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商品の説明
内容説明
This book gives a high level introduction to the main concepts of modern algebra. It contains numerous applications, such as: Polya colouring theory, latin squares, Steiner systems and error correcting codes are described, along with group and ring theory, which are all designed to show the relevance of algebra today. There are nearly 400 problems of varying degrees of difficulty, in order to test the reader's skill and progress.
Book Description
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra.
The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the readers skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe.
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Compact introduction to algebra
2008/2/17
形式:ペーパーバック
The first thing to not about this book is that it is dense. In my abstract algebra course we covered chapters 3-5 in an entire semester. However, it contained every proof we needed in class, and although it reads slowly, it was usually crystal-clear. Especially good is its treatment of group actions, which is sometimes lacking in introductory-level algebra books. There is a lot of additional material -- the author recommends covering chapters 1-7 in one semester, which may be feasible at institutions like MIT, but for the majority of students, the information contained in this book would be more than a year's worth. Chapter 8 contains almost a semester's worth of advanced linear algebra. Sometimes I wish there were a few more exercises in each chapter; especially in the beginning, because the proofs were relatively easy, it seemed like there wasn't a good enough selection of topics. The book is mercifully cheap, but even though it's paperback, it's very sturdy, and for such a low-cost choice, it has tons of content. Recommended.
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