Too Much Calculus – Gilbert Strang (2001) [pdf]
www-math.mit.edu
Too Much Calculus – Gilbert Strang (2001) [pdf]
1–10 of 137 posts
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#2heh, try teaching galois for a year, you'll understand why calculus is so popular.
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#3I 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"
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#4Possibly 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).
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#5heh, try teaching galois for a year, you'll understand why calculus is so popular.
it's a beautiful branch of mathematics though.
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#6Perhaps amusingly, the Computer Science education at the University of Copenhagen includes no mandatory Calculus course, but it does include a Linear Algebra course. Even so, students have a hard time seeing what they'll use Linear Algebra for, before later on in their education.
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#7As 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 free textbook:
http://joshua.smcvt.edu/linearalgebra/ (GFDL license, LaTeX source available)
(I get nothing out of recommending this open source textbook other than the joy of sharing a book I loved.)
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#8i actually have taught some linear algebra concepts on youtube and have gotten several hundred thousand views and some positive feedback. i think the key is trying to figure out a framework of intuition to help students through all the math but i liked the idea of four key equations we are trying to solve as a framework as well
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#9Perhaps amusingly, the Computer Science education at the University of Copenhagen includes no mandatory Calculus course, but it does include a Linear Algebra course. Even so, students have a hard time seeing what they'll use Linear Algebra for, before later on in their education.
I think this observation highlights the problem with Linear Algebra, the applications aren't encountered until upper level courses in other fields, and then they teach what you need to know for the course.
I took two semesters of Linear Algebra in college, the first course was an overview for physicists and engineers and was little more than the mechanics of matrix operations, and find eigen vectors and eigen values. The second course focused on Linear Algebra as an abstract algebra, with near zero application. Subsequently, reading this paper[1] and the way the author used Linear Algebra blew my mind, why wasn't I taught about THAT kind of Linear Algebra?
I suppose my examples illustrates: great teach Linear Algebra, but what facets to concentrate on? Abstract or concrete applications?
[1] http://www.geometrictools.com/Documentation/IntersectionSphe...
Re: Too Much Calculus – Gilbert Strang (2001) [pdf]
#10(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 very neat topics for these students (mathematics of voting, etc.) so I'd say math curriculum has already been successfully reformed for them.
As for the average STEM student, in my experience, most freshmen wouldn't be ready for linear algebra (unless by "linear algebra" you mean "matrix arithmetic"). They have enough trouble understanding functions in Calculus I: linear algebra's "functions are basically matrix multiplication" feature would NOT help.
Another thing to keep in mind is calculus has had much more impact on history/society than linear algebra. The fundamental theorem of calculus is a legitimately earth-shattering breakthrough: none of the theorems in linear algebra come anywhere near it in cultural importance.
Pragmatically, calculus is the most suitable mathematics for the type of testing-oriented, uniformizable/transferable pedagogy that a university really (in cold practical terms) must depend on for first-year students. It would be extremely difficult to force the kind of uniformity onto linear algebra that would be necessary if you seriously want to have millions of transfer students moving around between thousands of universities every quarter, gossiping about which linear algebra teacher gives the easiest grades, etc.