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Friday, December 28, 2012

Dr-r-r-r-rumroll.... Keith Devlin!

Math-Frolic Interview #9

“For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture.”
― Keith Devlin, from "Introduction to Mathematical Thinking"

For the possible long weekend ahead, a real treat and long post with lots to chew on from Keith Devlin. How Keith finds the time/energy to do all he does I don't know, but he found time to answer some wordy questions from me! (on some things I was really curious about)
I've added bold to a few bits here and there for emphasis of notions I thought particularly interesting.
Anyway, Dr. Devlin ought need no introduction here, so without further adieu....

**********************************

1) These days, you're very active with the MOOC (massive open online course) movement, which will likely bring major changes to higher education in this country. Could you briefly paint us a picture of what you think college (or even secondary) education in the US may be like say 20-30 years from now, as contrasted with how it is today?

As the saying goes, prediction is difficult, particularly about the future. There are two parts to what we call "education" and I think the distinction between them will become clearer. First, for people who have essentially learned how to learn and to think critically, there is what I would call "training" -- learning some new skill or a variant of something already known. For learning of this kind, the textbook, the training manual, the  classic instructional lecture, or the video instructional lecture are fine. A lot of vocational training is like this, as are many university level courses in computer science, mathematics, engineering, etc. This kind of teaching can easily be provided by MOOCs. Indeed, the first large scale MOOCs coming out of Stanford, then MIT, were all of this kind. With valued-brand universities offering this education online for free, possibly with payment required for certified accreditation, it's hard to see most middle ranked higher educational institutions surviving by focusing on such teaching. This kind of education is scalable.

Most of the media coverage of MOOCs has focused on this kind of education. But then there is the education that -- in theory, but I fear not always in practice -- the K-12 system is supposed to provide, and which most university courses in the Arts and Humanities, and many university courses in the Sciences and Engineering, do provide. These focus on learning how to learn in the lower grades, and on developing critical thinking and new ways of thinking at higher grades. The only way to provide that kind of education is with human-human interaction between learning and domain experts and the students, coupled with student-student interaction. This kind of education is not scalable.
The K-12 system will likely see little major change due to technology, and any change they do experience should be for the better, with teachers having more time to work individually with students. Higher education will focus much more on human interaction, with the classic lecture disappearing.

And relatedly, something you've often noted that I find interesting, is that college-level math and secondary school math involve very different skills (such that a person can sail through secondary math with high marks and yet hit a brick wall with college math) -- can digital resources help smooth out this transition, or will there likely always be a sharp inherent demarcation between the two levels of study?

The two kinds of mathematical education are almost separate disciplines. The demarcation lines are very similar to the ones I outlined above for education in general. Technology can help, but not very much, because, by definition, cognitive, conceptual mathematics is about the human brain.

2) You are consistently one of the clearest, most effective math writers/popularizers around for a general audience. To what do you attribute that knack? (have you always been a naturally good writer, or do you work especially hard at it, or just have super editors? ;-)

All of the above! Though all my mass market books have been written with great editors, and my early magazine articles and newspaper column were all professionally edited, these days hardly any of my articles -- and none of my blogs -- are edited by anyone except me.

3) I recently stumbled upon one of your older volumes (~1996), "Goodbye Descartes" -- another marvelous read. I was especially struck by the amount of material on linguistics and Noam Chomsky. My primary area of interest in grad school was actually psycholinguistics (though I had little interest in Chomsky's approach or work), so am curious how much you continue to follow work in that area, and has your opinion of Chomsky changed over the years?

Chomsky's early work on syntax has the same innate appeal as AI, and many mathematically-minded people such as I are initially seduced by the prospect, as were Chomsky himself for syntax and McCarthy for AI. But as soon as you delve deeper into the target domains, you realize that there are significant limits to the mathematical approach. Mathematics is a useful framework in both human domains, but it does not yield the same results that it does in the natural sciences. But in recent years I have continued to work in that general area, a lot of that work being for large corporations and for different government agencies related to national defense. In "Goodbye Descartes" I coined the term "soft mathematics" for such uses of the mathematical approach, where you blend mathematical thinking with other ways of working.

