Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Recommended Texts

  1. Nov 25, 2004 #1

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    I am doing Linear Algebra right now, but the text we are using sucks in my opinion.

    Elementary Linear Algebra /with Applications - Anton and Roberts

    If there exists a linear algebra text that has a Spivak (Calculus) style approach, that would be great. I would like a more rigorous approach to linear algebra.

    So, what text do you recommend?

    Thanks.
     
  2. jcsd
  3. Nov 25, 2004 #2

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    You might want to check out "Linear Algebra Done Right" by Sheldon Axler.
     
  4. Nov 25, 2004 #3

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Sounds like a Linear Algebra textbook book tag along kind of thing.

    Is it like Schaum's or what not?
     
  5. Nov 25, 2004 #4

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    Not at all. I suggest you try to find a copy and not judge it by it's title.

    Axler's is the closest analogue in the linear algebra world I've seen to Spivak's Calculus.
     
  6. Nov 26, 2004 #5
    Last edited: Nov 26, 2004
  7. Nov 27, 2004 #6

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Thanks guys.
     
  8. Nov 27, 2004 #7
  9. Nov 28, 2004 #8

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    the best standard linear algebra text is probably hoffman and kunze. anything by serge lang tends to be well done, but osme of his lineat algebra texts are bend over backward dumbed down.

    "finite dimensional vector spaces" by paul halmos is probably closest to a spivak type text.

    or just get a good algebra book that focuses on, linear algebra , like the excellent book Algebra, by michael artin.

    there is also an excellent book by paul detman, in paperback for a few dollars, in dover. anythoing written in the 60's as spivak was, will have hgiher stahndards thahn tdays c**ppy texts.
     
  10. Nov 28, 2004 #9
    Yes I too would also recommend Sheldon Axler's "Linear Algebra Done Right." It is much more rigorous than your standard intro to linear algebra text. You hardly use matrices and matrix manipulations at all. Determinants of matrices are explained in one of the very last chapters of the book. Axler explains the THEORY behind a lot of the linear algebra most students take for granted in their first course in LA.
     
  11. Nov 28, 2004 #10
    Is Shaums good?
     
  12. Nov 28, 2004 #11

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    schaum's books are always useful, utilitarian collectioins of facts and exercises. they are never, ever, anywhere near the category of book requested here, i.e. a serious theoretical text like spivak's calculus. They are pretty good at what they attempt, which is a minimal acquaintance with a subject, usually old fashioned, and often out of date.

    even their value as a problem solving source to me seems compromised in recent years as they get thicker and less challenging, responding to the new penchant for dumbing down the material.

    after years of recommending them, i found the schaum's calculus book almost useless this year, and regretted recommending it to my honors class.
     
  13. Feb 4, 2006 #12

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    the algebra books 843,844,845, listed for free on the website http://www.math.uga.edu/~roy/

    are fantastic, marvellous works of magnificent scholarship. Anyone who even holds them in his/her hand magically becomes algebraically literate.

    just as the prey caught in the mouth of the tiger is doomed to never escape, so the student who once gazes into the pages of these works will be forever tied into the community of algebra scholars.
     
  14. Feb 5, 2006 #13

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    I got a new text by Friedberg, Spinsel and some other guy.

    Seems really good so far.
     
  15. Feb 6, 2006 #14
    Does one know of a good linear algebra text with an emphasis on applications and MATLAB. Thanks.
     
  16. Feb 6, 2006 #15

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Linear Algegra by Anton Roberts has lots of great applications. In fact, a whole chapter is devoted to applications.

    He has some emphasis on the use of programs like MATLAB, but he doesn't show how to use the program.
     
  17. Mar 3, 2006 #16
    Is this Anton and Rorres? That's the book I used as an undergrad. It was decent--I still refer to it from time to time...
     
  18. Mar 3, 2006 #17

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    :smile: Friedberg, Insel, and Spence.
     
  19. Mar 4, 2006 #18

    0rthodontist

    User Avatar
    Science Advisor

    Can that be good? The book I used, "Linear Algebra with Applications" by Robert Lay, proved nearly everything but also had a good early focus on matrices and matrix manipulations. These manipulations I found very useful in understanding how proofs later in the book proceed. Doing a lot of them helps make it all more concrete and gives you a sense for what you're actually proving. Without determinants you probably can't even do eigenvalues well. The book seemed rigorous, not that rigor in basic linear algebra is so difficult. Once you've mastered the basic manipulation there are ample proofs for you to do in the problems. What did it leave out? Well, there was a theorem or two (I don't remember exactly which) later in the book that it said to consult more advanced texts on rather than proving it itself. Also most of the book focused on real-valued matrices, though I don't know if that would be different in any other introductory text. On the whole the book was a wonderful guide to a course I loved enough to do most of the rest of the book since the course ended.

    This is the _only_ book that I have had for linear algebra, and also I want to stress that the teacher I had was a very good lecturer. But I think the book contributed a lot, and maybe this weekend I'll finish the part on quadratic forms.
     
  20. Mar 4, 2006 #19

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    Yes, very. Linear algebra should not equal solving systems of equations, and I think a good motivated student will be able to start with the interesting parts of linear algebra from the start. Axler's might be difficult for most as a first course (he suggests it for a second), but I think is a good book to look at for someone who asked for a Spivak analogue (see OP).

    See http://www.axler.net/DwD.html it's a paper published by Axler on a determinant free approach to linear algebra that his text is partly based on.
     
  21. Mar 4, 2006 #20

    0rthodontist

    User Avatar
    Science Advisor

    Well, at that link he says it is intended for a _second_ course in linear algebra.

    I don't see why you don't like the manipulative approach. After all in applied math that's what the computer is doing. How can you understand LUP decomposition without doing row reduction yourself? I can't tell you how many times I've successfully thought through a proof in Lay's book by thinking about the nitty gritty rows and elements. Probably half of Lay's own proofs take that route. Also I especially like determinants because of their concrete area/volume/etc. interpretation.

    It's not as if you're spending the whole course just manipulating matrices, you just spend a few weeks doing manipulation and that gets you an intuition you can use.

    I think that all math should be grounded in some kind of practical, almost physical manipulation skill, something that lets you visualize what is going on when it gets abstract. I doubt we would even have any calculus or geometry without the manipulation in two and three dimensions that we do every day going about our lives.
     
    Last edited: Mar 4, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Recommended Texts
  1. Linear Algebra Text (Replies: 14)

  2. Recommend a text (Replies: 5)

  3. Decryption of a text. (Replies: 39)

Loading...