Abstract Algebra, 3rd Edition 3rd Edition by David S. Dummit (PDF)

Description

This revision of Dummit and Foote’s widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the student’s understanding. With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year. Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.

User’s Reviews

Editorial Reviews: About the Author David S. Dummit and Richard M. Foote are the authors of Abstract Algebra, 3rd Edition, published by Wiley.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a superb textbook on algebra that is notable for its extremely clear and well-organized presentation. Development of different sections carefully builds on what went for, and running examples that gradually become more developed (for example, the quaternions as group, then as a ring, then various structural aspects) throughout. The terminology is completely standard, avoiding the temptation that some authors – or perhaps older texts – fall into of using bizarre terminology that is its author’s favorite. The whole text has a very uniform, clear, well-architected feel to it: the sections stand on their own to the extent that they can, but also fit solidly into the rest of the presentation.The presentation itself covers many topics which, taken together, make this an invaluable reference, for example group theory includes Burnside’s theorem on solvability of certain finite groups (and at least mentions Feit-Thompson); ring theory includes a discussion of Gröbner bases; linear algebra includes symmetric and exterior algebras. A good introduction to algebraic geometry (the Nullstellensatz, localization, and some basic framework) is included. There is a solid introduction to representation theory via group rings and Wedderburn’s theorem – an approach which is really more useful for applications than a pure group-theoretic introduction might have been.Despite its broad coverage of topics, the book’s development is extremely clear and easy-to-read. Because of the many examples and easy exercises, it is one of the most easy-to-understand texts I have seen. Every new idea is carefully defined and illustrated with multiple examples, proofs are very clear and painstaking. Indeed, given the methodical and well-motivated development, it’s kind of a miracle that the text was able to include so much material; this is a testament to its excellent organization.It’s worth noting as well that the typographical layout is excellent for an advanced mathematics textbook. Rarely (if ever) have I read an advanced math textbook that was as well laid out typographically. There are, however, virtually no diagrams other than some subgroup lattices early on.Caveats: there is little category theory – a choice I agree with at this level – and there is not much motivation of ideas outside math (or even outside algebra).I would definitely recommend this book as an introduction, as a textbook, and as a reference. As a textbook, though, I might supplement it with some motivational notes on applications outside math (for example, coding theory, tiling, puzzles, and the like) and perhaps a few harder exercises, depending on the students.

⭐Readable; comprehensive. Bought mine (3rd edition) fifteen years ago; it is typo-free and has physically held up very well. Dismayed to hear about binding and printing problems; this book deserves to be published with care.

⭐I never took abstract algebra in college but the writing style, presentation, and wealth of informative examples made this text perfect for self study. It really is a classic for me now in my library and I refer to it almost daily now. The hardest part is sticking with the initial group theory which seemed odd, but by the time you get to Gallois theory it’s just remarkable how far the same few “techniques” can get you across all these various objects. It’s just beautiful. I cannot recommend this book enough and honestly, you don’t need any calculus at all or even analysis, just logic and set theory could get you started for the most part. I’m confused why abstract algebra is taught so late the more I’ve pondered over things in this book and realized how much more sense everything makes thinking about coordinate systems and mappings which before seemed contrived or very hazy.I did supplement the book with Benedict Gross’ Harvard lectures which really helped in some areas but overall I could have got by without.

⭐I used this book in an advanced undergraduate/master’s level algebra course. I mostly used this book for exercises but on the occasion that I read the chapters they were friendly enough and readily digestible. The real pro about this book is the high number of non-trivial exercises. There are more than enough to get a good feeling out of any topic in the book and problems range from relatively straightforward to moderately sophisticated. There are also a good deal of computational problems of varying difficulty and many worked out examples in the book. As for the book’s organization: the sections on group theory don’t follow the best pattern, to me, but there is nothing seriously wrong with it. Sometimes D+F’s proofs can be excessively wordy or miss proper quantifiers, but for the most part everything is easy enough to follow. D+F’s exposition is decent, but I’ve read better. I seldom used this book to teach myself a subject without first learning about it in lecture, so I can’t comment too much here.The price is fairly high, but the book is huge. There is plenty of material here and it’s arguably one of the few math books worth the list price. Nevertheless, you’d be better off finding a used copy as there are most likely many people who could not handle the subject and returned the book. If you’re serious about learning algebra this is a must-have book. It will prepare you well for more advanced studies. There also seems to be a problem with the binding as my book and many of my classmates had problems with the cover ripping or spine splitting.

⭐I received this book last week from delivery and I must say this is an amazing book with a lot of content and exactly what I needed for my algebra course. There were certain topics that seem to constantly ridicule me but not after I acquired this book!! After indulging within the content of my ridiculed topics in this book I was finally able to challenge my problems and overcome them in my course and am now feeling much more confident about this module. I am not sure what is with the negative commotion however it may be that they purchased the paperback version whereas I bought the hardback version which I strongly reccommend. You can find them from round about £75 from various Amazon sellers and I can vouch for this saying that thus is bargain. Overall I reccommend this book to anyone doing an algebra module or even number theory aswell it is helping me a lot!!(or just buy it to learn eagerly if you really want to)

⭐Ottimo libroThere are not many great books out there, but this one is a real gem. I can whole heartedly recommend this book.If you have a background in physics, like I do, it will help you with the more mathematical foundations of quantum mechanics.This book combined with J.J. Sakurai’s Advanced Quantum Mechanics is a great for studying.

⭐I find this book is too dry and talkative…Would recommend the two volumes by Jacobson instead.

⭐The purchase actually arrived ahead of time and the book was exactly as advertised.

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