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Linear Algebra Gentle Introduction to Linear Algebra

  1. Jul 30, 2015 #1
    Does anyone know of any gentle, introductory books to LA that assume little prerequisites, even in the way of vectors and matrices? I want something that will give intuition and reasonable proofs, and will provide enough background for something like computational neuroscience. I do not know calculus, but plan on learning that in tandem with/after LA.

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  3. Jul 30, 2015 #2
    You can try Elementary Linear Algebra by Paul Shields. It is an applied math book. Very good and well written. Shows you how to apply linear algebra to the sciences. Gives great intuition. The only problem with this book is that it only goes up to R^3.

    I would go over this book to get a feel for linear algebra. Then I would use something along the lines of: Anton, Lay, or other books in the same tier. Then I would move onto Axler or Friedberg.
  4. Jul 30, 2015 #3
    Is it true that Shields' book has no proofs? Also, is it possible to obtain a pdf online, or is there no such way?
  5. Jul 30, 2015 #4
    How do you think Shields' book compares to Linear Algebra: a modern introduction? Thanks so much!
  6. Jul 30, 2015 #5


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  7. Jul 30, 2015 #6
    Don't remember seeing proofs. What i do remember are well written examples and explanations of the applications, as well as, the why explained intuitively. Many Linear Algebra books at the introductory level suffer from an identity problem. They do not know if they wan't to be a pure math book or an applied book. Oftentimes the proofs are very messy and many details omitted. A great example will be Anton Linear Algebra. Even tho i recommended it, it suffers from an identity conflict. It fails to make it clear what it means by linear independence. Yes it does provide the definition, however the example or the paragraph explaining it, does it make it clear how to apply it. The book goes down the drain when it explains linear transformations. The chapter on change of bases is more complicated than it should be. Even the something called span, which is very important, required multiple uneaded reading if the author was better at writing english sentences.

    It would be hard to recommend you a proof book, such as, Friedberg or Axler, with your limited mathematical exposure. I will assume not having taken calculus, assumes you have not developed mathematical maturity.

    I would also recommended a book on proofs also. The faster you understand the basics the better. It helps reading one of these books. Gives you further insight on how to disect your textbook.

    @mathwonk. A quick google search for the Paul Shields, which I own already, led me to a book by the same author titled, "Linear Algebra." Did Shield's write a sequel or did the people titled the sale listing wrong?
  8. Jul 30, 2015 #7
    Thanks so much! Also, how do you feel Shields' book compares to the Strang book and MIT OCW lectures?
  9. Jul 30, 2015 #8
    One more question: what book on proofs do you recommend?
  10. Jul 30, 2015 #9
    Last edited by a moderator: May 7, 2017
  11. Jul 30, 2015 #10


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    I don't know Shields other books if any. My wife took a course in college from the elementary book and so i have had a copy for a long time and i like it. linear algebra is very abstract and he makes it concrete by sticking to 3 dimensions and below, which i agree if a great idea. the higher dimwnsional stuff is easy once you understand the 3 diml case. and the author was a stanford professor so the quality is really high. tyhere is no other book i know that keeps things that elementary and concrete. Strang's book is very different and to me not so appealing althugh I have to admit his video lectures, which are free, are awfully clear, even if a bit boring to me. It is hard not to learn something listeniong to his lectures but I do not enjoy reading his book. I will look again but i do believe shields has proofs, i mean don't all math books have proofs?...well i gave away myy copy when i moved but i think it does have proofs. i mean no stanford professor would write a math book without proofs, it just isn't done.
  12. Jul 30, 2015 #11
    Do you know what background shields' book requires?
  13. Jul 30, 2015 #12
    not much. just basic multiplication, addition, and subtraction. Limited mathematical maturity. You can learn typically right after a high school algebra course. A course of pre-calculus would make it easier than it is.

    Thank you for linking to the book.
  14. Jul 30, 2015 #13
    Ok. So it's better than Strang's book? Also, does it contain problems?

    Thanks so much,
  15. Jul 30, 2015 #14
    I had Strang's book and i chucked it into my closet. I even felt like throwing the book away. Something i had never though of before. I tend to dislike books that are verbose. Strang was extremely verbose and it made it hard to read, at least to me. It kind of lack examples. Many of the core-ideas which should have been in the text appeared in the end of chapter problems. I have a lot of books that do this, however, these books were extremely well written and it was easier to these type of exercises.

    I prefer the theorem/proof approach.

    Yes, Shield's contains many problems and is abundant and his examples. He makes the section regarding linear transformations extremely clear. Something i could not figure out from my other more "advanced book."

    At less that 5 dollars, it doesn't break the bank to try it.
  16. Jul 30, 2015 #15
    Okay, thanks. Do you think I should purchase from abebooks or amazon? Abebooks seems a bit sketchy, to be honest...
  17. Jul 30, 2015 #16
    very legit site. Purchase books were it is cheaper. I bought atleast 20 books from there.
  18. Jul 30, 2015 #17
    Oh! Okay, then, thanks!
  19. Jul 30, 2015 #18
    for proofs books. You have How to Prove it by Velehem and Mathematical Proofs: A transition to higher mathematics by Gary Chartrand.

    I am currently reading the latter and enjoy it. Make sure to get an older edition. I purchased my copy for 5.00 shipped. It is green covered.
  20. Jul 30, 2015 #19
    I had another question. Are you sure all that Shields' book requires is basic high school algebra? It seems, from the TOC I found online, that one should have basic vector and matrix knowledge...
  21. Jul 31, 2015 #20
    most introductory linear algebra books start with system of equations. Solving them by elimination and substitution. Then they go on how to preform matrix operations to make the busy work faster and easier. Then they do matrix algebra. Ie. how to add, subtract, and multiply matrices. Finally vectors are touched upon. Only high school math. Some more advance books on Linear Algebra expect you to know these things beforehand. However, a good introductory linear algebra does not.
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