代数学 第1卷
节选
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本书特色：抽象与具体结合，理论与应用结合。目前的代数书，常常单线地朝抽象方向发展，使读者–甚至一些数学家们–觉得代数学是抽象概念的游戏。各种数学理论的平行发展，到了代数学中，取得了整合与统一。
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本书特色
[
本书特色：抽象与具体结合，理论与应用结合。目前的代数书，常常单线地朝抽象方向发展，使读者–甚至一些数学家们–觉得代数学是抽象概念的游戏。各种数学理论的平行发展，到了代数学中，取得了整合与统一。
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内容简介
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The “abstract,””formal”or”axiomatic”direction,to which the fresh impetus in algebra is euc ,haw led ,haw led to a numbe of new formulations of ideas,insight into new interrelations,and far-reaching results results,especially in group theory ,field theory,valuation theory, ideal theory,and the theory of hypercomplex numbers.The principal objective of this reason ,genreral concepts and methods stand in the foregorund ,particular results which properly belong to classical algebra must also be give appropriate consideration within the framrwork of the modern development.
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目录
Chapter 1 NUMBERS AND SETS1.1 Sets1.2 Mappings ,Cardinality1.3 The Number sequence1.4 Finite and countable (denumerable)sets1.5 partitionsChapter 2 GROUPS2.1 The concept of a group2.2 subgrougs2.3 compleses.cosets2.4 Isomorphisms and automorphisms2.5 Homomorphisms ,normal subgroups,and factor groupsChapter 3 RINGS AND FIELDS3.1 Rings3.2 Homomorphism and Isomorphism3.3 The concept of a field quotients3.4 Polynomial rings3.5 Ideals,residue class rings3.6 divesibility .prime ideals3.7 Euclidean rings and principal ideal rings3.8 FactorizationChapter 4 VECTOR SPACES AND TENSOR SPACES4.1 Vector spaces4.2 Dimensional invariance4.3 The dual vector space4.4 Linear equations in a skew field4.5 Linear transformations4.6 Tensors4.7 Antisymmetric multilinear forms and determinants4.8 Tensor products,contraction,and traceChapter 5 POLYNOMIALS5.1 Differentiation5.2 The zeros of a polynomial5.3 Interpolation formulae5.4 Factorixation5.5 Irrdeucibility criteria5.6 Factorixation in a finite number of steps5.7 symmetric functions5.8 the resultant of two polynomials5.9 the resultant as a symmetric function of the roots5.10 partial fraction decompositionChapter 6 THEORY OF FIELDSChapter 7 CONTINUATION OF GROUP THEORYChapter 8 THE GALOIL THEEORYChapter 9 ORDERING AND WELL ORDERING OF SETSChapter 10 INFINITE FIELD EXTENSIONSChapter 11 REAL FIELDSINDEX
封面
书名:代数学 第1卷
作者:范德瓦尔登
页数:265 页
定价:¥35.0
出版社:世界图书出版公司
出版日期:2007-10-01
ISBN:9787506291606
PDF电子书大小:70MB