Dr. Robert Ghrist, professor of mathematics at U Penn is writing a Calculus text–the *Funny Little Calculus Text* (FLCT for short). The FLCT not your typical Calculus text. Check out his incredible, artistic, funny, and mathematically elegant work-in-progress here. He currently has completed these short little chapters, all of which are a delightful read:

Ghrist lectures in a similar style, with a tablet PC. And yes, his handwriting is really awesome.

**NOTE: I’m updating this post today (1-10-2013) because I’ve just noticed that Ghrist has placed these files behind a (very low) pay-wall. They are STILL worth checking out!! Pay for them for goodness sake! đź™‚**

*[Hat tip: Matthew Wright–my good friend, and one of Ghrist’s grad students]*

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Gaa, my eyes are bleeding from attempting to read that polychromatic ocular assault and its scripty stylings. Tell him to watch his back in dark alleys behind the art-department or he may be viciously assaulted by typographers.

I guess you’re entitled to your opinion, Tim! I think it’s much more engaging than any Calculus teacher’s notes I’ve seen before. I like it!

I’ll agree the content is much more engaging than your typical calculus text, but those gains are decimated by the presentation (mostly font/color choices). General rules of typography suggest that for print, one use sans-serif fonts for headings, serif fonts for body, and “script” (or “decorative” fonts, as he seems to use for the entire body) sparingly for emphasis (for lower resolutions found on screens, typography guidelines generally suggest sans-serif fonts for body text).

But reading more than about 3 pages of chapter 1 made me surrender to save my eyes/sanity, despite enjoying the content.

Is Tim aware that the text was generated in front of the students’ eyes as he spoke?

I really enjoyed Ghrist’s lectures on applied Algebraic Topology which he did in this way. Best lectures on that topic that I’ve ever heard.

So maybe this static version misses the nuance and inflection of the actual lecture.

OK, I finished the 3 chapters. Only one “error” found. Other infelicities.

sqrt(x) is a function despite what Dr. Ghrist says. If you want to invert y^2 = x, then you should write (*) y = +- sqrt(x). The sqrt(x) is a function. The +- says y could be either sqrt(x) or – sqrt(x). The equation (*) is a shorthand for y = sqrt(x) OR y = – sqrt(x)..

There’s some disagreement among math teachers:

http://www.purplemaths.com/learning/viewtopic.php?f=8&t=1448

about this.

But I am telling you what the standard is.

And I am also simiplifying, by saying that a function can’t be multivalued. We COULD call y = +- sqrt(x) a multi-valued function. But mathematicians are more likely to call it a (SINGLE-VALUED) function whose range is 2^R (that is, the power set of R). In that way, y’s value is { sqrt(x), -sqrt(x)}, which is a single thing, namely a set of real numbers.

Ghrist implies that he knows this by talking about functions of 2 (and later 17) variables which produce ORDERED pairs as output. My comments above simply generalize his examples to unordered pairs.

This problem arises again inn Chapter 3 when he defines antiderivative. AN antiderivative is not THE antiderivative, yet one may say that THE antiderivative is the SET of all functions which differ from one antiderivative by some constant.

Ghrist also uses some meaningless notation which he probably explained orally. E.g. in Lecture 2, he says “N(t=0)” when he means “N(t) when t=0.” N is not a function of truth values. Of course every mathematician uses this shorthand, but newbies can be confused.

Other “little lies” are forgivable at this level. E.g. he says in Chapter 3 that there is no algorithm for calculating an antiderivative. Wrong: Joel Moses in his MIT PhD thesis presented such an algorithm, which either presents the antiderivative or says that it cannot be expressed in terms of elementary function. Moses’s algorithm forms the basis for Derive, Maple, Mathematica, and other Computer Algebra Systems in their antiderivative modules.

As he says on pge 5 of Chapter 2, the book is designed for those who have already had Calculus. I don’t think that it lives up to his promise to write a book that explains the “why” instead of just the “what.” It looks like all “what” to me.

Good comments, dad.

Here are some of the things I appreciated about his pedagogy:

1. Using Taylor series for everything (derivatives, second derivative test, limits, L’Hopital’s rule).

2. His straightforward approach to differential equations. He presents some of the large concepts of ODE very clearly and concisely.

3. His interpretation of differentiation and integration–not just ‘slope’ and ‘area’. I’ve come to really prefer the ‘mass of the rod’ interpretation for the definite integral, too.

4. His vocabulary and humor. He even uses Greek along the way :-).

Re 1: That’s the way Newton did it. If “ontology recapitulates phylogeny” then that’s a good way to go. And I like it. Euler liked it. All “elementary functions” (technical term) can be handled fearlessly that way, even though it wasn’t until after Euler’s day that this was known.

Re 2. I agree that it’s clear & concise. I just wonder whether too concise. It reminds me of those plastic pages we used to be able to buy: Calclus I entirely on two sides of 8.5″11″. It can only summarize.

Re 3. Right.

Re 4 Vocab: I like it when teachers don’t talk down to students by avoiding big words. Humor: Not everyone appreciates it; I very mujch do; I suspect that those who like that kind of humor and the same kinds of folks who like Calculus, so this course may be designed for math majors. Greek: same comment, appreciated by those who want to learn, but seems like “snow value” for those that don’t. I always refer to the Greek or Latin primarily to provide mnemonic aids. E.g. elliptical, hyperbolic, parabolic, radical are all words of ordinary English specialized by mathematicans, as I said at

http://home.messiah.edu/~chase/mthessay.htm

I finished all the chapters and it was very fun to study them. Nice entry.