I am reading Abstract Algebra from Dummit Foote.
I need to cover the following topics for my upcoming exam:
Groups, homomorphisms, normal subgroups and quotients, isomorphism theorems, finite groups, symmetric and alternating groups, direct product, structure of finite abelian groups, Sylow theorems.
Rings and ideals, quotients, homomorphism and isomorphism theorems, maximal ideals, prime ideals, integral domains, eld of fractions, Euclidean rings, principal ideal domains, unique factorization domains, polynomial rings.
Fields, characteristic of a field, algebraic extensions, roots of polynomials, separable and normal extensions, finite fields.
Elementary number theory and combinatorics:
Divisibility, congruences, standard arithmetic functions, permutations and combinations.
However I find that an enormous amount of material has been given in this book and the book also has a great volume.I don't know when will I finish this book.
Is it necessary to cover all the topics related to above from the book?
Are there any alternatives to Dummit Foote as a standard text which also has good problems and exercises and would serve me well on these topics for my upcoming exam allowing me to finish the topics in a reasonable time??