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I'm a mechanical engineering Ph.D. student, currently self-studying mathematics. I want to learn abstract algebra, which is entirely new to me. My goal is to build a strong foundation for advanced-level algebraic topology.

I've already completed courses in measure theory and real analysis, so I believe I'm not a complete beginner when it comes to proof writing. Therefore, I'm confident that with the right book, I can manage the subject.

I'm looking for a book that is neither too basic nor overly advanced—something suitable for senior undergraduate or first-year graduate students. Ideally, this book would also serve as a good reference. I would appreciate any book recommendations on this topic. Additionally, I have a few books in mind and would like to know which one would be the best fit based on my needs. I've read the post about books recommendation for abstract algebra and come up with these choices, but I want your help to choose between them.

  1. Abstract algebra by Dan Saracino
  2. Abstract algebra by Dummit and Foote
  3. Abstract algebra by Serge Lang
  4. Contemporary Abstract algebra by Gallian
  5. Abstract algebra by Herstein
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I recommend Algebra by Hungerford. This book will teach you as a beginner first. You mentioned that you have some mathematical background. This book will only briefly mention some too basic content, and will not spend a lot of space. Second, when you're going to study algebraic topology, you're going to have to deal with some advanced stuff, and this book covers some of the basics of category theory and free groups and so forth that you might use in algebraic topology, which is definitely good for a reference book. Also, this book is easy to read and has some solutions for the exercises. Bob Gardner has made some PPT to explain some of the ideas in the book and detailed proof for propositions, lemmas, and theorems. If you don't understand the proof or want to see more, you can read that. This book has solutions that you can find here. It has only $400+$ pages, which helps you save time and improve efficiency. If you want to preview this book, click this.

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    $\begingroup$ Thank you so much for providing link of Professor Bob Gardner website. Those PPT are really helpful. Though, there are few typos in PPT and sometimes (very rare) misleading filling details, for instance Theorem V.6.4. $\endgroup$ Commented Jun 22, 2024 at 17:06

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