4) Much of what you write concerns the logic, history, and philosophy underlying mathematics. You don't often delve into recreational math, and I've not seen you reference Martin Gardner very much in your writings (though I've missed much of your prolific output). So I'm wondering what your view was of Gardner and if you ever had occasion to spend significant time with him? Is any lack of his mention in your writings just due to a lack of overlap in your interests, or does it possibly relate to basic disagreements over mathematics itself? -- I ask this especially because Martin was a very vocal and clear "Platonist" in his view of mathematics, while you have become a vocal NON-Platonist....

I corresponded occasionally with Martin, and re-read everything he had written when I started out on my popular writing, but I've never had much interest in recreational mathematics per se, except as a device to interest people in mathematics and as a pedagogic device. Mathematics has such power to do things in the world, I was never motivated to spend a lot of time on "recreational problems." It's not an issue of pure mathematics versus applied. My doctoral work was on infinitary set theory, which to date has no applications and may be one of the very few parts of mathematics that never finds (direct) applications. But it was a major piece of mathematics -- an abstract edifice -- developed over many decades, and that gave it purpose beyond any individual problem.

5) The whole Platonist/Non-Platonist debate actually fascinates me. Most working mathematicians I meet seem to assume a Platonist view is the norm, and that only a few 'fringe' elements out there hold the Non-Platonist perspective! Yet, over recent years, I've read more and more prominent math writers (like yourself), who started out as Platonists, but who have swung to the Non-Platonist side (and feel quite confident about it now). Do you have any sense of what percentage of professional mathematicians fall into each camp (in short, is it as heavily Platonist as some would have me believe, or not so one-sided in your view)?

My sense is the same as yours, that the non-Platonistic view has become more common, and maybe even dominant among successful professional mathematicians. But maybe I no longer mix with the Platonists!

And one follow-up to that: some I've talked to feel the whole P/Non-P debate is silly and unimportant; all that is significant is that we are able to successfully apply mathematics in life and science as well as we do; i.e. the Platonist debate is just mushy, mumbo-jumbo wordplay… what, if anything, might you say to that outlook? -- in short, does the debate even matter, beyond an intellectual exercise?

I think that the fact that doing mathematics seems to ENTAIL a Platonistic perception is of great interest. Why does it do that? I published a tentative explanation of that some years ago: "A mathematician reflects on the useful and reliable illusion of reality in mathematics" Proceedings of the workshop Towards a New Epistemology of Mathematics, held at the GAP.6 Conference in Berlin, September 14-16, 2006. Erkenntnis, Vol. 68, No. 3, May 2008, pp. 359-379.

-- This is a rich read (~20 pgs.) if you're interested in cognition, neuroscience, or even philosophy.

6) A second person I've not seen you discuss (completely apart from Gardner), and who I find very interesting, is the autistic savant Daniel Tammet. His introspective analysis of his own incredible math abilities seem fascinating. Have you read his writings on the subject of his own remarkable mathematical skills, and do you have any views regarding his talents or his personal analysis of them?

Actually, if you go back to my writing in the 1980s and 90s, you will find many references to Gardner -- but of course that was in the pre-Web era, so Google searches won't come up with what I wrote. I know nothing about Tammet and never heard of him. Prompted by your question, I'll take a look. Thanks.

[Wow, I was VERY surprised to learn of Dr. Devlin's unfamiliarity with Tammet who has received much publicity in recent years, and who writes frequently about his own keen mathematical cognition. I've finally received Tammet's latest book, "Thinking In Numbers," and will probably write some sort of blurb on it in the future... but this all seems to me to be a great example of just how broad and wide the mathematical landscape is -- that someone I simply presumed Dr. Devlin would be well-acquainted with and might have definite opinions about, is in fact, not even on his radar -- and I certainly don't mean that as a criticism, but rather as a tribute to how vast the sphere of mathematics is.]
 

7) Are you currently working on a new book, and if so, what about?

I probably am, but don't yet know it. I do have one finished in draft form that I have not yet figured out how to market -- a decision that will for sure entail a rewrite.

...something for us all to look forward to!

