Elements of Abstract Algebra (eBook, ePUB)
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The book preserved the emphasis on providing a large number of examples and on helping students learn how to write proofs. The presentation of the sections given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and a proof the Primitive Element Theorem. First semester course should probably include the material of Sections 0-13, and some of the material on...
The book preserved the emphasis on providing a large number of examples and on helping students learn how to write proofs. The presentation of the sections given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and a proof the Primitive Element Theorem. First semester course should probably include the material of Sections 0-13, and some of the material on rings in Section 16 and the following sections. Sections 14 and 15 allow the inclusion of some deeper result on groups. In second semester it should be possible to cover the whole book, possibly omitting Section 21.The changes include the simplification of some points in the addition of some new exercise, and the updating of some historical material. All the topics are given in step by step method with simple language to understand the concept easily. This book is intended for use in a junior-senior level course in abstract algebra. The students who used the book for the five sections as text and pointed out to me parts of the presentation that needed clarification.
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