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So resistance is futile: You will be derivitated! Or perhaps the Grateful Dead really meant to sing: We will de-rive. Oh well, I'm outta here...

Wow, Jennifer... great post. And how did you find that YouTube video? I searched for "calculus" and came up with this one -- voiced over by Don LaFontaine, no less: http://www.youtube.com/watch?v=wyAHmIesMlk

I read an article about gambling years ago, and a guy they interviewed had in fact found a way to make a living as a gambler - instead of gambling against the house, he would make bets on the craps game (or any other game) with other bystanders. Essentially, he was his own casino.

Clever guy! Don't try to beat the House, BE the House. It all sounds very Zen. :)

Nice entry.

Crapaud, not crap is frog in French.

Cheers,

Igor.

One of Australia's more notorious science presenters is often asked about gambling maths, and his point is that the key is to minimize the number of bets- preferably to one. So when interviewed on the topic, he advises folks who must gamble to take all the money they're going to spend*, drop it on a roulette wheel, and walk away afterwards regardless of the outcome.

*obviously you need to decide this ahead of time.

Your Aussie presenter is ignoring the "fun factor." See, it's FUN to shoot craps, so you want to get the most bang for your buck, i.e., lose money slowly over as long a period as possible. If one minute of heart-pounding excitement at the roulette wheel suffices for some people, so be it: place one bet on that. But I think it's a pretty boring game.

Jen said: The trick is figuring out how to tweak things to fit them to the abstract model. In other words: teach us to think like physicists.

This is an astute observation. I work on changing the way we teach our junior physics majors at the university. One of the things that I've seen, over and over, is the difficulty that these students have in translating what they learned in math class to what we're doing in physics. They take Calculus I, II, and III and can integrate with the best of them. But then they get into this electricity & magnetism class and they no longer have the integrals *given* to them, as in math class. Now they have to look at the physical problem (for instance, a charged ball) and decide *what* they need to integrate over. They have to take the physical situation and figure out how to apply the abstract models that they've learned. It's a real brain twist, and is what makes physics tough, at all levels. I mean, after all, once the equation is set up, many of us can calculate it. But which equation do we use, and what do we plug in for the little symbols? That's the physics of it.

Love the working title of the book; especially "the Dangerous Curves" part.

I hope your book goes into my school library when it comes out - so I can borrow it!

:)

"Your Aussie presenter is ignoring the "fun factor.""

Yes, he was a math major.

I'd been wondering how that video lecture course was going. Now if only they had one for linear algebra, I'd be all set.

***The Spousal Unit noted approvingly that there were actual equations/derivations involved in the lectures, so it wasn't just a lightweight "concept" course. Whatever. The two need not be mutually exclusive; a truly good teacher, like Starbird, will include both.***

In my experience (which is, granted, now a year out of date and becoming more so every day), there are two things about the c-word (conceptual, that is, not calculus). The first is that really teaching and grasping the concepts is quite difficult-- more difficult, as Eric Mazur might attest, than teaching how to play with the equations. And, the second is that most courses billed as "conceptual" are nothing of the sort, but are more "term memorization" types of courses. Sadly, the latter has given the whole notion of "conceptual" courses a bad name.

A professor at Vanderbilt observed that many incoming freshmen don't really *understand* algebra, even if they know how to do it. I saw this in my non-majors freshman, and indeed in retrospect remember *myself* working this way with math in college. Sometimes it's all a magical incantation that you do according to memorized rules, without really knowing why the rules work. (E.g. "cross-multiplying". I remember liking that in high school, because it was easy. When I started teaching freshman and heard them mention it, it sort of brought me back; once you really understand algebra, you don't think about it any more because it's just obvious.)

Of course, as you point out, most people don't study math for the pure love of the ideas, they use it a toolbox. So, even if you truly teach the concepts without teaching people how to use it, you're not really doing the subject justice. Then again, I'm not convinced that you really can get the concept of a lot of things in math and science without also having to be able to use it.... "I get the concepts, I just can't do the problems" is something students would say sometimes. Alas, they were wrong about the first part; if they can't do the problems, chances are they don't really get the concepts, they are just able to memorize the definitions. Sad that too often memorizing definitions is seen as getting concepts.

(Re: the Teaching Company, they contacted me to audition for them a bit more than a year ago. Alas, when I informed them that I was no longer going to be a professor at Vanderbilt, they were no longer interested in me.)

So you did your calculus and got a book out of it, too! Win-win.

OK, now you just gotta get vector calculus and differential equations down pat and you're ready to start with quantum mechanics.


When I was in, say, ninth grade, calculus was this mysterious thing in the here-be-dragons territory just outside the borders of comprehension. I knew, from science history books and such, that it involved taking smaller and smaller pieces of things, like breaking a shape into a zillion little slices to figure out the area of the whole, but as to how the ideas I'd received actually fit together, or how to apply them in any practical way to solve a definite problem, I didn't have a clue. I had to sit down and work through the textbook problems, one after the other, before it all "clicked". Now, integrating or differentiating is a routine action -- what would have been an exam question in AP Calculus is the step from equation 17.22 to equation 17.23 in a physics book. Thinking back over the change gives me a bit of a weird feeling. . . .

Oh, and you can get a fair number of free video lectures from MIT's OpenCourseWare programme, such as these lectures on linear algebra:

http://www.youtube.com/view_play_list?p=E7DDD91010BC51F8

Excellent post. Throughout my years of learning math at many levels as well as physics, I have always disliked the 'bottom up' approach of teaching a bunch of tools first, with little or no discussion of their application or relevance, before teaching problem solving involving the synthesis of those tools. This method isn't how physics and mathematics evolved as disciplines and isn't how one approaches most science. Rather, one first identifies the problem to be solved and breaks it down as necessary until one is able to solve it, using either existing tools, or creating ones own.