8) Speaking of books, an unusual one I recently finished is a self-published volume from Britain, entitled "The Mystery of the Prime Numbers" by Matthew Watkins [...I hope to have an interview here with Dr. Watkins soon]. It is one of the most fascinating/extraordinary math books for a mass audience I've ever read (entirely on the topic of prime numbers), and yet barely known because of weak distribution. I'm curious if you are familiar with it (and/or the author) and if so what you think of it?

No, I have not come across it or the author. Again, your question prompts me to take a look. I am very proud of having "discovered" Paul Lockhart and launched his large-market writing by publishing his "A Mathematician's Lament" in my MAA column. If I come across someone else with Paul's writing talent, I will try to do the same again.

...I do hope you access Watkins' book. I'd love to know if it is as exquisite as I find it, or are there flaws/failings I'm not competent to detect. Next time I contact Dr. Watkins I may even suggest he send you a complimentary copy.

9) To round yourself out a bit, when you're not involved in mathy things, what are some of your primary interests/hobbies/activities?

I am a physically active guy and like to spend a significant part ofd most days engaged in a physical pursuit. I used to be a distance runner (and before that a rock climber and skier), but when my knees started to complain in earnest about ten years ago I switched to cycling, and now own several different kinds of bikes, from upper end, all carbon road bikes to mountain and cross bikes. My website (http://profkeithdevlin.com/) and my Stanford homepage (http://www.stanford.edu/~kdevlin/) both have sections devoted to my biking.

10) What words of advice might you give to young people who are thinking they may want to pursue mathematics in college and professionally?

Just do it. The only prerequisite is a high tolerance for hard work, frequent frustration, and repeated failure. But those are what it takes to achieve the great highs that come with the successes.

**********************************

Several quite fascinating responses here on so many levels... I really can't thank Dr. Devlin enough for taking time out of his insane schedule to indulge me.

If you want more Devlin, he's all over the internet/blogosphere/YouTube etc., just google him, but I'll quickly cite 2 other references:

Another transcribed interview with Keith here:

http://www.guidetoonlineschools.com/interviews/how-to-become-a-mathematician

And to hear his British accent ;-) the very first podcast that "Wild About Math" blog ever did was fittingly with Dr. Devlin here:

http://wildaboutmath.com/2012/02/14/keith-devlin-inspired-by-math-1/

In the right-hand column, I also have several other past Math-Frolic posts 'tagged' for "Keith Devlin."

Hearing from Dr. Devlin is a fantastic way to close out the year, in the (possible) event that I don't get another post up before Jan. 1.....





Thursday, December 27, 2012

Wonderful Series of Posts

(via WikimediaCommons)

I don't check out the "Better Explained" website often enough!... they have a wonderful series of posts on mathematical thinking or intuition -- in fact, I think this series might make a GREAT pre-read BEFORE one tackles Keith Devlin's "Introduction To Mathematical Thinking" which I was extolling just a couple days back. There are currently 8 posts in the series, beginning here (there are links to all posts in the series at the end of each post):

http://betterexplained.com/articles/how-to-develop-a-mindset-for-math/

The 7th post ("Finding Unity In the Math Wars") is actually a bit tangential, focusing on Khan Academy and the controversy surrounding it. However, this post is one of the best discussions I've seen on the whole Khan debate, and I would start with it, since it is such a hot topic in education today, and then go back and read the other posts. A fine series!

Wednesday, December 26, 2012

Coral Reef Math

Science writer Margaret Wertheim talks about art, coral, crochet… and, non-Euclidian geometry in this TEDTalk:



The math begins around the 5:25 point…
...enjoy the math AND the art!


Monday, December 24, 2012

Author, Professor, Columnist, Lecturer, Radio Personality...


 The prior post noted John Allen Paulos as recipient of a math communicators award for 2013. In 2001, that very same award went to Keith Devlin, and the more I read from Dr. Devlin, the more I'm blown away by his talents/insights… Keith is as close as it gets to being a "rock star" in popular mathematics (...he even sounds a bit like Paul McCartney!). If I was a Devlin fan before, I'm a near Devlin groupie now after reading two more of his volumes this month.

