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>a more hands-on linear algebra course as a first course It is ideal (and indeed, not uncommon) to have linear algebra and calc 1 in parallel --- for special h

by xamuel 12y ago

>a more hands-on linear algebra course as a first course It is ideal (and indeed, not uncommon) to have linear algebra and calc 1 in parallel --- for special honors classes. It wouldn't be realistic to do it for the general freshman class. Do you realize just how many students that includes, in a big state U.? "a REPL like octave or matlab" would be wonderful, amazing, if it weren't about as realistic as the space elevator. Do you know how many endless headaches there are with software-augmented courses, even when it's just software you run in the browser? I applaud your ambitiousness but let's just say I don't want to be in your shoes when you've just told a thousand 18-year-olds to install Matlab! >the notion that calculus has had more impact on history/society Linear algebra is hard to even put your hands on, historically. There was no Isaac Newton figure putting the finishing touches on an amazing breakthrough "Fundamental Theorem of Linear Algebra". It is the book-keeping field of mathematics. "All the numerical modeling that has been done using matrices" almost entirely arises by discretizing differential equations so linear algebra doesn't win any points there.

mturmon 12y ago
No, linear algebra does not have an Isaac Newton figure. The historical development was different. The different history does not bear on the ultimate impact and general utility of the tools offered by calculus or by linear algebra. Eigenvalues and orthogonality are not just "book-keeping". Why give forth empty slurs like this?
- xamuel 12y ago
  Wasn't meant as a slur, I love linear algebra. Especially graduate-level, when you learn about the abstract (commutative diagram) approach to tensor products! :D Current-day impact doesn't retroactively grant historical value, though: the smartphone has not had a big impact on history (yet). If you can do a decent treatment of eigenvectors in a non-honors freshman course, my hat goes off to you. Even in a 2nd-year course where students are more mature, that's hard (first time I took LA, eigenvectors were rushed at breakneck speed in the very last lecture). And while they're very important, eigenvectors are still a shadow of the historico-cultural impact of calculus.

by xamuel 12y ago

mturmon 12y ago

No, linear algebra does not have an Isaac Newton figure. The historical development was different. The different history does not bear on the ultimate impact and general utility of the tools offered by calculus or by linear algebra. Eigenvalues and orthogonality are not just "book-keeping". Why give forth empty slurs like this?

xamuel 12y ago
Wasn't meant as a slur, I love linear algebra. Especially graduate-level, when you learn about the abstract (commutative diagram) approach to tensor products! :D Current-day impact doesn't retroactively grant historical value, though: the smartphone has not had a big impact on history (yet). If you can do a decent treatment of eigenvectors in a non-honors freshman course, my hat goes off to you. Even in a 2nd-year course where students are more mature, that's hard (first time I took LA, eigenvectors were rushed at breakneck speed in the very last lecture). And while they're very important, eigenvectors are still a shadow of the historico-cultural impact of calculus.