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# For All You Math Geeks, from Jeff Watson

January 16, 2011 |

Here's a superb video course on calculus in 20 minutes, but unfortunately it only includes 9 minutes…

Here's a calculus video done to Queen's "Bohemian Rhapsody"

Another "Bohemian Rhapsody" video that teaches and parodies integration by parts.

This parody of "I will Survive", "I will Derive" is very entertaining.

A parody of M.C. Hammer's song, "Can't Touch This," "U Can't Graph This"

Not to leave out the rappers– "This Is Why I Graph"

Another good rap song, "Take it to the Limit"

These videos make a good argument that the total decline of education

and learning, the dumbing down, has been greatly exaggerated.

# Comments

4 Comments so far

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I think the dumbing down of college math has been vastly understated not exaggerated. Here briefly are the reasons.

1. Limits without epsilons and deltas makes no sense. Symbol pushing can only go so far and very unreliably.

Differentiation is presented as a mere algebraic rule and the fundamental theorem of calculus is an abstract statement founded on basically nothing that students can easily use but must accept like manna from heaven just like high schoolers who learn to sing the quadratic formula or Pythagorean theorem. I’m not saying we all learn Dedekind cut arithmetic first or do metric spaces first but it stuns me how nearly all students believe they know what a limit is and how it’s “obvious”. They learn multiple recipes for telling whether this function of that converges to some value but have no notion of what convergence means in the first place. Same with continuity.

2. There isn’t anything even resembling problem solving. There’s plenty of exercises but nothing very helpful in learning how to reason. This is perhaps the most dangerous drawback of the present curriculum because it persuades students they have a level of expertise they simply don’t possess. An example of a problem… How many unique ways can one make $1.00 out of pennies, nickels, dimes, quarters and half dollars? How many many unique 6 digit licence plates can be made if each plate is different from every other in at least two places? What’s the ratio of the volume of largest possible sphere contained inside a pyramid to the volume of the pyramid itself? Such problems are elementary and require no special background. Sadly, these problems which some (maybe most) teachers cannot answer correctly are dismissed as “not advanced enough”. Thus the circle of boredom is unbroken and students are taught “related rates problems” and made to believe they’re actually thinking and accomplishing something.

3. The choice of topics is horrible. Without going into anything too deeply linear algebra is by far more useful to science than calculus. Calculus should be taught but I think the method needs to improve. Books in Discrete Math (Rosen) are excellent and they would do well to bring Rosen’s ideas into a calculus curriculum. This might lower the pool of students willing to take the course by a factor of two but do we go on pretending were doing something we’re not? Give the students who wouldn’t take such a calculus course something real and appropriate to their level of learning. Nearly all mainstream calculus books are abominations and should be burned. Even crappy Schaum outlines are superior to most of those monstrosities.

Math was a rather hard subject in the 70’s and it still remains rigorous. I suspect that the people who would have had a problem solving an easy third order differential equation in the 1970’s would have the same problem today, and vice versa. I still look at college texts of higher math courses and they seem to be basically the same as the 1970’s but there has been more computer stuff added. Algebra books are still garbage, but they were garbage since I can remember. There has never been a crowd of people beating a path to mathematics, and I suspect that there never will. Most people minor in math, much like I did, to complement their major studies. Since they need their practical usage of the math, the absolute proofs might not be necessary for an engineer, physicist, or chemist. Take the course of differential equations….the engineer might only need a high level overview with familiarity of everything, but he would need to really know and use the “big three” DifE’s such as heat, wave, and Laplace.

But then again, Wolfram has programs that can do any integration, differentiation etc. Perhaps higher mathematics is becoming arithmetic, and we can use a box to do our integration such as here. http://integrals.wolfram.com/index.jsp Tools like this might free up our minds to concentrate on other, more important things. Seriously, this Wolfram Mathematica program has brought high level, advanced mathematical capabilities to the masses, and that cannot be a bad thing. Obviously, with Wolfram, they designed their engine because they responded to a free market need. Somehow, I predict that if the invisible hand determines a need for more mathematicians, there will be more.

I have often wondered about the dumbing down of America. I also wonder why there never seems to be a dumbing down of Canada— or any of the other countries written about.

Is this because people look at the United States as their leader… though they don’t want to acknowledge it? Or is it because the United States is so infested with centered-selves that it doesn’t really care about any other countries?

It could also be that all these other countries are so damn smart that they are free of the dumb…. or, they are dumb and hate it and attack the smart.

Other possible explanations and probably the most likely: no American is going to write about the dumbing down of Canada, because he would probably get beaten with hockey sticks after crossing the border.

AND…. the United States is still the best market to sell to. After all, most of the major publishers are in the United States and who wants to read about the dumbing down of Canada? Certainly not a Canadian (especially if it is written by an American, and probably not even if it was written by a Canadian,) nor an American. But we all want to read about how dumb Americans are becoming.

Regarding education: Math is very important, but I think the dumbing down of America has much more to do with an over-reliance on specialization, and an under-development of the necessary education that holds the foundation up.

Many people today, (especially the younger generation,) are somewhat indifferent to serious political problems. But, their “who cares” — is dangerous. Maybe what is worse though, is the hubris they receive from the guise of distinction or education their chosen speciality gives them.

Whether it’s a PHD or money in the bank that society uses as its gauge, are they really all that much smarter than their ancestors? What is education? And what sort of education does a healthy country need for its citizens to sustain their families lives and freedoms?

This leads me to think that maybe what we are suffering from today is unknown hubris and self importance. We need more doubt and questioning.

“This leads me to think that maybe what we are suffering from today is unknown hubris and self importance.”

Who’s “we”? Are you included?