His latest book, "Introduction to Mathematical Thinking" is possibly the best 92-page, slim math book with a blue cover, and a 4-word title, written by someone with the initials "K.D." I've ever read ;-) …no, seriously it is a fabulous book that packs more into 92 pages than most books twice that long. But having said that, it is NOT an easy read (AND there's hardly any actual MATH in it! much more logic and set theory) -- it was the basis for the recent MOOC course, of the same title, Keith taught in the fall, and I can understand why most of the 1000s of students who signed up dropped out of the course… I'm sure the material in this book is NOT what they were expecting.
I'm not quite finished with it… but when I am, I will need to start all over and read through it again… much more s-l-l-l-l-owly and carefully. The slimness of the volume disguises the density of the ideas. Again, if you're happier just 'doing' math and feel no need to 'understand' what underlies it, this volume WON'T be for you, but if you want to pull the curtain back and try to grasp what is happening behind the process that delivers math's whiz-bang results, read and savor these 92 pages.
Below is a recent, and excellent podcast interview with Devlin specifically on his experience with his first-ever MOOC course -- for anyone interested in MOOCs, this is must-listening, so set aside the hour required to hear Keith out. If you're not interested in MOOCs you can skip it… but if you're concerned about the future of education at all, you should be interested in MOOCs!:

http://pulse-project.org/node/492


The other Devlin book I just finished (stumbled upon in a used book shop) is an older work (1997), "Goodbye Descartes" which I'm tempted to call the richest work of Devlin's I've read -- chockfull of interesting discussion of logic, philosophy, linguistics, cognition, artificial intelligence… covers a LOT of ground. Once again, NOT necessarily much "mathematics," just a great deal of thought-provoking material related to the cognitive processes that impinge on mathematics.
The book ends with a subject Devlin christens "soft mathematics" -- I'd never heard of the concept before, so I'm not clear if it has gained much traction since he introduced it (and I'm not myself convinced of its utility), but you can never sell Keith short. The idea is that, just as there are 'hard' sciences (physics, astronomy, engineering…) and 'soft' sciences (sociology, psychology, economics….) we need a different sort of (soft) mathematics to study various human problems. If you don't want to wade through "Goodbye Descartes" (but you should ;-) you can read a synopsis of this particular idea from the below older Devlin column:

http://www.maa.org/devlin/devlin_10_09.html

an excerpt from it:
"There is little or nothing [in soft mathematics] that looks like, or is, traditional mathematics. There may not even be any mathematical symbols tossed around -- though in many cases there are. Soft mathematics is not mathematics as that discipline is generally thought of, and it remains an open question whether at some time in the future our conception of what constitutes mathematics will change to incorporate such activities…
"What is clear, however, is that the mathematical way of thinking is such a powerful one that, when applied in a soft manner, it has on occasion led to considerable advances in our understanding of various phenomena in the messy, and decidedly non-mathematical social realm of people. One of the best examples I have come across was in the field of linguistics…"
He then goes on to use Paul Grice's analysis of everyday conversations as an example of soft mathematics.

Anyway, while I found the notion of "soft mathematics" mildly interesting, I found the 10 chapters that preceded it FAR moreso!
I might say more about one or both these books at some point in the future (they contain so much grist for discussion), and also may have some more Devlin material coming up shortly... but, that's all for today.
...And Merry Christmas everyone!!!


Friday, December 21, 2012

Congratulations! John Allen Paulos


 Author and Temple University professor John Allen Paulos, author of "Innumeracy" (a favorite of mine) as well as several other books and writings, was awarded the 2013 Math Communicators Award given out by a joint group of mathematical societies recently (he'll actually receive it Jan. 10, 2013):

http://math.mit.edu/mathcomm/archives/john-allen-paulos-to-receive-math-communications-award/

The very illustrious list of past winners is here:

http://www.maa.org/awards/jpbm.html

Paulos won a similar award from the American Association for the Advancement of Science back in 2003.

Thursday, December 20, 2012

Monday, December 17, 2012

Geometer/Author Extraordinaire...


