Free Math Textbooks | Open CultureJudson 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. The index uses a similar approach, choosing to display a collapsed link to the first paragraph in which the term is used, which is often a formal definition.
Abstract Algebra: Theory and Applications
Whitehead's Geometric Algebra by Stephen Blake, , pages, 1. Abstract Algebra by John A. Beachy, William D. Blair, Abstract Algebra Wikibooks, Abstract Algebra I by Marcel B.
subject of abstract algebra and no student should go through such a course without a placed either on theory or on applications. A typical.
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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. This text is intended for a one- or two-semester undergraduate course in abstract algebra and covers the traditional theoretical aspects of groups, rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included.