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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…
Treats all standard topics for a first course in detail, moving from rings to modules to groups to fields, which allows for a more gradual entry into the subject
Emphasizes a modern perspective, with hints toward category theory, exposing students to advanced topics and preparing them for graduate courses and applications of algebra in other subjects
Includes 400+ exercises, with 150 worked-out problems from the main text, and plenty of examples to help students better understand the material
Uses a conversational style and strong narrative flow that makes the material easier for students to follow and appreciate as a whole
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Author
Paolo Aluffi,Florida State University
Paolo Aluffi is Professor of Mathematics at Florida State University. Aluffi earned a Ph.D. from Brown University with a dissertation on the enumerative geometry of plane cubic curves, under the supervision of William Fulton. His research interests are in algebraic geometry, particularly intersection theory and its application to the theory of singularities and connections with theoretical physics. He has authored about 70 research publications and given lectures on his work in 15 countries. Beside Notes from the Underground, he has published a graduate-level textbook in algebra (Algebra: Chapter 0, AMS) and a mathematics book for the general public, in Italian (Fare matematica, Aracne Editrice).