Who doesn't love geometry!!? (well, I know there are some of you, but I'm not sure I trust you ;-) ...I recently mentioned geometrician Alfred Posamentier's "The Secrets of Triangles" on my list of 10 books to consider during the Holidays for your math-enthusiast friends, and I was delighted to wake this morning and find that Sol Lederman's latest 'Inspired by Math' podcast is with Dr. Posamentier. They not only discuss his most recent book, but geometry and math education more generally, as well as some history; and also good to hear he has yet another new book on the way (on mathematical mistakes)!
This is a great interview with a great educator. It's 50 minutes, so you'll need to set aside some time (or just play it in the background while doing other Webby things), but ought not be missed:

http://wildaboutmath.com/2012/12/16/alfred-posamentier-inspired-by-math-13/

Thanks for another inspiring podcast Sol!

Saturday, December 15, 2012

Nerdy News...


couple more education tidbits today….

1) a "triumph of the Nerds" piece on Nate Silver (possibly you've heard the name somewhere lately) and the possible influence that his ascendency could have for improving math education:

http://blogs.kqed.org/mindshift/2012/12/why-nate-silver-can-save-math-education-in-america/

…a quick couple of lines therefrom:
"Math is taught as computation rather than a means of exploration and discovery. Instead of engaging in meaningful problems and learning in depth rather than breadth, kids are assigned frivolous, repetitive problems. And finally, the way math is generally taught has no relevance to real life."

"Sol Garfunkel and David Mumford in a New York Times Op-Ed summed it up nicely: 'Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering'."
2) I won't spend too much time focusing on the newly-opened Museum of Mathematics (MoMath) in NY city (since it is of somewhat local/regional interest, and there are a jillion articles available on it -- see HERE), but this NY Times article (which includes criticisms) is too good not to pass along:

http://www.nytimes.com/2012/12/14/arts/design/museum-of-mathematics-at-madison-square-park.html?_r=0

…and again, a quickie excerpt:
"For those of us who have been intoxicated by the powers and possibilities of mathematics, the mystery isn’t why that fascination developed but why it isn’t universal. How can students not be entranced? So profound are the effects of math for those who have felt them, that you never really become a former mathematician (or ex-mathematics student) but one who has 'lapsed,' as if it were an apostasy….
"The goal, each principal emphasized in conversations this week, was to show that math was fun, engaging, exciting. MoMath is a proselytizing museum. And despite its flaws, it is exhilarating to see math so exuberantly celebrated. And while fourth through eighth are said to be the intended grade levels, it is hard to imagine a younger child or mature adult not drawn in by some exhibits here. In many ways the sensations of the displays are more compelling than the explanations of their content. "
(p.s... one other thing I learned from the article, that I was unaware of, is that there is a Museum of Sex (or MoSex) nearby to MoMath!! -- insert your own joke here ______________).

Friday, December 14, 2012

Doors About to Open...

(Galton Board)

New York city's brand spanking new $22 million Museum of Mathematics (known as 'MoMath') finally has its public opening tomorrow, to begin exciting young minds about mathematics. No doubt there will be a slew of press articles (actually there already have been) on this grand new destination. Here is one from yesterday:

http://www.sciencefriday.com/blogs/12/13/2012/momath-exhibits-for-ending-math-apathy.html

From the article:
"While MoMath’s hands-on exhibits may get kids excited about math for the day, Cindy Lawrence, the museum’s associate director, wants that excitement to stick with them for the rest of their lives. She suggests that math isn’t just an interesting hobby--it’s a lucrative career. 'The biggest employer of mathematicians in the United States is the National Security Agency. There aren’t enough qualified people to fill the available positions. It’s the same for companies like Microsoft and Raytheon,' Lawrence says."
…I'm tempted to say, 'Ohhhhh, to be a kid again!'… but, then, in a sense, I've always thought those of us who love mathematics are already eternally kids!! ;-)

YouTube channel for MoMath:

http://www.youtube.com/museumofmathematics

Wikipedia page:

http://en.wikipedia.org/wiki/Museum_of_Mathematics

One of the earliest posts I ever did on this blog concerned my own childhood fascination with a large Galton box (or quincunx) demonstration at a museum in my home state many decades ago… The below George Hart video of MoMath gives a hint of how much museum demonstrations have progressed since then!:





