Since the introduction of open lectures by progressive thinking educational institutions like M.I.T., Stanford, Duke, Yale, and others, many exceptional presentations have bubbled to the top and should be watched.

Here are five must see open course video lectures as recommended by Virginia Heffernan of the NYTimes.

1. Walter H. G. Lewin, Powers of 10, M.I.T. (At about 2:40 watch Power of Ten video that is cut from the lecture)
2. Randy Pausch, Really Achieving Your Childhood Dreams, Carnegie Mellon
3. Dan Ariely, Predictably Irrational, Duke and M.I.T. (the rest of his short clips)
4. Langdon Hammer, Modern Poetry, Yale
5. Christine Hayes, Introduction to the Old Testament (Hebrew Bible), Yale

I also recommend Mark Schlissel, Introduction - The Cell Theory, Bacteria, Animal Cells, Evolution (Viruses and Midochondria). (The good stuff starts at about 13:00).

I listened to about a quarter of all the lectures from this course—most of which were over my head, but the first and second (mp3) classes are fascinating and make me wish I studied biology at school.

Remember the audio track I linked to awhile back about 0.02 dollars not equaling 0.02 cents? “Eyeless Writer” has done some follow-up research:

I did some research in early 2007 for an article that I ultimately never got around to publishing. It was a follow-up article to the story told by VerizonMath.com, where a customer recorded 6 different Verizon managers quoting a rate 100 times less than they actually charged, and then not being able to see the mistake when it was pointed out to them. The results of that research—an informal survey in which I called Verizon’s sales line 56 times—are as relevant now as ever. With the recent battles between Google and Verizon Wireless over so-called, “open networks”, now seems like an excellent time to wonder exactly how bad a phone company can get if they’re allowed to trap their customers. This article seems like pretty good evidence that Verizon Wireless should not be the entity deciding future wireless laws.

Here is a video made by “Eyeless Writer” that compiles those 56 calls to Verizon Wireless and asks them to answer two questions about their rates. The operators misquote Verizon’s rate 93% of the time.

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Quick, which is more pizza: two 8″ pizzas or one 12″?

The story of how a little bit of (what turns out to be easy) geometry saved a guy some money (and who says you’ll never use math in real life?)

P.S. If pi seems too difficult to multiply, just round down to 3, it’s close enough.

As a follow-up to the recent Malcolm Gladwell speech at the New Yorker 2012 conference, here is a documentary all about Fermat’s Last Theorem (wikipedia) and its proof by Andrew Wiles in 1994.

Even if math isn’t your thing, there is something intriguing about following Wiles’ seven year struggle to solve the mystery. In general I get a bit of a rush out of the beauty of mathematics but watching Wiles create a proof for Fermat’s Last Theorem was just magical.

Hit play or watch fullscreen at Google Video.

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Math skills are not Verizon’s strong point. A man patiently relates his bill problem to Verizon Wireless for 22 minutes, but unfortunately Verizon doesn’t know the difference between .002 cents and .002 dollars. It would be funny if it wasn’t so aggravating. Listen and despair.

See verizonmath.com for more.

Rick Garlikov has written a compelling piece titled, The Socratic Method: Teaching by Asking Instead of by Telling. In it he demonstrates the power of the Socratic method (teaching by asking) for both teaching and also for getting students involved and excited about the material being taught.

It’s a very absorbing read—my only complaint is that he hasn’t formatted the story into nice readable columns, but if you resize your browser window and give this one a chance, I think you may find it very interesting. It works on many levels: as a method for teaching, a lesson on binary numbers, and how important it is to ask the right questions.

From the sound of this article from physorg.com, Dr Norman Wildberger, a University of New South Wales academic, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit.

Does this mean schools the world over will be updating their curriculum? It makes me happy because I was one of those students that memorized the old rules for trigonometry long enough to take the tests and then promptly forget about them. I hope it’s safe to assume these new rules can be applied to computer programming and physics as well.

Zero by Zero: Quote: “Our society seems to be very technologically advanced. Looks like everything has been thoroughly studied but the depths of the oceans. Our mathematics is so advanced that it’s mind boggling to many people. We have built buildings way high in the sky. Bridges longer than many cities. Obviously we are capable of great technological know how. And yet it saddens me to bring this topic up at such a late stage in the game. Yes the old division by zero problem. [...]“

I was always bothered that my calculator came up with an error when it seemed logical enough that the answer was actually 0. I guess I should never have automatically assumed that all the math teachers I ever had were right.