Good Modern/Abstract Algebra book?

In summary, Fraleigh's "A First Course in Abstract Algebra" is a good book for an introductory/intermediate undergraduate course on Modern Algebra, but Dummit and Foote's "Abstract Algebra" is a better book for a graduate-level course. Birkhoff and MacLane's "Survey of Modern Algebra" is not appropriate for an introductory/intermediate undergraduate course.
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The title says it all...I'm looking for a comprehensive, in depth book for an introductory/intermediate undergraduate course on Modern Algebra. I've got Fraleigh's "A First Course in Abstract Algebra" and Warner's "Modern Algebra." But Fraleigh's book is my text for this Fall's course and Warner's covers a bit too much and doesn't go as in depth on the topics I need. Also: budget is low, so the less expensive the better. Thanks.
 
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It is worth noting that Artin is available in international edition from places like AbeBooks for much less than the US version (~ $25). I've got both and they are the same content. The quality of the international edition is perhaps a little less - thinner paper.

Of the ones that have been cited above, Artin is I think by far the best fit for the requirements that are given. Artin has nice features such as some discussion of Riemann surfaces and Hopf fibrations and so on which connect the algebra with areas that are relevant to physics. Lang is a graduate text and I think somewhat dry. Dummit and Foote is workman-like.

As always YMMV.
 
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Have you looked through Fraleigh? I have browsed through the older editions, and it seems the newer editions have changed quite a bit of the book. It is a very good introduction, and he included some a neat application to homology groups in the early editions. Dummit and Foote is the standard graduate text in algebra. From the Amazon reviews, it seems Artin is a non-standard unique text, which may make it a bad selection to use as a reference book while you're learning from Fraleigh. Abstract Algebra by Herstein seems to be good, never read it though. My undergraduate course used Contemporary Abstract Algebra by Gallian and was likable and easy to read.
 
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I second Dummit & Foote. It covers a lot of topics, and does so in a rigorous but readable fashion. Definitions, theorems and proofs are clearly indicated and seperated, as opposed to Artin.
 
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I am currently learning Abstract Algebra from Dummit and Foote. It is a great text and a must have for an algebraist.
 
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Great suggestions, thanks, all.
 
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You might also want to take a look at https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20, but this is a graduate book so probably too advanced for "an introductory/intermediate undergraduate course". Although some universities may use Dummit & Foote also for graduate courses, I think it is really suitable for an (2nd year) undergraduate.
 
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Since they recommended Fraleigh, I think it's because the students are at that level, and Fraleigh does very well what it sets out to do: that is, provide material for a semester long course for students who are knew to proofs or not to strong with proofs, or non-mathematics students.

Artin and Herstein, mentioned above, are very good books, but at a slightly higher level than Fraleigh, i.e. those two books will require a lot more commitment from you, but are more rewarding in return. I am not too familiar with ther books, besides Birkhoff and MacLane's Survey of Modern Algebra, which is inappropriate I think.
 

What is the difference between modern and abstract algebra?

Modern algebra is a broad term that encompasses various branches of algebra, including abstract algebra. Abstract algebra is a more specific branch that deals with algebraic structures and their properties in a general and abstract setting.

Why should I study modern/abstract algebra?

Modern and abstract algebra are important branches of mathematics that have numerous applications in fields such as computer science, physics, and engineering. They also provide a deeper understanding of algebraic concepts and their applications in other areas of mathematics.

What topics should a good modern/abstract algebra book cover?

A good modern/abstract algebra book should cover topics such as groups, rings, fields, vector spaces, and modules. It should also include examples, exercises, and applications to help readers understand and apply the concepts.

What are some recommended modern/abstract algebra books for beginners?

Some recommended modern/abstract algebra books for beginners include "A First Course in Abstract Algebra" by John B. Fraleigh, "Abstract Algebra" by David S. Dummit and Richard M. Foote, and "Algebra" by Michael Artin. These books provide a solid foundation in the subject and are suitable for self-study.

How can I improve my understanding of modern/abstract algebra?

To improve your understanding of modern/abstract algebra, you can practice solving problems and working on exercises from textbooks or online resources. You can also attend lectures or join study groups to discuss and clarify any difficult concepts. It is also helpful to read different books and seek out additional resources to gain a deeper understanding of the subject.

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