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Too Much Calculus – Gilbert Strang (2001) [pdf]

www-math.mit.edu

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Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#55

Post by dcosson »

ekidd wrote: post #7

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's…

Thanks for the link to the book.

I had a similar experience where my college linear algebra class was not good, taught by a grad student who seemed to have no enthusiasm for the material or for teaching, plus his accent was hard to understand at times. It was also the first exposure to proofs in the math curriculum so from the beginning I remember being overwhelmed by those and totally losing sight of the forest for the trees.

I sat through the whole semester thinking it was a pretty useless subject. My senior year I happened to take a machine learning and a quantum mechanics class at the same time and had a big ah-ha moment when I realized how big a role linear algebra plays in such a wide range of subjects. I went back through my old textbook and notes at that point and that new perspective made a huge difference, it was like it was completely different material and it was a lot easier to understand.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#56

Post by jmilloy »

jeffreyrogers wrote: post #48
jmilloy wrote: post #33

> We need to present the mathematics that is most useful to the most students. I wish it weren't this way! Mathematics is a wide and fascinating field, and I think more students could find interest if our schooling reflected that. But moving some of the detail and drudgery that is the calculus sequence to subject matter that requires it, in order to make way for linear algebra, is a great start.

I agree completely, but calculus touches so much of advanced math that at some point you have to learn it in depth (assuming you actually want to learn advanced mathematics). I'd argue that linear algebra is a more interesting subject for most people, but calculus contains more important ideas that are crucial if you intend to continue studying mathematics.

I have a major in Mathematics, and I truly didn't need calculus after the multivariable/vector calculus course I had to take my Freshman fall. Why did I have to do so much if it wasn't going to be necessary until graduate school at the earliest, or perhaps never depending on specialization? And why was it a prerequisite for my other math courses (in algebra, topology, real analysis, number theory, and combinatorics)?

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#57

Post by sporkenfang »

ekidd wrote: post #7

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's…

BLESS YOU. I have a computer vision exam on Tuesday. Naturally, the prof is awful at explaining math and only seems to care about the theory part.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#58

Post by tel »

You can probably do worse than to cut mathematics up into "algebra" (not just linear) and "analysis" (calculus). They're almost completely diametric points of view by the bulk modern mathematical canon [0].

There's a fair point to say that one shouldn't learn so much calculus as to lose your linear algebra, but the opposite is just as true. There are a lot of comments in this thread along the lines of saying that linear algebra is far more useful than calculus in CS. This statement feel not exactly unfair but certainly like it's a reactionary measure.

Whenever you have a notion of change you have some kind of calculus underlying it. Even if you end up having to view that notion of change algebraically. For instance, there's a famous functional programming result that there is a well-defined "derivative of an algebraic data type" which allows you to talk about changes in data "over time".

I'd also feel very bad for anyone who tried to learn too much probability without studying quite a bit of calculus first.

[0] Sure there's discrete calculus and algebra underlies the mechanism of most calculus computation. Likewise there are continuous groups and you can't avoid how topology mixes the two concepts.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#59

Post by ams6110 »

ekidd wrote: post #7

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's…

As a programmer, I've used calculus and linear algebra exactly never in my professional (20+ years) career. It just doesn't really come up doing web apps, sysadmin or dba work.
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