This comprehensive presentation of modern algebra proceeds from the simplest structures involving only binary operation to the more complex. The authors believe that the student can develop the ability to construct and present proofs of theorems more easily when working with a system in which only one binary operation is under consideration. Features of this book include: the treatment of Z of convergence classes modulo n, discussed throughout most of the book; optional sections on some results of finite abelian groups; and ...
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This comprehensive presentation of modern algebra proceeds from the simplest structures involving only binary operation to the more complex. The authors believe that the student can develop the ability to construct and present proofs of theorems more easily when working with a system in which only one binary operation is under consideration. Features of this book include: the treatment of Z of convergence classes modulo n, discussed throughout most of the book; optional sections on some results of finite abelian groups; and real and complex numbers included for the benefit of students who would not otherwise cover this material. The second edition has new sections which place more emphasis on the composition of mappings, expanded treatment of mathematical introduction, additional material on rings and more thorough coverage of polynomials. Numerous examples, exercise sets and problems are included, key words and phrases are summarized at the end of each chapter and many figures and tables help the student to assimilate material more easily. References are listed at the end of the book, together with answers to about half of the computational exercises. The answers for the remaining computational exercises and some of the answers requiring proofs are available in the Instructors' Manual. This book should be of interest to degree and diploma students on introductory courses in algebra.
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