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March 8th, 2009, 08:42 PM   #1
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Looking for a few good math books

Hi, I'm new to this forum and I was wondering if someone could help me in finding a few good math text books. Currently I am studying Calculus in several variables to the point where I am about to begin learning directional derivatives and integrals in my final quarter of Calculus. However, I really want to stay well versed in all of my mathematical areas including past and present. So I want to have a few good books to review with and learn new things as well that my schooling hasn't covered (eg: I never studied much abstract algebra like rings and fields and I'd like to learn how.). So this is what I am looking for:

-Algebra: I want a book that encompasses all algebraic content from basic equation solving to the ends of abstract algebra (eg. eq solving, linear systems, matrices, quadratic functions, conic sections, imaginary numbers, rings, fields, etc). I want the book to be understandable, but I'd like it to be rigorous as well. I understand that having all of those topics encompassed in one book is large so I feel I may have to look for a few books for everything (maybe a book would have to be dedicated to ring and field theory)

-Trigonometry: I want something similar in this book as in the book I am looking for in Algebra. I want it to be understandable but rigorous as well. I also want a broad amount of topics encompassed in this book as well with a large amount of application problems (but I assume that is standard for any good trig book).

I really want to solidify my mathematical understanding in these areas and beyond what my public schooling did. I keep trying to find good books using Google but it usually turns up selling prices on some e-tailer or a list of top 10 books which are generally super-easy and almost guaranteed not to contain rigorous definitions and proofs. I appreciate any help that anyone can give me on this. Thank you!
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March 12th, 2009, 04:40 PM   #2
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Re: Looking for a few good math books

Nobody has any suggestions?
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March 12th, 2009, 08:49 PM   #3
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Re: Looking for a few good math books

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Originally Posted by cmmcnamara
Nobody has any suggestions?
No, sorry. I read more advanced books; I don't know anything at the high school level.
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March 15th, 2009, 10:58 AM   #4
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Re: Looking for a few good math books

Hi!
I can advice a very good book that covers almost all topics you need with a lot of examples.
The link to this book:
http://depositfiles.com/files/rnoc4hxzm
Regarding abstract algebra (groups, rings, fields),
the second chapter of the book 'Handbook of Applied cryptography ' should be of use for you.
The link to this book:
http://depositfiles.com/files/zolwrjocr.

Really hope that it helps you.
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March 17th, 2009, 07:45 AM   #5
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Re: Looking for a few good math books

Quote:
Originally Posted by cmmcnamara
-Algebra: I want a book that encompasses all algebraic content from basic equation solving to the ends of abstract algebra (eg. eq solving, linear systems, matrices, quadratic functions, conic sections, imaginary numbers, rings, fields, etc). I want the book to be understandable, but I'd like it to be rigorous as well. I understand that having all of those topics encompassed in one book is large so I feel I may have to look for a few books for everything (maybe a book would have to be dedicated to ring and field theory)
I sincerely doubt that there is such a book. A good high school Algebra II/Precalculus (though, I must say, "precalculus" is just a blasphemy) textbook would include quadratic equations, conic sections, imaginary numbers, matrices, and linear systems. You will have to refer to a linear algebra textbook to actually learn about matrices and linear systems. Any introductory text in the subject would suffice--my class used Elementary Linear Algebra by Spence, Insel, and Friedberg.

At this point, you should have at least a year of calculus background (that is, the single-variable portion) to proceed. Of course, an adequate background in multivariable calculus is borderline indispensable, for linear algebra and differential equations share a strong bond. I am assuming, however, that you didn't want to hear a speech on integrated mathematical education.

Anyhow, depending on how far you want to go, you can take different routes. If you just want a taste of abstract algebra, you can start reading an easy abstract algebra textbook at this point. I heard Abstract Algebra: An Introduction by Hungerford is a relatively easy introductory text. If you want a more serious exposure, it is highly recommended that you obtain a background in abstract linear algebra before you proceed. Linear algebra is essentially the most accessible subset of abstract algebra (module theory, specifically), for it contains tons of very much concrete examples. I don't know how good you are at reading textbooks on your own, but you can technically skip the introductory linear algebra textbook and go straight into a more theoretical one. My class uses Linear Algebra by Spence, Insel, and Friedberg (this is a different textbook). I heard Linear Algebra by Hoffman and Kunze is also very good. After that, you can go about reading an abstract algebra text at the advanced undergraduate level. Notable ones include Algebra by Artin, Topics in Algebra by Herstein, and Abstract Algebra by Dummit and Foote.

That was probably a lot more than what you wanted to hear. Technically, you can go straight ahead to Artin's text after high school algebra, since it does cover some linear algebra (rather quickly). I can guarantee you, however, that you will not be able to read an abstract algebra textbook without any background in college mathematics. A year or two spent in calculus classes is not wasted--it is a good transition to more abstract math.
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March 21st, 2009, 07:38 AM   #6
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Re: Looking for a few good math books

http://www.mininova.org/tor/1258178

Grab that torrent. Pick out these 3:
Apostol T.M. Calculus & Linear Algebra. Vol. 1 (2ed., Wiley, 1967)(686s)
Apostol T.M. Calculus & Linear Algebra. Vol. 2 (2ed.,Wiley, 1969)(T)(696s)
Artin M. Algebra (PH, 1991)(633s)

I can vouch for those. Don't be a torrent pirate though, if you find them accessible and informative, order a copy.

EDIT: You will need some bit torrent software to download them. I recommend uTorrent. You will need software to view them. WinDjView works fine.
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