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【内容】
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
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
