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I saw the list of books suggested by my college. There are two categories, one for text book and the other for reference book. For abstract algebra, they have Dummit and Foote, Abstract Algebra as textbook, and Herstein, Topics in Algebra as reference book. Both seem to be similar, but, don't know, the difference in how they were categorised.

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  • $\begingroup$ Maybe the text book defines the curriculum and the reference book is the recommended book for those who want more material? $\endgroup$
    – Arthur
    Jul 21, 2018 at 11:42

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In general terms, a textbook is a book you can read from the beginning to learn a new subject - perhaps on your own, perhaps in a course. Not necessarily quite that linear, since you will need to double back to reread and refresh. When you're done with the book and the course (do the exercises!) you will more or less know the material.

If you need to check some particular definition or theorem a textbook might not be the best place to look, since the idea may be spread out over several pages or sections. A reference book is likely to be more compact. (Sometimes wikipedia is a good "reference book" for things you already know something about.)

That said, both the books you ask about are textbooks, designed for an abstract algebra class. Herstein is harder/deeper/faster than Dummit and Foote. Your college is suggesting that the course will rely on D&F but that you may be able to learn a little more from a different perspective from Herstein. They may also be suggesting that you should buy D&F but consult Herstein in the library.

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  • $\begingroup$ "Herstein is harder/deeper/faster than Dummit and Foote." - Precise expression of experience. Will get into Herstein too. Thank you. $\endgroup$
    – Sensebe
    Jul 21, 2018 at 11:56
  • $\begingroup$ To know the difference clearly in the context, can you suggest a abstract algebra reference book? $\endgroup$
    – Sensebe
    Jul 21, 2018 at 11:58
  • $\begingroup$ As I say in my answer, wikipedia is a good reference book. For example, early in abstract algebra you will learn Lagrange's theorem. I don't know where it is in either of those books, but here is a quick overview: en.wikipedia.org/wiki/Lagrange%27s_theorem_(group_theory) $\endgroup$ Jul 21, 2018 at 12:01

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