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What books are there that cover elementary algebra, but are not bloated with pedagogically padding?. I searched in this website and the web in general, but the books I could find about elementary algebra are full of pedagogical padding (lots of meta, repetitive examples, fancy formatting, little-relevance images and so on, as if they were written for kids); I find that distracting, and it makes harder to locate material as the density is much lower than in a book like Serge Lang's Algebra or Rudin's Prinicples of Mathematical Analysis.

Could you please recommend a book that covers (even if it is not its main topic) elementary algebra, but from an approach closer to that found in undergraduate-level books (including proofs and excluding pedagogical padding)?.

I know most of what is included in an elementary algebra course, but I want to review this area to make sure I will not miss something elementary when studying more advanced mathematics. I mainly want to review the manipulations of real and complex expressions, rather than things like what a function or a linear equation is.

Thanks in advance.

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  • $\begingroup$ Look for old freely available texts by Lennes, Cajori, Fine, etc. Do this by searching google-books with the date restricted to something like 1880 to 1920. Even some books with arithmetic in their titles might be what you want, such as Bakst's 1944 Arithmetic for Adults and Buckingham's 1947 Elementary Arithmetic. $\endgroup$ – Dave L. Renfro Feb 3 '15 at 22:26
  • $\begingroup$ @DaveL.Renfro: For books that old, they are hard to find printed or for download. I wouldn't use Google; it abuses its cilents in several ways and its Google Books don't allow downloads, only seeing through Google's proprietary reader. Thanks for commenting nonetheless. $\endgroup$ – Mario Robles Feb 4 '15 at 20:57
  • $\begingroup$ It may be your browser. I can't access the date search option or the "download .pdf file" option in Internet Explorer, but both work when I use Chrome. In Chrome, the download option for me is in the upper right corner with some kind of six-sided wheel (not labeled and I have no idea why this symbol is used) that opens up to a menu with six options, one of which is "Download PDF". Over the past 7 or 8 years I've accumulated several hundred such books and probably roughly this number of old math journal volumes, the books arranged in folders by topic and the journals in title-labeled folders. $\endgroup$ – Dave L. Renfro Feb 5 '15 at 14:55
  • $\begingroup$ For an example of how useful this resource can be, see my answer to Did Galileo's writings on infinity influence Cantor?. If you don't want to use google, you can still find tens of thousands of math books at archive.org (e.g. this) and the HathiTrust (e.g this). When googling with an author and title include "archive.org" or "HathiTrust" as one of your search words to quickly find the book. $\endgroup$ – Dave L. Renfro Feb 5 '15 at 15:06
  • $\begingroup$ @DaveL.Renfro: Chrome is the same. Its not completely free (as in freedom) software and it contains Google spyware, so I wouldn't use it either. Thanks for the comments. The "Internet Archive" is good, it actually treats its users like persons. Check too Lib Gen. Thanks for the help. P.S: The "Internet Archive" seems to have joined the fill your website of non-free JavaScript and applets group; it used to allow plain downloads without this crap (Like Lib Gen). $\endgroup$ – Mario Robles Feb 5 '15 at 15:36
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Take a look at Serge Lang's Basic Mathematics. It may be slightly more basic than you would probably like but it is nonetheless a great book. It is based on deriving and proving things from previously introduced concepts instead of just introducing things seemingly out of the blue and then spending several pages motivating the uses and talking endlessly about history. Surely there is some pedagogical method to it but it is aimed at people who find the topic interesting already and can appreciate the mathematics without seeing pictures of the space ship launch or elaborate 3d scenes involving cubes and spheres.

I would put it at a level somewhere between high school and college. I'm studying it right now but since I have very little true knowledge and understanding of mathematics from high school I find it a bit challenging in places, e.g. we never proved a thing in school so I had/have to learn how to go about proving things. I have learned so much about mathematics and proofs and how things really work, and I am only at the start of the book so there is quite a journey ahead of me!

Other books that may be of interest to you: Gelfand's Algebra, Method of coordinates, Functions and graphs, and Trigonometry. I've read some great things about them and I work through Algebra alongside Lang's text and I find them to complement each other fairly well. However, there is no coverage of complex numbers in this one. They are all very short and packed with great insight and challenging problems.

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I'm not 100% sure that this would fit your needs, but the Art of Problem Solving books series by Richard Rusczyk and Mathew Crawford go very indepth and have little "padding".

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