Hacker News new | past | comments | ask | show | jobs | submit login

You sound like exactly the constituency Gil Strang's corrective essay is addressed to.

I don't see any of the points you mention as particularly strong. There would be nothing wrong with presenting a more hands-on linear algebra course as a first course for freshmen. (Calling it "matrix arithmetic" does not do the notion service.) The material seems very immediate, and you can use a REPL like octave or matlab to reinforce concepts. You could deepen it as you wished by introducing more abstract concepts and by doing proofs, but I don't think that's necessary. I learned a lot from Golub and van Loan, for instance.

Second, the notion that calculus has had more impact on history/society than linear algebra is very hard to defend. Think of all the numerical modeling that has been done using matrices. Think of all the large-scale computations/optimizations that are done first by finding a linear system, or approximating one. I'm not saying there is a clear answer to this question, just that it can't be the foundation of an argument, because it's so undecidable. Another thing that makes it undecidable is cases where you need both (e.g., weather forecasting).

And saying it would be hard to teach the subject in a uniform way -- really, this is a very bureaucratic objection.




>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.


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?


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.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: