=lets-make-a-probabilistic-deal-a-fr-11-06-25

Nothing new here, but if someone prefers a verbal/vocal description of the puzzle over a written description this podcast may fill the bill.

Jason Rosenhouse's book-length treatment of the puzzle, "The Monty Hall Problem," remains a great (and thorough) source of information on this classic.

Friday, June 24, 2011

Friday Puzzle

A simple probability problem today that James Tanton tweeted a bit ago:

In my pocket I have a fair Head-Tail coin and an illegal Head-Head coin. I pull one of the 2 from my pocket at random and flip it. It shows Heads. What is probability that the other side is also Heads?
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answer: 2/3

Thursday, June 23, 2011

A Poll For Math/Computer Science Geeks

A poll on the eventual resolution of P vs. NP:

http://blog.computationalcomplexity.org/2011/06/i-am-conducing-new-poll-on-p-vs-np.html

(Be sure and read the 'comments' as well, several of which are quite interesting.)

Addendum: I should have anticipated that RJ Lipton would be weighing in on the poll, here:

http://tinyurl.com/6hezpa7

Tuesday, June 21, 2011

The Pigeon-hole Principle


I've mentioned the "pigeon-hole principle" briefly before, and it crossed my radar again when James Tanton put up a video on it here:

http://www.jamestanton.com/?p=810

It is one of those intuitive mathematical concepts that seems so obvious upon first glance that one wonders why it must even be stated, or how it could possibly be of any use... and yet that is the essence and beauty of mathematics: that basic, seemingly obvious ideas can be massaged by logic to produce significant and less obvious outcomes and ramifications.

If you're familiar with the pigeon-hole principle (it is especially used in combinatorics) you understand what I mean; if you're not familiar with it, then I won't even state it lest you think it too boring to bother with, but direct you instead to another link further elucidating it:

http://mindyourdecisions.com/blog/2008/11/25/16-fun-applications-of-the-pigeonhole-principle/

Monday, June 20, 2011

Humanistic Mathematics!

Hmmm... a new online, open-access journal has appeared, the Journal of Humanistic Mathematics. Haven't had a chance to peruse it yet, but notice it's in part from my ol' alma mater, Pomona College, so got to be good! ;-):

http://journal-of-humanistic-mathematics.org/

(Reuben Hersh and Philip Davis are among the contributors to the first issue.)

From the "Aims and Scope" section of the Journal's website:
"The Journal of Humanistic Mathematics aims to provide an open forum for both academic and informal discussions on the various threads of mathematical inquiry. The focus of submitted papers should be on the aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects of doing, learning, and teaching mathematics. Authors should keep in mind that the Journal intends to publish work that appeals to a general mathematical audience. This includes people who are seriously interested in mathematics, but may come from a variety of backgrounds both within and beyond academia."

Saturday, June 18, 2011

Friday, June 17, 2011

Car Talk Puzzler

Fortunately, I'm not a radio program director... because if I were, and 30 years ago two scruffy guys had walked through my door and said, "hey, we propose to do an hour-long radio show during which listeners call in with questions about their car repair needs for us to answer," I would've bellowed, "get out of my office you @*(%$#;!! knuckleheads with your lame-brained idea, and don't ever waste my precious time again!!"

If there is a person on the planet today who doesn't enjoy NPR's "Car Talk" with Tom and Ray Magliozzi  I don't know who it is. And one of the best parts of their weekly schtick is a "puzzler," that they ask listeners to solve during the next week (sometimes with a mathematical component).

All this is by way of introduction to this simple Friday puzzle which I've adapted from a Car Talk offering of a few weeks back -- admittedly, it's not so much a math puzzle as an elementary thought or logic puzzle that I liked:

In Borneo, there is a bridge connecting two islands, constructed of bamboo, lashed together with hemp, and used for hundreds of years. The bridge is 4 miles long and it has a strict weight limit of exactly 20 tons.
One day, a truck full of sedated pigs pulls up to cross the bridge. The weigh station finds that the truck weighs precisely 20 tons. The bridge is emptied and the driver allowed to drive across.
But as he drives forward, a flying sparrow begins to follow alongside, and just when the truck passes the halfway point, the sparrow lands on the truck!

What does the driver do to keep the truck and sedated pigs from plunging into the abyss below? (Note: jumping out of the cab or tossing articles of clothing out are not options.)

answer below:
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answer: It's a trick question and the driver need not do anything: In driving from the beginning of the bridge to the halfway point a 20-ton truck consumes fuel, and will easily consume an amount of fuel that's greater than the weight of the sparrow, so when the sparrow lands on the truck, nothing happens!

