- #1

Avatrin

- 245

- 6

I recently read a book called "The fundamental theorem of algebra" by Fine and Rosenberger. It focused specifically on polynomials, and proved the theorem using several fields of mathematics; Two of the proofs were algebraic.

Abstract algebra has been very difficult for me; Mostly because it is hard to think in terms of groups (I reckon fields and rings will get easier as well once I get a firm grip on the group). It is a very abstract concept that is hard to visualize. Also, it is very different than anything I have encountered before (like metric spaces or measure theory).

The aforementioned book is structured as a textbook; It has exercises and teaches the theory needed to understand the proofs. I think by focusing on something familiar, this book somehow made it easier for me to get a better grasp of abstract algebra. However, since it focuses on the fundamental theorem of algebra, its scope is limited. It barely goes through some core concepts in abstract algebra, and it skips a lot of theory I need.

I am having trouble properly understanding factor groups, the isomorphism theorems, Sylows theorems and Galois theory. Most books I have encountered barely dedicate a chapter to each of these concepts.

I think the isomorphism theorems and Sylows theorems are the ones I am struggling with the most. Does anybody know of a book on abstract algebra that has an approach that sounds similar to the one I have described above? Maybe it focuses on construction problems? Or something else I should be relatively familiar with?