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I am looking for any recommendations or suggestions for a good book covering an introduction to the following; Relation , sets and functions, divisibility theory and modular arithmetic , groups, rings, ideals, fields, etc.

It would be intend for preparing for a intro course in university algebra.

It would also be best if it was to be introductory book as I have no prior courses done in algebra. I have knowledge up to multivariable calculus, but I don't think that will matter.

I also have some knowledge of the fundamentals of linear algebra.

I would preferably be looking for a user friendly book, and if possible links to any pdf's or recommended text books.

Thank you everyone,

davidlowryduda
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Quality
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  • This is a really wide set of questions, many of which are fundamentally opinion-based. You might instead consider asking this question(s) in the math chat room and seeing what people think there. – davidlowryduda May 09 '15 at 20:30
  • Somebody has an excellent algebra book available for download here: http://homepages.math.uic.edu/~acamer4/aluffi.pdf – Gregory Grant May 09 '15 at 20:30
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    I think the first part of the question, namely, the book recommendation, is a valid and useful one. The last paragraph contains too many questions! – Andrea May 09 '15 at 20:31
  • Okay, I edit it, sorry for mix up – Quality May 09 '15 at 20:32
  • There's also this one: http://abstract.ups.edu/download.html – Gregory Grant May 09 '15 at 20:34
  • This has been asked and answered many times before. Those answers are still relevant. I direct you to http://math.stackexchange.com/questions/11626/good-books-for-self-studying-algebra, http://math.stackexchange.com/questions/49253/requesting-abstract-algebra-book-recommendations, http://math.stackexchange.com/questions/317938/abstract-algebra-book-recommendations-for-beginners, http://math.stackexchange.com/questions/54839/good-abstract-algebra-books-for-self-study – davidlowryduda May 09 '15 at 20:35
  • Thanks all, I made a separate post with my other question as that seems to be a better idea. – Quality May 09 '15 at 20:45

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I recommend Topics in Algebra by Herstein. I used it to prepare for an undergraduate honors abstract algebra course knowing zero algebra beforehand. I took the first semester of the course and it was so easy for me that the next semester I took second semester graduate algebra.

The secret is that the problems in Herstein are hard, yet elementary. You won't find many hints on how to solve the problems in the text, yet it's always possible with what one already knows at that point (except for one double starred problem. There's a disclaimer next to that one). It's not for everybody but it worked for me.

Note: it is indeed an introductory text. The exposition is clear and easy to understand.

Matt Samuel
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  • That double starred problem... – Eoin May 10 '15 at 00:03
  • Thanks, I picked it up a while ago from the library and so far I find it great. Do you have any recommendations for a similar level/style text but for undergrad analysis? – Quality Jun 11 '15 at 01:24
  • @Quality the one I've had contact with is "Principles of Mathematical Analysis" by Rudin. Very popular, similar difficulty. I didn't spend quite as many hours with it though. – Matt Samuel Jun 11 '15 at 01:29
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What about A Concise Introduction to Pure Mathematics or Introductory Mathematics: Algebra and Analysis (Springer Undergraduate Mathematics Series) Both begin without previous knowledge and they are very good for building a solid basis. Maybe What Is Mathematics?: An Elementary Approach to Ideas and Methods

D1811994
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