Disassembling a problem generally isn't something taught until later in ones learning career, when the act of disassembling is what gives context and validity to 'spherical cow' and 'vacuum world' assumptions, and, thus, removes, or at least explains, the seeming disconnect between real life experience and that studied in physics courses. Likewise, this disassembly can help remove the 'mysticism' surrounding calculus to demonstrate that the seemingly abstract concepts have a solid grounding in day to day existence.

A favorite example of my own was an epiphany I had while taking a class on Fourier analysis is that our brains perform Fourier transformations constantly in that everything we see and hear is transposed from a time domain into a frequency domain. We perceive light and sound not as rapid fluctuations in time, but as (relatively) constant signals. We don't see one color as 'faster' than another, just different. Neither do we hear different pitches as faster or slower, but rather higher and lower. This I find fascinating.

And speaking of the calculus of sound: http://calculusthemusical.com/audio/

Take a look that this blog: http://betterexplained.com/

He explains calculus (and mathematics in general) in a really accessible way.

Great post. Your calculus is excellent even if your Greek is not. Miso means hate. Gyn means woman. Thus misogynist. Your "mathogynist" comment, while funny, translates "woman who does math" and I don't think this was your intent. You'll want to go with "misomathist" if striving for accuracy (as "misomathogynist" would be "person who hates women who do math"). And, now that you've conquered this, be sure to visit Philomath Oregon sometime when you are wandering around the pacific northwest ;-)

I was not striving for accuracy, merely playing around with a pun -- although I am, technically, a woman who does math! Sometimes.... It's always the science types -- including the Spousal Unit -- who feel compelled to point out that "mathogynist" doesn't make sense. :) Rest assured, I will (probably) not be using the term in the book...


I thought the pun was very funny even if it didn't compile in the translation portion of my brain. In this case, note that it is a theologian rather than a scientist quibbling with your root choices. Though, I guess if you want to get medieval on me, in the 14th century theology was called "the queen of the sciences" ;-)

Jennifer, I've found the perfect t-shirt for you to wear while writing that book. "I'm an English Major, You do the Math" It's available at www.mentalfloss.com

Thani you! I had that t-shirt in college and have been looking for a replacement because of the book. Although the Spousal Unit bought me a fantastic t-shirt to reflect my new change in attitude: "YOU MESS WITH CALCULUS, YOU MESS WITH ME!"

Rob, good to hear from you! I've actually used the phrase, "I get the concepts, I just can't do the problems" in the past. I think we mean different things by it: we mean that we get the basic idea of what it's supposed to be/do, we just can't make the critical connection to how that gets translated into a meaningful problem with a solution. Which as you say, means we don't "get it" at all. And we know it. :)

Blake, Sean said the last pieces of the calculus puzzle really finally clicked for him when he used in physics, too. Which makes me wonder why schools don't just teach them together... or at least offer that option. These are two subjects that really shouldn't be segregated...

Ben, one of the chapters of the book deals specifically with the Fourier transform, illustrated by surfing (wave dynamics), and of course, sound. That's actually how this all got started. I wanted to write a book on acoustics, decided I needed to learn the Fourier transform to do justice to the topic, which meant I had to learn to calculus. And an entirely different book grew out of that. C'est la vie.... But I loves me some Fourier transforms! :)

And Andy, the vector and differential stuff will have to wait; got my hands full with the book at the moment. But we'll see! I do have an in-house tutor, after all, to help me over the rough spots....

Jennifer, Why is it "the calculus" and not "calculus"? You should discuss this in your book. Seriously.

All kinds of perfectly normal people (seriously normal!) can discuss calculus just fine, but as soon as the question of who invented it first - Leibniz or Newton - they get all fancy and start dropping "The calculus"'s all over the place. Seriously. Why?

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    • Heavy G
      The perfect pick-me-up when gravity gets you down.
      2 oz Tequila
      2 oz Triple sec
      2 oz Rose's sweetened lime juice
      7-Up or Sprite
      Mix tequila, triple sec and lime juice in a shaker and pour into a margarita glass. (Salted rim and ice are optional.) Top off with 7-Up/Sprite and let the weight of the world lift off your shoulders.
    • Listening to the Drums of Feynman
      The perfect nightcap after a long day struggling with QED equations.
      1 oz dark rum
      1/2 oz light rum
      1 oz Tia Maria
      2 oz light cream
      Crushed ice
      1/8 tsp ground nutmeg
      In a shaker half-filled with ice, combine the dark and light rum, Tia Maria, and cream. Shake well. Strain into an old fashioned glass almost filled with crushed ice. Dust with the nutmeg, and serve. Bongos optional.
    • Combustible Edison
      Electrify your friends with amazing pyrotechnics!
      2 oz brandy
      1 oz Campari
      1 oz fresh lemon juice
      Combine Campari and lemon juice in shaker filled with cracked ice. Shake and strain into chilled cocktail glass. Heat brandy in chafing dish, then ignite and pour into glass. Cocktail Go BOOM! Plus, Fire = Pretty!
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      Dr. Strangelove's drink of choice.
      3/4 Triple sec
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      Fill shot glass 3/4 with Triple Sec. Layer Bailey's on top. Drop Grenadine in center of shot; it should billow up like a mushroom cloud. Remember to "duck and cover."
    • Mad Scientist
      Any mad scientist will tell you that flames make drinking more fun. What good is science if no one gets hurt?
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      1 oz Southern Comfort
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      1/2 oz sloe gin
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