Please recommend textbook for self study

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I know there are several threads asking for textbook recommendations, but I need something special: I am teaching myself math, and need a Linear Algebra textbook from which I can learn on my own. I really want to obtain a thorough math education, and I'm almost done with calculus (Stewart's), so I want to move on to the next important subject, which I'm guessing is Linear Algebra. I would like to eventually be able to understand quantum mechanics and relativity in full mathematical glory, although I'm also interested in econometrics and mathematical methods for economics. Is a standard Linear Algebra book the wisest choice, or could a more encompassing book that includes LA but also other subjects be the way to go? I want to know it all :smile:

What complicates making a selection is that, even though I'm learning on my own, I don't want some stripped-down book like Schaum's, but rather a thorough, rigorous text that will give me a deeper understanding of the subject and leave me prepared to go into more advanced subjects; but then again I also need it to have lots of exercises with answers, and that's what makes finding a good book difficult, since many "serious" texts do not bother to include all or most answers, not even when a study guide is offered. Probably what I'm asking for is linear algebra's equivalent of Stewart's calculus.

Does such a beast exist? Thanks in advance!!

ps. I also need a good differential equations text :biggrin:
 
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Answers and Replies

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"Linear ALgebra Done Right" by Sheldon Axler is by far one of the most thorough LA books on the market. Don't be fooled by the title, the Axler's book is pretty hardcore for the begining student of LA. Determinants aren't even discussed until the very last chapters.
 
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hoffman/kunze's text is pretty good, as is halmos' "finite-dimensional vector spaces". they have problem sets separate from the rest of the text which may not be exactly what you have in mind, but personall i don't think that matters. every textbook is chock-full of exercises if you only read the definitions & theorem statements and cover up the proofs.
 
es
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LINEAR ALGERBA - friedberg.
 
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thank you all for your suggestions :smile:

how do you guys like these couple of books I've stumbled upon?:

Gilbert Strang - Linear Algebra and Its Applications

John H. Hubbard and Barbara Burke Hubbard - Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach

David C. Lay - Linear Algebra and Its Applications

thanks again!!!
 
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gravenewworld said:
"Linear ALgebra Done Right" by Sheldon Axler is by far one of the most thorough LA books on the market. Don't be fooled by the title, the Axler's book is pretty hardcore for the begining student of LA. Determinants aren't even discussed until the very last chapters.
LINEAR ALGERBA - friedberg
both look good, but do they include exercises with answers?
 
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strang's book is good for matrix theory, which is a small part of linear algebra. that book would be better for scientists & engineers. it has answers for some exercises though.
 
Ron_Damon said:
both look good, but do they include exercises with answers?
Axler's book does not include an answer key, but like Spivak's text on calculus, its problems are leading and meaningful. As you get to more proof-oriented texts, you'll find answer keys lacking. You can always get help from friends/professors and at these and other mathematics forums.
 
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hypermorphism said:
Axler's book does not include an answer key, but like Spivak's text on calculus, its problems are leading and meaningful. As you get to more proof-oriented texts, you'll find answer keys lacking. You can always get help from friends/professors and at these and other mathematics forums.
:frown: how can one learn if there is no way of checking one's work? There really is no excuse for not providing answers in textbooks :mad: What this does is exclude anyone outside of established centers of "education" from acquiring knowledge. How despicably elitist is that? :grumpy:
 
You don't need to be a member of a center of education to get help at these and other mathematics forums. Mathematics is just as social as other sciences, and one should try to get more than just one point of view on a topic of interest. For any nontrivial theorem, there are a myriad of ways of proving it, some more elegant/intuitive than others.
Including an answer key in proof-oriented texts can decrease the amount of work the student does to understand the topic by there being a ready solution to each proof. If none is included, the student may come back to a problem more than once. If none is included and the student cannot even start to approach the problem, then the author has not done his/her job.
 
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Ron_Damon said:
:frown: how can one learn if there is no way of checking one's work? There really is no excuse for not providing answers in textbooks :mad: What this does is exclude anyone outside of established centers of "education" from acquiring knowledge. How despicably elitist is that? :grumpy:
how can you not know whether or not you understand something? you don't need another person to answer that for you. you check your work by asking yourself "did i do anything wrong here?" & if not then you understand it. simple.

re: "proof-oriented" books they all have 'solutions' to the 'problems'. except the problems aren't labelled 'problem' in the text, they're usually labelled "proposition" or "theorem" or "lemma" etc. the 'solutions' are labelled 'proof' in most books. just cover them up & try to figure it all out by yourself.
 
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But I do hundreds of calculus, physics and chemistry problems each week, so asking someone every time I have a doubt is extremely inefficient (and annoying). Sometimes I just sit there for hours trying to figure out why the answer provided might make sense; and I don't get up until I discover why. That's how I learn. It's not about obtaining a figure to match my own; rather, it's to get a glimpse at mathematical reality.

Learning the stuff on your own, even when answers are provided, is challenging enough. And, contrasting what I know with the training some friends have acquired in leading universities, I'd say my method yields better results.

But now I'm almost done with calculus and general chemistry, and can't seem to find good textbooks (with answers) to move on to :cry:
 
shmoe
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At some point you have to get used to the idea of trying to answer problems that don't have a solution a few pages away. This is how problems you meet "in real life" will appear, otherwise they aren't problems. Beyond a first year calculus class it's also reasonable to expect students to be able to judge their own work for accuracy.

Another thing, it's ok if you aren't able to solve every problem in a book like Axler's. There's nothing wrong with putting a few of the toughie's aside.
 
mathwonk
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there are no top level books with answers to all problems. there is a reason for that. learning at the deepest level includes learning to check your own work, and to become independent of someone else having to tell you always whether you are right or not. it involves learning to understand why things are true or false, and to use those criteria to verify your own work.

Good books do not omit answers because the authors are lazy, but because they understanbd answers are more harmful than helpful to deep learning. If you really want to "get it all", you need to graduate to this higher level of learning.

Stewar for examplew is not a top level calculus book.

If you really want to understand calculus and linear algebra together, get Apostol, or some other good book that combines them rigorously.
 

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