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I am soon going to start my study of abstract algebra, most probably with Anthony Knapp's Basic Algebra. Here's the page for the book on Amazon.

Before starting with abstract algebra, I was hoping, time permitting, I could go over some book on geometry, or some book in an other area that naturally paves the way for one to study abstract algebra. I am hoping this exercise will make abstract algebra seem more intuitive, making one understand the point, the need and the utility of the subject.

It is easy enough to make the transition to, say, real analysis based on one's experience of having worked with real numbers and functions of one or several variables for a good part of one's life. I think, however, this can't be said for abstract algebra. Yes, we are taught Euclidiean geometry in high school, but most it is taught in a very ad-hoc, trivial manner. I suspect this will make it difficult for me to understand the abstract algebra inside out. A similar question on this issue, for instance, can be found at this link.

So, I was wondering if someone could recommend a list of books which one could either study before starting off with abstract algebra or keep on the side while covering abstract algebra to make sure one is able to understand the subject holistically.

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    $\begingroup$ I think that elementary number theory "makes the subject area of abstract algebra" perhaps more intuitive than geometry. Many statements in group theory can be condensed to some elementary number theory, like divisors of integers (Lagrange, class equation, Sylow subgroups, index of normalizer etc.); and the integers as infinite cyclic group $\endgroup$ – Dietrich Burde Mar 31 '17 at 12:58
  • $\begingroup$ I think the geometric prerequisites for a first (or even third) encounter with abstract algebra are essentially nonexistent. I wouldn't expect you to see more than "symmetries of a regular polygon/polyhedron," which doesn't really require any formal geometry. The more geometric aspects tend to be approached via linear algebra, which would be good to revisit (although it still isn't necessary). $\endgroup$ – pjs36 Mar 31 '17 at 13:00
  • $\begingroup$ @pjs36 I have always felt that the the linear algebra books that I have studied from thus far have lacked a geometric flavor. Perhaps that has been because of the textbooks I have used thus far. I went through Anton and Rorres' Elementary Linear Algebra for my first course and Friedberg, Insel and Spence's Linear Algebra* for my second course. Any suggestions on this front? $\endgroup$ – Junaid Aftab Mar 31 '17 at 13:05
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There are many introductory textbooks in Algebra you may use. First of all, you must master high-school algebra (factorization of polynomials and so on, in order to understand how to do counts).

I suggest you: Fraleigh's A First Course in Abstract Algebra. Abstract Algebra by Dummit and Foote

You can use Herstein's Algebra or Lang's Algebra for a further level.

Concerning Knapp's Basic Algebra, it is well written but you can find the same contexts in all textbooks. If you want to integrate the subject by many textbooks, you can consult it, but I suggest you to not use many textbooks to learn algebra. On the contrary, you should only a pair of good textbooks and then, after you understand the various arguments, to use other textbooks.

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  • $\begingroup$ Any opinion on Knapp's Basic Algebra? $\endgroup$ – Junaid Aftab Mar 31 '17 at 12:57
  • $\begingroup$ For opinions on algebra books see here. There are many recommendations. $\endgroup$ – Dietrich Burde Mar 31 '17 at 13:00

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