What do you think Hubski users? Are there more benefits to students in modern day math classes for Linear Algebra rather than the succession of calculus classes?
It seems to me that much of Linear Algebra is more helpful in many applications. Including things like computational physics, electrical engineering, or general computer science.
I certainly missed out on Linear Algebra in school; I don't even know what it is. My favorite paper on math education is "A Mathematician’s Lament" by Paul Lockhart. He argues that math should be taught like art, for fun, rather than as a science. I described how it gave me the nudge I needed to get to the bottom of a Project Euler problem. (The link in my post now goes to a collection of articles by Keith Devlin which looks worth perusing.)
If you liked "A Mathematician's Lament" I would suggest reading Lockhart's "Measurement" which is a followup which introduces (mostly geometrical) concepts leaving the student to write (and improve upon) their own proofs. It's a very cool idea and I enjoyed it.
Thanks for the recommendation. I just sat down with a cup of coffee to look it up and read it ... and found that it's a 416-page book. So I owe you a proportionally bigger "thanks" for recommending so much more content than I expected! I will add it to my wish list. A (mostly positive) reviewer notes "With Measurement, Lockhart demonstrates how much more difficult it is to do something right than to point out the flaws in how others are doing it." That's a truth I would like to see more widely observed (perhaps even in that review).
The author's Essays in Linear Algebra is great, anyone with an interest in math (or taking a linear algebra class!) should read it, but I don't think we need to stick undergraduates with more linear algebra. I had two semesters of linear algebra, plus a good chuck of calculus 3 and 4, plus a good chuck of the second semester of analysis, plus a good chunk of numerical analysis, plus ... Linear algebra isn't that complicated in itself. It's well worth giving a lower-division class in the basic theorems, geometric interpretation and matrix-juggling, and an upper division class on vector spaces and noncommutitive rings (because they get shorted in intro to modern algebra classes), but there doesn't need to be more than that. The theory doesn't get any deeper, or rather when it does it becomes something else. Linear algebra's applications are best covered in the classes on the subjects where those applications belong; the physics, engineering and computer science departments will cover them better, and students encountering them there are more likely to care about the application.
Yeah I think this is a good point bfv, the mathematics ends up colliding with other maths and as you say "it becomes something else" I know that the math professors are, for the most part, scared of applications based mathematics[1] and favor "pure mathematics" but I think there is something really to be said for teachers using applications to solidify an idea. [1] This is a joke, mathematics professors are really only scared of one thing: x^2 + y^2 = (x + y)^2