Algebra (Cambridge Mathematical Textbooks)
Product ID: 253572954
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From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory. Review: Nice, but not groundbreaking - I've had this book for a few days so far. From a first look it looks pretty decent. But it failed to excite me in the way Aluffi's 'Algebra: Chapter 0' did by its freshness of organization and presentation. The material and presentation is more or less what can be found in other good undergraduate books like Artin or Lang's undergraduate text. The innovations are having rings first and a greater sprinkling of commutative diagrams, but I'm not sure either actually makes the subject more accessible or interesting for the beginner. Also, so far I have not been able to understand the reason for the Dostoevsky reference in the subtitle. Need to figure that out. Review: Excellent text for self-study - This is a phenomenal book. The content is broad, the examples plentiful, the prose is engaging, and the exercises are inviting and accessible.
| Best Sellers Rank | #281,851 in Books ( See Top 100 in Books ) #267 in Algebra & Trigonometry #288 in Algebra |
| Customer Reviews | 4.8 out of 5 stars 28 Reviews |
J**A
Nice, but not groundbreaking
I've had this book for a few days so far. From a first look it looks pretty decent. But it failed to excite me in the way Aluffi's 'Algebra: Chapter 0' did by its freshness of organization and presentation. The material and presentation is more or less what can be found in other good undergraduate books like Artin or Lang's undergraduate text. The innovations are having rings first and a greater sprinkling of commutative diagrams, but I'm not sure either actually makes the subject more accessible or interesting for the beginner. Also, so far I have not been able to understand the reason for the Dostoevsky reference in the subtitle. Need to figure that out.
R**O
Excellent text for self-study
This is a phenomenal book. The content is broad, the examples plentiful, the prose is engaging, and the exercises are inviting and accessible.
C**N
My favorite intro to Algebra
Having worked through other Algebra texts I think this might be my favorite intro to the subject. First and foremost, it’s a book written in anti-Bourbaki style; ie, it’s written to be understood first-hand and avoids that miserable laundry-list approach of Definition-Lemma-Theorem-Corollary without any comentary, examples or motivation in-between. Professor Aluffi really cares about that the reader can grasp the material, and that’s a rare feat among many mathematics textbooks. Furthermore, there’s a great amount of exercises and the most relevant through the rest of the text are marked and have full solutions at the back of the book. This is specially useful if you’re self-studyin to check your work. Last but not the least, I really like the rings-first approach. By the time you reach to more abstract constructions like the quotient ring, you’ve already gone through the integers mod n’s, and it feels like a natural generalization. It’s a really gentle approach in that sense. The icing in the cake! It also covers module theory, something that most textbooks pitched at this level omit and so it is welcome. I cannot recommend it enough, more so for independent learners.
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