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I will be taking abstract algebra course in a month from now. I am first time taking and algebra course and will be sitting with math majors. Can someone suggest me a book suitable for me i.e for beginner,inexperienced and lots of motivation as well as rigorous. I have A First course in abstract algebra by John Fraleigh in my mind. Can someone suggest similar or some more books or any material which will be helpful to me

Review of basics, Permutations, sign of a permutation, inversions, cycles and transpositions, groups, subgroups and factor groups, Lagrange's Theorem, homomorphism, normal subgroups, Quotients of groups, Cyclic groups, generators and relations, Cayley's Theorem, group actions, Sylow Theorems. Direct products, Structure Theorem for finite abelian groups. Simple groups and solvable groups, nilpotent groups; Free groups, free abelian groups. Rings, Examples (including polynomial rings, formal power series rings, matrix rings and group rings), ideals, prime and maximal ideals, rings of fractions, Chinese Remainder Theorem for pairwise comaximal ideals. Euclidean Domains, Principal Ideal Domains and Unique Factorizations Domains. Polynomial rings over UFD'; finite field and field extensions.

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When you study abstract algebra, it is important to think examples.

For an introductory text

  • Hungerford, Abstract Algebra: An Introduction

More examples and broad view

  • Artin, Algebra
  • Dummit and Foote (Although it is a graduate text, but it will be helpful because it gives a tons of examples)
  • Paul Garrett, Abstract Algebra (it gives all model solution)

will be helpful.

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  • $\begingroup$ i fear that this is a graduate course i am taking.. $\endgroup$ – Gathdi Jun 13 '16 at 13:53
  • $\begingroup$ In that case, I add some more references. $\endgroup$ – Will Kwon Jun 13 '16 at 13:54
  • $\begingroup$ And if you have not done so before, make sure you have some exposure to set theory, where you see rigorous definitions of basic math concepts from sets to cardinality to bijections to products of sets, etc. As a side product, or maybe as the main product, you get to learn how proofs are done in mathematics, and what types of arguments are thematic. Don't plunge into group theory right away, I would say. $\endgroup$ – Behnam Esmayli Jun 13 '16 at 13:55
  • $\begingroup$ @Gathdi Maybe, Paul Garrett's lecture note will be helpful. It gives a solution of exercises also. If you are not familar with mathematics rigorous proof, see math.berkeley.edu/~hutching/teach/proofs.pdf $\endgroup$ – Will Kwon Jun 13 '16 at 13:56
  • $\begingroup$ @WillKwon i read little bit about types of proofs like contrapositive,induction but i do not have much exposure to that. Thanks $\endgroup$ – Gathdi Jun 13 '16 at 13:58

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