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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…
(Speaking from my experience as a calc teacher at a big U.S. state U.; mileage may vary elsewhere) Most non-STEM students won't see the 'Calculus I, Calculus II, Calculus III' that starts the essay so dramatically. Increasingly, liberal arts students are able to get by with no more than a "math appreciation" course and maybe what amounts to high school algebra. The "math appreciation" course might actually touch on v…
I've had linear algebra from the onset in my engineering school and it was wonderfully useful. Comparing which one is "better" (calculus or linear algebra) is like arguing whether multiplication or exponentiation is a better operation -- don't do it, you're going to sound cliché without reaching a conclusion. The main use of linear algebra to me is describe local behavior of functions/dynamical systems. Sure, calculu…
Possibly understated... not only is there the three course sequence + diff eq, there's usually also a two-sequence real analysis course (more or less "careful calculus") and probably either PDEs or complex analysis to boot. I took the discrete emphasis when I studied and I think I actually ended up with fewer discrete classes (5, IIRC) than calculus classes (6).
I watched Prof. Strang's Linear Algebra courseware, great stuff. He is a wonderful teacher. http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... As someone who hadn't studied it for 20 years, it was invaluable to revisit the subject as an adult with the ability to reflect "ah, I can use that for... " instead of "Ok but when am I ever going to use this"
I ended up scoring one of the highest grades in the class.
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I've had linear algebra from the onset in my engineering school and it was wonderfully useful. Comparing which one is "better" (calculus or linear algebra) is like arguing whether multiplication or exponentiation is a better operation -- don't do it, you're going to sound cliché without reaching a conclusion. The main use of linear algebra to me is describe local behavior of functions/dynamical systems. Sure, calculu…
I'm unfamiliar with it: what is the cliché about multiplication vs exponentiation?
I really can't agree with this strongly enough. I had enough Calculus and Differential Equations courses to kill a horse in college (Chemistry major) and I've never used that knowledge once in my entire programming career. But I find uses for linear algebra and matrices in coding all the time. Thank god Strang's excellent course is available online for free.
heh, try teaching galois for a year, you'll understand why calculus is so popular.
it's a beautiful branch of mathematics though.
can't image teaching point-set topology, teaching uryshons proof to undergrads, gee.
I also had to go through a lot of heavy calculus courses which were very proof-centric and built from first principles. Rarely we skipped a proof of a theorem and we were expected to be able to reproduce and understand all of them at exams. I hated it often back then. However, these days I can appreciate the rigor it has taught me and I would wish I could send some of the programmers I met to similar courses so that they would learn to think clearly and precisely and be able to spot unmet or missing assumptions.
Our teachers and the creators of the curriculum were not stupid or naive. They knew well how much of hands on calculus we would use in practice vs. algebra or linear algebra. One of their main reasons for including calculus was to teach us rigor. I know that once someone overheard two teachers talking - the calculus teacher was asking someone from a CS department what to teach the CS graduates and the reply was that he can teach us whatever he wants, he just should make sure to teach us to think. I think they were quite successful at it even if it wasn't a very pleasant experience for most.
That also reminds me of this very relevant and true comic: http://savethepenguins.net/image/237344573 ("Wtf, man. I just wanted to learn how to program video games.")
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I'm amazed that you say that calculus has had a much greater impact on society when virtually every database, graphics manipulation or economic analysis uses principles of linear algebra. Can you substantiate "millions of transfer students between thousands of universities every quarter"? That seems like outlandish hyperbole. Irrespective of the precise number, a system with momentum is not sufficient justification f…
FWIW, I have a math degree and work in tech. Both are incredibly important. I would say that linear algebra and discrete methods are more important for computing, but calculus has had a larger impact on science especially physics. Newtonian physics - a revolution in thinking and unification of mathematics and science - is intricately tied to calculus. Even in the example of economics that you cite, calculus is used h…
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…
Hey, thanks!