Some background:

I went to a very good school when I was in grades 7-10. In grade 7 we started algebra. First we started with basic set theory, then we covered the axioms of equality, ordering, and field axioms (we didn't call them that though). We also were forced to solve equations step by step providing every axiom we used in each step (which at the time I despised lol). It wasn't until I started studying Analysis and Abstract Algebra that I realized how "rigorous" our intro to algebra was.

We moved and my sister goes to a not very good middle school. She's in grade 7 now. I want her to have a very good foundation in math like I did. I'm prepared to teach her, but need a book that she can at least look over what we cover and do exercises from. I also need it as a guide, since I don't remember the order in which we covered the topics back when I was in grade 7.

Just to summarize:

I want a middle school level algebra book that covers some set theory and "axioms of algebra", requires some rigor, and hopefully includes some harder problems with the routine ones.

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    $\begingroup$ See whether this helps you: books.google.co.in/… $\endgroup$ – Rohan Nov 14 '17 at 13:59
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    $\begingroup$ Gelfand's algebra book doesn't do set theory, but it is extremely insightful and ought to be read as soon as possible by every serious high school student. $\endgroup$ – symplectomorphic Nov 14 '17 at 14:17
  • $\begingroup$ @Rohan wow this book is very new, in fact it's not even released yet! Sounds very useful though, will definitely keep an eye on it. Thanks! $\endgroup$ – Jean Nov 14 '17 at 14:57
  • $\begingroup$ @symplectomorphic I like this book, I might use it if I don't find something with set theory. $\endgroup$ – Jean Nov 14 '17 at 14:57

It sounds a lot like you're talking about Dolciani's Modern School Mathematics. Algebra 1, which was widely used for what was then 9th grade algebra in the U.S. when I was in high school (mid 1970s). There are several nearly identical editions, such as the 1962 edition AND the 1968 edition AND the 1975 edition.

You may also want to look over the Art of Problem Solving books and the MEGSSS (Elements of Mathematics) books. Regarding the MEGSSS books, see my answer to Logic and set theory textbook for high school.

  • $\begingroup$ So I looked this up on archive.org and found this archive.org/details/modernalgebrastr01dolc , pretty much matches your description except for the name. Now the book I studied from is different because it was made by the school I went to. However this is exactly what I was looking for: set theory, axioms, a lot of exercises! Thank you very much. Now the challenge is to find a printed version of the book. $\endgroup$ – Jean Nov 16 '17 at 14:43

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