Thursday, June 16, 2011

Bookshelf



Always fun to construct Top 10 lists, so I looked over my mini-library of popular math books to put together a list of favorite volumes I'd take to keep me richly entertained on a desert island (these are not technical or academic works, and I've deliberately limited myself to one selection per any given author):


1)  How Mathematicians Think -- William Byers

2)  The Colossal Book of Mathematics -- Martin Gardner

3)  Mathematics: the New Golden Age -- Keith Devlin

4)  Mathematical Fallacies and Paradoxes -- Bryan Bunch

5) Beyond Innumeracy -- John Allen Paulos

6) The Riemann Hypothesis -- Karl Sabbagh

7) Mathematical Mysteries -- Calvin Clawson

8) A Passion For Mathematics -- Clifford Pickover

9) Mathematical Amazements and Surprises -- Alfred Posamentier and Ingrid Lehmann

10) Chances Are... Adventures In Probability -- Michael Kaplan and Ellen Kaplan


... and several Honorable Mentions:

The Big Questions: Mathematics -- Tony Crilly 
Stalking the Riemann Hypothesis -- Dan Rockmore

The Music of the Primes -- Marcus du Sautoy
Everything and More -- David Foster Wallace
The Drunkard's Walk -- Leonard Mlodinow
Mind Tools -- Rudy Rucker

lastly, not really a math book, but always worth mentioning (for entertainment on a desert island), Godel, Escher, Bach -- Douglas Hofstadter

I'm sure there are easily 20 more math books out there though that I've never seen, or simply forgotten about, that would be just as satisfying...

Wednesday, June 15, 2011

Not That That Would Ever Happen...

Nice quickie guide (pdf) to common statistical flaws (design errors/analysis errors) in scientific papers:

http://bit.ly/fFtptE

Friday, June 10, 2011

Thursday, June 9, 2011

Pointing Out Papert

MathMama had a post today on one of those names, Seymour Papert, who I've long heard about, but never gotten around to reading... I think she has stimulated me to put him in the reading queue though; if you're not already familiar with him check out her post and the several links she includes:

http://mathmamawrites.blogspot.com/2011/06/seymour-papert.html

Wednesday, June 8, 2011

Monday, June 6, 2011

Friday, June 3, 2011

The Meandering Cat

For a Friday puzzle this straightforward algebraic one I've taken directly from Raymond Smullyan's "The Riddle of Scheherazade" (which is chock-full of puzzles):

"...one day a pet cat walked away from its home at the rate of three miles an hour. Suddenly, she remembered it was dinner time, and so she trotted back twice as fast. Altogether she was gone fifteen minutes. How far did she go?"

answer below:
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answer: 1/2 mile

Thursday, June 2, 2011

Happy Birthday To Me...

...well, not really to me, but to this blog which marks it's one-year anniversary today! The blog was originally inspired/motivated by the then-recent death of Martin Gardner whose zest for math (and contributions to it) I can't come close to, but I do hope those visiting here may get at least some of the same sense of fun and mystery, beauty and wonder, that Gardner consistently conveyed regarding mathematics.

R.I.P. Martin, and I'll commence year #2 by listing, in no particular order, 10 of my favorite posts from the last 12 months:

1) http://math-frolic.blogspot.com/2011/01/seemingly-impossible-task-that-isnt.html
2) http://math-frolic.blogspot.com/2010/07/museum-piece.html
3) http://math-frolic.blogspot.com/2010/10/math-talking-heads.html
4) http://math-frolic.blogspot.com/2010/08/plug-for-raymond-smullyan.html
5) http://math-frolic.blogspot.com/2010/07/thomsons-lamp.html
6) http://math-frolic.blogspot.com/2010/12/gardner-strikes-again.html
7) http://math-frolic.blogspot.com/2010/06/savant-mind-at-work.html
8) http://math-frolic.blogspot.com/2010/06/mandelbrot-set-to-music.html
9) http://math-frolic.blogspot.com/2010/09/book-and-crafty-law-student.html
10) http://math-frolic.blogspot.com/2010/07/youtube-introduction-to-cantor.html

[BTW, I regularly follow about 26 other blogs in running this site and probability says there is a better than 50/50 chance that at least one of them also has its anniversary today ;-) ]