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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…
Earlier quoted context omitted.
Finding out the Fourier transform was a way to multiply matrices was a mind blower :)
I suppose you mean this? http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr... I was a bit confused by your statement. You mean that the FFT can be done by matrix multiplication? I tried to interpret your statement the other way around, that you can somehow transform two matrices before you multiply them, trying to fit it into the convolution theorem, but I couldn't make sense of it that way.
Perhaps 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.
Make them code simple wolfenstain 3d clone with opengl, directx or even unity3d. It was a revelation for me when I've tried to get into game programming, and half of the math taught in primary and secondary school became immediately useful, also linear algebra (which was only started at the final year of high school). Made linear algebra courses on the university a lot more interesting. There's a difference if you lo…
I think Strang has some good points, and his advice is true for the majority of students who won't go on to use substantial amounts of mathematics or need to learn much math in the future. However, if you do want to learn more math beyond calculus and linear algebra, then a thorough understanding of calculus is absolutely a prerequisite and you honestly probably haven't learned it well enough taking the typical seque…
While studying mathematics in college, once I had finished my Real Analysis requirement, I jumped headfirst into the algebraic side of things and never found myself using any sort of calculus. Even in my Topology course, we focused much more on using techniques from Real Analysis than specifically calculus topics (the former just being a generalization of the latter).
Probability theory is somewhat deceptive in its classification, since much of it "feels" a lot like a discrete mathematics course; however, much of the concepts, like you say, are underpinned by measure-theoretic principles, which is heavily analytic. It makes sense that calculus would come in handy in a much deeper study of probability theory.
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…
What I wish I had done a lot more of is statistics. Being able to reason about probabilities clearly, getting an idea of how a system performs given various variables, and most importantly, being able to communicate this to others has been very useful to me. I think anyone (front end, backend, etc) can benefit from learning about statistics.
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.
Not for me! Heck, I never took freshman calculus or pre-calculus and, instead read a book and started on sophomore calculus then continued with, right, ordinary differential equations, advanced calculus for applications, and advanced calculus, topology, modern analysis, measure theory, functional analysis, exterior algebra, etc. Not enough calculus for me!
Strang, of course, is emphasizing linear algebra. Great! It's terrific stuff. I had an abstract algebra course that started on vector spaces and matrix theory. Then I got famous book from Princeton on multi-variable calculus and read the first chapters on linear algebra, e.g., learned Gram-Schmidt. Then I got a linear algebra book and read a few chapters and applied them to some problems in classical mechanics. Then I wrote my math honors paper in group representation theory, right, more linear algebra. The out of school, I wanted to know linear algebra better and read a good book cover to cover, carefully. Then I got Halmos, Finite Dimensional Vector Spaces and read it cover to cover. Wrote Halmos about his proof of the Hamelton-Cayley theorem and got back a nice answwer!
Then I got another famous text on multi-variable calculus and read it cover to cover, including the parts on exterior algebra. Then I did that again from Spivak's Calculus on Manifolds -- right, a lot of both calculus and linear algebra. Then I got Forsythe and Moler, Computer Solution of Linear Algebraic Systems, read it cover to cover, directed a project in interval arithmetic for linear algebra, took a course in numerical analysis with a lot of linear algebra for solution of partial differential equations, e.g., iterative solutions (Gauss-Seidel) and wrote corresponding code.
I also used linear algebra in work with the fast Fourier transform, multi-variate statistics, and more.
For more on linear algebra, I read the first part, linear algebra, of von Neumann, Quantum Mechanics.
From a world class guy in linear algebra, I took an advanced course in linear algebra -- by then the course was beneath me and I led the class by a wide margin. Favorite theorem -- the polar decomposition.
Read Coddington's book on differential equations -- gorgeous book.
The combination of linear algebra and calculus, with other math, continued.
At one time a little calculus did a lot: The initial value problem for the little first order, linear ordinary differential equation
y'(t) = k y(t) ( b - y(t) )
saved FedEx, that is, kept it from going out of business. So, useful calculus!
So, sure, I like linear algebra and like the combination!
I definitely do not see that I had too much calculus!
Here's what I saw, and still fume about: All I could get in chemistry was one too simple course in high school and one too simple course in college. All I could get in physics was one too simple course. I college, by the time I got to Maxwell's equations, I didn't know enough calculus to do really well. In college I never got math enough to do well with quantum mechanics.
But in grades 9-12 and then in the first two years of college, I was force fed like a goose with six years of English literature, with each year yet another play by Shakespeare. I agree that there was a good writer in England in the 1600s -- Newton! So it was also Chaucer, Milton, Wordsworth, ..., Dickens, the great natural order (all corresponding theorems and proofs omitted!), etc. With good information about people? Nope.
Then there was history: It never got to the 20th century. It never touched on technology, economics, or any other causes. There was plenty of time in history courses; it's just that the courses didn't have much content.
If my startup works, then I'll get back to more in calculus, functional analysis, stochastic processes, and mathematical physics. "More calculus, Ma!".