Thursday, December 13, 2012

Thoughts From Marcus du Sautoy

Not sure how soon I'll have another Math-Frolic interview to post (awaiting for a couple to come in), but in meantime here's a recent quite long interview with Marcus du Sautoy, the wonderful British math popularizer, discussing, among other things, love, war, philosophy, language, prime numbers, Marxism, post-modernism, climate change, and MORE!!:

http://www.kindlemag.in/srorys_details.php?id=NTM3&&displayid=Nw==

One answer (of many) I particularly found interesting:
"...although I am a reductionist at heart and believe that everything can be reduced to maths but as I had already said, sometimes it’s not helpful – for example, the migration of a flock of birds, that can be reduced to a Schrodinger wave equation for every single particle inside that flock of birds, and if ultimately, I could solve that system of equations, it would tell me, that the birds are going to migrate from one place to another. But this isn’t the right language to explain that… sure… in reductionism, Schrodinger wave equations control that, but that’s the point about all of these different disciplines, actually, sometimes there is a better language to explain things, which are not fundamental physics or mathematics and  that’s what all of these hierarchies of knowledge are there for… sometimes you need to not have complete information… complete information can often just overwhelm you, and that’s where, as you said, maths stops and philosophy takes over and sometimes, yes, the language of philosophy is the right one to apply to a particular context, not the language of science or mathematics."
And also love the final sentence he closes with (in reference to Gödelian Incompleteness): "The amazing thing for me is that we have used our own methods, the methods of mathematical logic, to show the limitations of our subject."
So true!



Wednesday, December 12, 2012

3 New Rules For P-Values

               
                  P < .05

Statistical p-values have been (rightly) taking a battering in the blogosphere for awhile now, and "Neurobonkers" chimes in with a nice posting here, based largely on a paper entitled, "The Cult of Statistical Significance":

http://bigthink.com/neurobonkers/the-statistical-significance-scandal-the-standard-error-of-science

Succinctly he quotes others near the beginning of the piece: “In a nutshell, an ethical dilemma exists when the entity conducting the significance test has a vested interest in the outcome of the test.” It goes on to pass along 3 simple additional pieces of information researchers ought include in their statistical reportage.

...it also includes an hour-long video of a Charles Seife talk at end, as well as several additional good links.

Tuesday, December 11, 2012

Monday, December 10, 2012

What If....

P = NP...!

I've reported previously on the independent film "Travelling Salesman" and now Plus.Maths.org has posted a (23-min.) podcast with the writer/director of the award-winning film here:

http://plus.maths.org/content/sites/plus.maths.org/files/podcast/pluspodcastnov2012.mp3

The thriller movie has to do with the consequences for a world in which the P vs. NP millennium problem is solved by proving that P = NP.

Wikipedia page on the film here:

http://en.wikipedia.org/wiki/Travelling_Salesman_%282012_film%29

A review of the movie here:

http://www.examiner.com/review/travelling-salesman-walking-the-tightrope-of-morality-math-science

A more technical take on the film from KW Regan here:

http://rjlipton.wordpress.com/2012/04/22/the-travelling-salesmans-power/

And finally, homepage for the film here:

http://www.travellingsalesmanmovie.com/

Unfortunately, though the film has been out for awhile now on the festival circuit, I can't find any info as to actual schedule dates where it is playing, nor if it would perhaps ever get wider distribution? (if anyone knows where to look for a schedule of play dates please let us know).

Friday, December 7, 2012

Why Infinity Will Drive You Bonkers…



You have an infinite number of balls labelled from "1" to infinity.
At one minute to midnight you place balls #1 through #10 in a box and simultaneously the #1 ball is removed.

At 1/2 minute to midnight you place the #11 through #20 balls in the same box and simultaneously remove the #2 ball.

At 1/3 minute to midnight you place the #21 through #30 balls into the box, removing the #3 ball.

At 1/4 minute to midnight…....... removing the #4 ball.

...and you continue on with the same pattern. . . . .

How many balls are in the box at midnight???  At first glance it would seem there could be an infinite number, i.e. 9+9+9+9+…
However, for ANY ball "#n" that you might assume remains in the box, it can be deduced that THAT ball was REMOVED from the box at the 1/n-of-a-minute time point... thus all balls get removed; the box is empty!

