《Springer大學數學圖書》是清華大學出版社出版的圖書，作者詹森。
基本介紹
- 書名：Springer大學數學圖書
- 作者：詹森
- ISBN：9787302214786
- 定價：34.00 元
- 出版社：清華大學出版社
- 出版時間：2009年11月
- 開本：16
內容簡介,圖書目錄,
內容簡介
這是一本優秀的數學教材，適用於數學系本科生和其他專業對數學有興趣的本科生用作數學參考書或課外讀物。
圖書目錄
1.MetricSpaces and their Groups
1.1 Metric Spaces
1.2 Isometries
1.3 Isometries of theRealLine
1.4 Matters Arising
1.5 Symmetry Groups
2. Isometries of the Plane
2.1 Congruent Triangles
2.2 Isometries ofDifferentTypes
2.3 The NormalFormTheorem
2.4 Conjugation of Isometries
3.SomeBasic Group Theory
3.1 Groups
3.2 Subgroups
3.3 Factor Groups
3.4 Semidirect Products
4. Products of Reflections
4.1 The Product ofTwoReflections
4.2 Three Reflections
4.3 Four or More
5. Generators and Relations
5.1 Examples
5.2 Semidirect Products Again
5.3 Change of Presentation
5.4 Triangle Groups
5.5 Abelian Groups
6. Discrete Subgroups of the Euclidean Group
6.1 Leonardo's Theorem
6.2 A Trichotomy
6.3 Friezes and Their Groups
6.4 The Classification
7. Plane Crystallographic Groups: OP Case
7.1 The Crystallographic Restriction
7.2 The Parameter n
7.3 TheChoiceof b
7.4 Conclusion
8. Plane Crystallographic Groups: OR Case
8.1 A Useful Dichotomy
8.2 The Case n = 1
8.3 The Case n = 2
8.4 The Case n = 4
8.5 The Case n = 3
8.6 The Case n - 6
9. Tessellations of the Plane
9.1 Regular Tessellations
9.2 Descendants of (4, 4)
9.3 Bricks
9.4SplitBricks
9.5 Descendants of (3, 6)
10. Tessellations of the Sphere
10.1 Spherical Geometry
10.2 The Spherical Excess
10.3 Tessellations of the Sphere
10.4 The Platonic Solids
10.5 Symmetry Groups
11. Triangle Groups
11.1 The Euclidean Case
11.2 The Elliptic Case
11.3 The Hyperbolic Case
11.4 Coxeter Groups
12. Regular Polytopes
12.1 The Standard Examples
12.2 The Exceptional Types in Dimension Four
12.3 Three Concepts and a Theorem
12.4 Schlafli's Theorem
Solutions
Guide to the Literature
Bibliography
Index of Notation
Index
……
1.1 Metric Spaces
1.2 Isometries
1.3 Isometries of theRealLine
1.4 Matters Arising
1.5 Symmetry Groups
2. Isometries of the Plane
2.1 Congruent Triangles
2.2 Isometries ofDifferentTypes
2.3 The NormalFormTheorem
2.4 Conjugation of Isometries
3.SomeBasic Group Theory
3.1 Groups
3.2 Subgroups
3.3 Factor Groups
3.4 Semidirect Products
4. Products of Reflections
4.1 The Product ofTwoReflections
4.2 Three Reflections
4.3 Four or More
5. Generators and Relations
5.1 Examples
5.2 Semidirect Products Again
5.3 Change of Presentation
5.4 Triangle Groups
5.5 Abelian Groups
6. Discrete Subgroups of the Euclidean Group
6.1 Leonardo's Theorem
6.2 A Trichotomy
6.3 Friezes and Their Groups
6.4 The Classification
7. Plane Crystallographic Groups: OP Case
7.1 The Crystallographic Restriction
7.2 The Parameter n
7.3 TheChoiceof b
7.4 Conclusion
8. Plane Crystallographic Groups: OR Case
8.1 A Useful Dichotomy
8.2 The Case n = 1
8.3 The Case n = 2
8.4 The Case n = 4
8.5 The Case n = 3
8.6 The Case n - 6
9. Tessellations of the Plane
9.1 Regular Tessellations
9.2 Descendants of (4, 4)
9.3 Bricks
9.4SplitBricks
9.5 Descendants of (3, 6)
10. Tessellations of the Sphere
10.1 Spherical Geometry
10.2 The Spherical Excess
10.3 Tessellations of the Sphere
10.4 The Platonic Solids
10.5 Symmetry Groups
11. Triangle Groups
11.1 The Euclidean Case
11.2 The Elliptic Case
11.3 The Hyperbolic Case
11.4 Coxeter Groups
12. Regular Polytopes
12.1 The Standard Examples
12.2 The Exceptional Types in Dimension Four
12.3 Three Concepts and a Theorem
12.4 Schlafli's Theorem
Solutions
Guide to the Literature
Bibliography
Index of Notation
Index
……
