Our goal: Find the best Abstract Algebra books according to the internet (not just one random person's opinion).
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If you're interested in studying abstract algebra, some of the best abstract algebra textbooks include "Abstract Algebra" by Dummit and Foote, "A Course in Abstract Algebra" by Khanna and Bhambri, and "Algebra" by Artin. Each of these books showcases the strengths of abstract algebra and provides an in-depth treatment of the subject matter.
Yes, "Algebra" by Michael Artin is a great algebra textbook that strikes a balance between theory and applications. It covers a range of topics in abstract algebra, including groups, rings, and fields. The book's approach to algebra is theoretical but it includes numerous examples and problems for practical application.
It's rare to find a single textbook that offers an introduction to both real analysis and abstract algebra as they are advanced topics in mathematics usually studied in separate courses. However, you can look at "Introduction to Topology and Modern Analysis" by G.F. Simmons for real analysis and "A Course in Algebra" by E.B. Vinberg for abstract algebra.
For complex analysis, I recommend "Complex Analysis" by Ahlfors. This book is widely regarded as a classic in the field. For an introduction to abstract algebra, consider "Algebra" by Michael Artin. It covers a variety of algebraic structures with a focus on groups, rings, and fields.
For an undergraduate level course, a good book would be "Abstract Algebra: An Introduction" by Thomas W. Hungerford. This book is designed for beginners, covering topics such as groups, rings, and fields with clarity and depth, making it ideal for a semester-long study.
Amazon reviews of abstract algebra books can be very helpful. Consider the book's item weight in terms of content. Is the book for beginners, intermediate students, or advanced learners? Check if the reviews mention if it's good for self-study or better suited for a course.
For advanced topics in abstract algebra, such as the study of Lie groups and algebraic topology, I recommend "Topics in Algebra" by I.N. Herstein and "Introduction to Lie Algebras and Representation Theory" by J.E. Humphreys. Both books provide comprehensive and advanced introductions to these topics.
Indeed, "An Introduction to the Theory of Numbers" by Niven, Zuckerman, and Montgomery is a great book that complements abstract algebra study. It covers number theory in detail, one of the main branches of pure mathematics.
Reddit is a great resource. The subreddit r/mathbooks has many threads discussing abstract algebra books. You can follow the reddit newest recommendations and comments. Just search "abstract algebra" or "algebra abstract" in the subreddit's search bar to find relevant threads.