I adapted this from a version at another site:

http://tonysmaths.blogspot.com/2012/12/my-current-favourite-infinity-paradox.html  

This is known as the Ross-Littlewood Paradox and you can read more about it here:
http://en.wikipedia.org/wiki/Ross%E2%80%93Littlewood_paradox

It is similar to a more involved Raymond Smullyan puzzle I've posted about previously (...if your mind isn't already blown):

http://math-frolic.blogspot.com/2011/01/seemingly-impossible-task-that-isnt.html


Thursday, December 6, 2012

Books Bought, Books Left Behind


Always fun for me to talk books….

I recently posted some math-related book suggestions for the holiday season, but then also played Santa to myself, ordering 4 books online I'd been considering for awhile:

 One volume was autistic savant Daniel Tammet's "Thinking In Numbers," which was on that prior suggestion list. It hasn't arrived yet, but I very much enjoyed Tammet's first two books, and expect to enjoy this one as well (Tammet's introspective analyses of how his own incredible mind works are usually fascinating).
 "The Mystery of the Primes" by Matthew Watkins is another British book which hasn't arrived yet, but I've seen consistently good reviews of it and it covers material I'm interested in. Looking forward to it.

 Am very pleased with the two books that have arrived: "Introduction to Mathematical Thinking" by Keith Devlin is a wonderful, succinct treatise on… drrrumroll… mathematical thinking. It's under 100 pages and by the end I expect to have a much better understanding of why so many of us get through elementary and high school mathematics with some ease, yet hit a brick wall in college math (Devlin's recently-completed MOOC course was based on this slim volume).
The other book received is an oldie-but-goodie: "Satan, Cantor, and Infinity" by Raymond Smullyan, another grand collection of puzzles and paradoxes by one of the Masters (and with a title like that, how could the volume be anything but good!).
I'm set for the Holidays!!

Lastly though, an oddball book I DIDN'T purchase, and not a math book...

I tend to think I'm acquainted with most of Martin Gardner's works, certainly his recreational math volumes and also his various essay volumes… but the man was incredibly prolific (over 100 books!), and apparently I've missed a few along the way:
Just today, browsing the used books in a thrift store I stumbled across, "Urantia: The Great Cult Mystery" by Martin Gardner (1995) …I could hardly believe my eyes! Martin Gardner found the time, the desire, the wherewithal to write a 400-page book on the Urantia Book and the wacky cult it spawned. Scanning through it, it seemed filled with his usual, detailed, meticulous writing as if he was addressing recreational topology instead of debunking a cult. It would probably have been worth the $1 price just to enjoy Martin's writing… still, I passed on this one.
But... I never cease to be amazed at how the man's mind worked!!

Wednesday, December 5, 2012

Education: The Times They Are A Changin'...


…Forgive an old 60's buff a little nostalgia:



Two wonderful links today (both just posted yesterday), one on the so-called "flipped classroom" and the other on MOOCs, two facets of the digital revolution we are witnessing in education:

1) Math teacher Robert Talbert summarizes his (positive) experience doing a "flipped classroom." I'll assume readers here know what the "flipped classroom" concept is all about, but if you don't you can read about it at the 2 sites below before going to Robert's piece (essentially the 'lecture' part of a class takes place at home off the internet from Khan Academy-type videos and the 'homework' or learning/problem-solving part takes place in the classroom with increased student-student and teacher-student interaction):

http://en.wikipedia.org/wiki/Flip_teaching
http://flipped-learning.com/

Talbert's post here:
http://tinyurl.com/afwdx5z

Some lines therefrom:
"Students were learning and it was not because they were listening to me. The flipped class has left me with a profound appreciation of how mysterious human learning is. Our reduction of learning to lectures, note-taking, and homework seems almost offensively simplistic in light of that mystery. I think our students need more of the mystery...

