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Traditonally this was so; today I'd say linear algebra gives more over a larger range of subjects.
by chalst 4y ago
Traditonally this was so; today I'd say linear algebra gives more over a larger range of subjects.
- auggierose 4y agoBoth linear algebra and calculus are classic introductory math classes. A lot of calculus IS linear algebra, given that derivations are linear approximations.
- selimthegrim 4y agoDerivatives are (derivations are the generalization so of course are but I would be surprised to see an undergrad class treat them)
- auggierose 4y agoMy mistake. I meant derivatives.
- sshlocalhost98 4y agoYea, theorems like least square prove that A^T * A * X = A^T * B. but how exactly is this related to calculus though?
- peterhalburt33 4y agoThe equations you quoted result from minimizing the square of the norm of the residual of Ax-b over all inputs x, so in a sense least squares is just calculus…
- sshlocalhost98 4y agoThanks @peterhalburt33
- selimthegrim 4y agoTransposes correspond to integration by parts, and the question of whether A^T*A has an inverse can get involved. Also for infinite matrices the analogies hold more readily, see the observation due to Alan Edelman on page 8 of https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf
- sshlocalhost98 4y agoThanks @selimthegrim.
- chalst 4y agoI had three years of high school with a substantial amount of calculus; by contrast while I was introduced to matrices and Gaussian elimination at high school, the treatment of the algebraic side was almost completely superficial and focussed on solving systems of linear equations. At university that changed, with a clear treatment of vector spaces and linear algebra as generally interesting topics. But still, they received far less time than calculus in my first year in a maths degree. Now that was over 30 years ago and things might be a bit different today. But I have the impression that the more generally applicable subject of linear algebra gets less time unless students get interested in the applications that demand it be taught properly.
- peterhalburt33 4y agoI’d agree, but most first year students aren’t ready to work at the level of abstraction required for a rigorous LA course (i.e., more than just matrices and Gaussian Elimination etc.)