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,
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.