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内容推荐 数论与代数结构这门课是数学学院信息安全专业的一门专业基础课。通过该课程的学习,让学生掌握密码学所需要的重要的数学基础理论,熟悉密码体制中常用的数学基本算法及其复杂性理论。具体分为下面几个方面的内容:1.整除:整除的基本理论,辗转相除法;2.同余:同余、剩余类的基本理论,同余方程,Euler定理;3.原根:指标的基本理论,原根基本定理;4.群、环、域基本理论;5.群、环、域进一步的理论,扩域、有限域的理论;6.基本算法、及其复杂性理论;7.格理论。 目录 Foreword Preface Preface to the English Edition Chapter 1 The origin of generalized metric spaces 1,1 Notations and terminologies 1.2 Distance functions 1.3 Bases 1.4 Stratifications 1.5 Networks and (rood k)-networks 1.6 k-networks and weak bases 1.7 Generalized countably compact spaces 1.8 Examples Chapter 2 Mappings on metric spaces 2.1 Classes of mappings 2.2 Perfect mappings 2.3 Quotient mappings 2.4 Open mappings 2.5 Closed mappings 2.6 Compact-covering mappings 2.7 s-mappings 2.8 ss-mappings 2.9 7r-mappings 2.10 Compact mappings 2.11 a-locally finite mappings Chapter 3 Generalized metric spaces 3.1 Spaces with point-countable covers 3.2 Z-spaces 3.3 a-spaces and semi-stratifiable spaces 3.4 k-semi-stratifiable spaces 3.5 Mi-spaces 3.6 Developable spaces and p-spaces 3.7 M-spaces 3.8 R-spaces 3.9 g-metrizable spaces 3.10 Open questions Appendix A Characterizations of several covering properties A.1 Paracompact spaces A.2 Metacompact spaces A.3 Subparacompact spaces A.4 Submetacompact spaces A.5 Meta-LindelSf spaces Appendix B The formation of the theory of generalized metric spaces B.1 A historical review B.2 The foundation laying period B.3 The formation period Bibliography Index Mathematics Monograph Series |