I am teaching (for the first time) a 2nd course in linear algebra. The students will have had a beginning course in linear algebra and a beginning course in abstract algebra. I am considering Hoffman and Kunze (which I had in an undergraduate course) or Curtis. Would you please tell me about your experiences with this course and/or these books or others? Thank you.
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1$\begingroup$ I think Insel Spence and Friedberg is an easier read. But, it's been a while since I read Hoffman and Kunze (didn't work well for me as an undergrad) $\endgroup$– James S. CookJul 17, 2014 at 16:45
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2$\begingroup$ Roman's text is worth a look as well. $\endgroup$– James S. CookJul 17, 2014 at 18:50
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4$\begingroup$ What material do you want to cover? $\endgroup$– Pete L. ClarkJul 17, 2014 at 20:35
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1$\begingroup$ I want to cover the basics of vector spaces, linear transformations, Jordan Canonical Form, and time permitting some applications. I just picked up Cooerstein's book and I like it at first glance. It's definitely easier than HJoffman and Kunze (although I love that book). $\endgroup$– AngelaJul 21, 2014 at 18:28
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3$\begingroup$ Are you picturing a second course in linear algebra as in a two-semester linear algebra course, or more like, a return to it in upper-division with more formal proofs and the assumption they've studied things like calc 3 and foundations...? $\endgroup$– James S.Jul 25, 2014 at 17:10
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2 Answers
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Rob Beezer at the University of Puget Sound has an open "Second Course in Linear Algebra" which, though I believe still in draft form, he has used for an advanced linear algebra course a few different places, and contains many of the topics you just mentioned. (Well, actually the vector spaces are in the first course.) I'm not familiar with the other texts you mention, though, so I can't compare - this is just a data point, if a very late one.
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$\begingroup$ For a first-semester course, there are at least two serious contenders that are open source. Beezer has a first-semester book, and so does Hefferon. I like Hefferon's a lot, haven't looked as carefully at Beezer's. $\endgroup$– user507Jan 16, 2019 at 2:04
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$\begingroup$ Yes, and aimath.org/textbooks/approved-textbooks has a couple others I am not familiar with; you may also want to look at lyryx.com/products/mathematics/linear-algebra-applications along those lines. That said, the OP was about a second course, which I think there are a lot fewer resources for - and what people think a "second course" is probably varies extremely widely, for that matter. $\endgroup$– kcrismanJan 16, 2019 at 14:22
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Sergei Treil Linear Algebra Done Wrong is used in a first course for honors linear algebra at Brown, so could be useful for a second course at some other places.
https://sites.google.com/a/brown.edu/sergei-treil-homepage/linear-algebra-done-wrong?authuser=0
