| 書目名稱 | Fields and Galois Theory | | 編輯 | John M. Howie | | 視頻video | http://file.papertrans.cn/343/342676/342676.mp4 | | 概述 | Modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations.Features plenty of | | 叢書名稱 | Springer Undergraduate Mathematics Series | | 圖書封面 |  | | 描述 | Fieldsaresetsinwhichallfouroftherationaloperations,memorablydescribed by the mathematician Lewis Carroll as “perdition, distraction, ugli?cation and derision”, can be carried out. They are assuredly the most natural of algebraic objects, since most of mathematics takes place in one ?eld or another, usually the rational ?eld Q, or the real ?eld R, or the complex ?eld C. This book sets out to exhibit the ways in which a systematic study of ?elds, while interesting in its own right, also throws light on several aspects of classical mathematics, notably on ancient geometrical problems such as “squaring the circle”, and on the solution of polynomial equations. The treatment is unashamedly unhistorical. When Galois and Abel dem- strated that a solution by radicals of a quintic equation is not possible, they dealt with permutations of roots. From sets of permutations closed under c- position came the idea of a permutation group, and only later the idea of an abstract group. In solving a long-standing problem of classical algebra, they laid the foundations of modern abstract algebra. | | 出版日期 | Textbook 2006 | | 關鍵詞 | Abstract algebra; Field theory; Galois theory; Group theory; Polynomials; algebra; finite field | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-84628-181-5 | | isbn_softcover | 978-1-85233-986-9 | | isbn_ebook | 978-1-84628-181-5Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | Springer-Verlag London 2006 |
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