"I never had one remotely negative comment from students about how we were doing the class — and they had plenty of opportunities. In fact one student told me that he couldn’t see how this class could be taught in any way other than flipped. I think the flipped structure benefitted students in every conceivable way. It gave them more structured tasks to do outside of class, which helped their time management and cognitive load (especially the few students in my classes who had kids). It gave them time, space, and a social network in class to encounter difficult tasks and complete them…

"I’ve always felt that, within 5–10 years, we won’t be talking about the “flipped classroom” — we’ll just be talking about the “classroom”. This way of teaching, in other words, will be normative and it will be straight lecturing that will seem odd, out of place, and ineffective."
2) And then Keith Devlin once again perceptively touting the fast-evolving role of MOOCs (Massive Open Online Courses) in higher education:

http://devlinsangle.blogspot.com/2012/12/the-darwinization-of-higher-education.html

Again, several excerpts, from his long piece:
"…when you look a bit more deeply at the way MOOCs are developing, you see that the real tsunami is going to be a lot bigger than that. It's not just higher education that will feel the onslaught of the floodwaters, but global society as a whole…

"Right now, the most popular MOOCs draw student enrollments of about 50,000 to 100,000. In this it’s not unreasonable to expect those numbers to increase by at least a factor of 10, once people realize what is at stake…

"Right now, the media focus on MOOCs has been on their potential to provide (aspects of) Ivy League education for free on a global scale. But an educational system does more than provide education. It also identifies talent - talent which it in part helps to develop. That makes a MOOC the equivalent of Google, where it is not the right information you want to find but the right people…

"For those of us in education, MOOC education requires a major adjustment in attitude. Most of us go into the profession because we care about the individual. We love to interact with our students. Moreover, universities have all kinds of structures in place to catch and help struggling students. But in a MOOC, all of that goes out the window…

"If we are going to witness a tsunami, it is likely to be the true globalization of higher education and talent search."

For all in education we are living in an incredible time, with so much to ponder!

...And now (today), Keith has a new related post up at his MOOC blog (the above is from his monthly column for MAA):

http://mooctalk.org/2012/12/05/mooc-reflections-and-courseras-business-model/


Tuesday, December 4, 2012

One Heckuva Mathematician…

  …but not my grandparent :-(

Bernhard Riemann is likely my favorite historical mathematician (...and thus my adoption of his name for this blog); he is easily one of the greatest mathematicians who ever lived… no telling how much more he would've accomplished had he not died at the all-too-young age of 40.

 A biography of him here:

http://www-history.mcs.st-andrews.ac.uk/Biographies/Riemann.html 

And someone has put together this nice (10-min.) video tribute to
him (the treatment of the zeta-function/"Riemann Hypothesis" beginning at the 4:30 min. mark is especially entertaining):





ADDENDUM: This is WAAAAY beyond my neuronal capacity, but Dick Lipton/Ken Regan have just put up a seemingly fascinating new post concerning Riemann's zeta function for those able to follow it here:

http://rjlipton.wordpress.com/2012/12/04/the-amazing-zeta-code/




Sunday, December 2, 2012

Listen Up…

2 interviews for the price of 1 today (i.e. free!):

A new podcast (50 mins.) from WildAboutMath blog, this time with Ed Burger, Williams College math professor and co-author of  "The 5 Elements of Effective Thinking." This interview covers more than just math… if you are an educator, a learner, a thinker, or someone who's ever failed or gotten something wrong, this podcast should be of interest (if you don't fall into any of those categories, well, then just pass on it ;-):

http://wildaboutmath.com/2012/12/02/ed-burger-inspired-by-math-12/

And as long as we're in interview mode I'll throw in this bonus 2-year-old interview (15 mins.) from YouTube with some bloke named Strogatz who appears to know a bit about math ;-) (he talks about both math and writing here, including, if you're not already familiar with it, poignantly relating the story of his earlier book "The Calculus of Friendship"):




Saturday, December 1, 2012

Will Rogers, Humorist... and, Mathematician?

"When the Okies left Oklahoma and moved to California, they raised the average intelligence in both states." - Will Rogers

A new post from Richard Elwes on the "Will Rogers phenomenon," an interesting, yet simple situation that can arise when considering sets and averages (and sometimes a concern for epidemiological studies):

http://richardelwes.co.uk/2012/12/01/the-will-rogers-phenomenon/

(...it all reminds me a tad of "Parrondo's Paradox" from game theory, where once again straightforward mathematics leads to a somewhat unexpected result.)