# Abstract algebra theory and applications

## Abstract Algebra: Theory and Applications by Thomas W. Judson

Abstract Algebra: Theory and Applications is an open-source textbook written by Tom Judson that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.## Abstract Algebra: Theory and Applications (2019)

For many students, abstract algebra is the most daunting of math classes. Many students particularly those who do not have a strong theoretical bent see abstract algebra as symbol-twiddling with no apparent rhyme or reason. To them, group theory proofs are just so many rabbits pulled from hats. For this reason, I needed a textbook that made heavy use of familiar mathematical structures such as the integers mod n, complex numbers, symmetries, and permutations to motivate and illustrate the more abstract concepts. I also needed a more pedestrian book that valued clarity and gradual unfolding above elegance and conciseness. The exercises should be progressive, with a generous number of relatively easy problems for student practice.

Everything you wanted to know about abstract algebra, but were afraid to buy. Tom Judson's Abstract Algebra: Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Rob Beezer has contributed complementary material using the open source system, Sage. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory. This textbook has more freedom than most but see some exceptions.

An open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Tag s : Linear Algebra. Publisher : Orthogonal Publishing L3C. Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound , where he has been on the faculty since

Tom Judson's Abstract Algebra: Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college.

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Judson covers all of the basics one expects to see in an undergraduate algebra sequence. The coverage of ring theory is slimmer, but still relatively "complete" for a semester of undergraduate study. Three chapters on rings, one on lattices, a chapter reviewing linear algebra, and three chapters on field theory with an eye towards three classical applications of Galois theory. I will note here that Judson avoids generators and relations. The coverage is all fairly standard, with excepting the definition of Galois group see accuracy , and the referencing system in the HTML version is extremely convenient. For example, Judson leverages HTML so that proofs are collapsed but can be expanded which allows him to clean up the presentation of each section and include full proofs of earlier results when useful as references.

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Abstract Algebra: Theory and Applications | Mathematical Association of America

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