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I have no idea if this question is appropriate for this forum, but I hope you guys can overlook the fact that I asked it on a wrong forum (if I did) and still help me answer it (of course, if this is indeed the wrong forum for the type of question I'm about to ask, do please say so).

I am a 16 year old guy who is passionate about physics and as a result wants to increase his knowledge in mathematics, the language of physics. I've read and heard a lot about Linear Algebra and how crucial it is to physics and I am deeply motivated to self study this intriguing part of mathematics. However, I have limited knowledge of maths. I (for example) know basic algebra, trig, diff/int calc and some analytical geometry, but I wouldn't say I master these subjects past the high school curriculum. Now my question is: Would you kind people say I am able to self study Linear algebra or is it too tough and/or does it require too much of a math background? And are there any good books out there for BEGINNERS in LA? I found this (free) e-book called: Elementary Linear Algebra by Kenneth Kuttler and another one called 'Linear Algebra: Theory and its applications' also by Kuttler? Are these any good? Or would you recommend other books? If you guys have any tips regarding books for LA but also tips in general, please, I'd appreciate them!

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I don't know the books you mentioned, but I would recommend Introduction to Linear Algebra by Gilbert Strang. I didn't read through the whole book, but it has a lot of good examples that are helpful for beginners. –  Shankara Pailoor Sep 7 '12 at 22:50
    
Just be aware, in the beginning, the actual math is not hard, you should have the knowledge to do pretty much all of it. The thing that makes the class hard is the concepts and wrapping your brain around it. –  Joseph Skelton Sep 8 '12 at 0:42
    
Yes, a bright high-school student with some basic mathematical aptitude should have excellent chances of successfully self-studying linear algebra. It's usually taught in first year at universities, both because it is useful in many other areas and because it's so relatively easy that it can double as a first introduction to real mathematical standards of proof and abstraction. It also has very few technical prerequisites beyond elementary arithmetic, and whatever other drawbacks you face should be more than offset by the fact that you deliberately choose yourself that you want to learn it. –  Henning Makholm Sep 8 '12 at 1:10
    
Also, be sure to stick around here. Inevitably you will run into points that whichever book you choose explain in a way that just doesn't resonate with you. You will need someone in lieu of a teacher to ask for clarification then -- and lots of people here will jump at the chance to answer questions that seeks understanding rather than "please do my homework for me". –  Henning Makholm Sep 8 '12 at 1:18
    
Thank you guys immensely! I have created a permanent account for the inevitable moments when I don't understand something. Again thanks and I will follow my dreams! –  JohnPhteven Sep 8 '12 at 7:15

1 Answer 1

First, bravo to you for taking initiative and immersing yourself in the beauty of learning!

Here are some thoughts for your consideration:

  1. Elementary Linear Algebra [Hardcover] Ron Larson (Author)

  2. Schaum's Outline of Linear Algebra Seymour Lipschutz (Author), Marc Lipson (Author)

  3. Also, try your local university library and see if you find books that suit your needs.

You can also try open course-ware like:

  1. http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-1-the-geometry-of-linear-equations/

  2. http://www.khanacademy.org/math/linear-algebra

  3. http://cnx.org/content/search?words=linear+algebra&allterms=weakAND&search=Search&subject=

I would also recommend you learn a Computer Algebra System (CAS) like Mathematica or Maple (you can purchase Student Versions) or other free ones (like SAGE or Maxima) because that will really help exploring and learning this topic so much richer!

See: http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

Lastly, I think you should consider learning proofing methods and here are some books that do a reasonable job at teaching those.

General Proof Strategies

  1. How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) [Paperback] G. Polya (Author)

  2. How to Prove It: A Structured Approach [Paperback] Daniel J. Velleman (Author)

  3. The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs [Paperback] Antonella Cupillari (Author)

  4. How to Read and Do Proofs: An Introduction to Mathematical Thought Processes [Paperback] Daniel Solow (Author)

Hope that helps and gives you some ideas!

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+1 for recommendations re proof strategies. –  Drux Jan 5 '13 at 23:25
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+1 from mine to my friend here. –  Babak S. Feb 16 '13 at 6:37
    
Nice. very nice+1 –  Basil R Mar 11 '13 at 12:33
    
I $2^{\text{nd}}$ the above comments! –  amWhy May 19 '13 at 0:30

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