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Tables of Contents for Symmetry in Science
Chapter/Section Title
Page #
Page Count
Preface
vii
What Is Symmetry?
1
4
The Mathematics of Symmetry: Group Theory
5
33
The Group Concept
6
13
Mapping
19
4
Isomorphism
23
4
Equivalence Relation
27
2
Homomorphism
29
5
Subgroup
34
2
Summary of Chapter Two
36
2
Group Theory Continued
38
28
Conjugacy, Equivalence Class, Invariant Subgroup, Kernel
38
5
Coset Decomposition
43
3
Factor Group
46
3
Anatomy of Homomorphism
49
4
Generators
53
1
Direct Product
54
2
Permutations, Symmetric Groups
56
4
Cycles, Transpositions, Alternating Groups
60
3
Cayley's Theorem
63
1
Summary of Chapter Three
64
2
Symmetry: The Formalism
66
26
System, State
66
2
Transformations, Transformation Group
68
5
Transformations in Space, Time, and Space-Time
73
5
State Equivalence
78
2
Symmetry Transformations, Symmetry Group
80
6
Quantification of Symmetry
86
2
Quantum Systems
88
2
Summary of Chapter Four
90
2
Application of Symmetry
92
34
Causal Relation
93
4
The Equivalence Principle
97
7
The Symmetry Principle
104
2
Minimalistic Use of the Symmetry Principle
106
15
Maximalistic Use of the Symmetry Principle
121
2
Quantum Systems
123
1
Summary of Chapter Five
124
2
Approximate Symmetry and Spontaneous Symmetry Breaking
126
8
Approximate Symmetry
126
3
Spontaneous Symmetry Breaking
129
4
Summary of Chapter Six
133
1
Symmetry in Processes, Conservation, and Cosmic Considerations
134
23
Symmetry of the Laws of Nature
134
8
Symmetry of Initial and Final States, the General Symmetry Evolution Principle
142
3
The Special Symmetry Evolution Principle and Entropy
145
5
Conservation
150
3
Cosmic Considerations
153
2
Summary of Chapter Seven
155
2
Symmetry: The Concept
157
12
The Essence of Symmetry
157
3
How Is Change?
160
2
Symmetry of the Universe
162
2
Analogy as Symmetry
164
3
Summary of Chapter Eight
167
2
Symmetry in Science
169
15
Science
169
2
Reduction as Symmetry
171
1
Observer and Observed
172
2
Quasi-Isolated System and Surroundings
174
2
Initial State and Evolution
176
2
Reproducibility as Symmetry
178
2
Predictability as Symmetry
180
2
Symmetry at the Foundation of Science
182
1
Summary of Chapter Nine
182
2
More Symmetry in Science
184
7
Analogy in Science
184
1
Symmetry of Evolution
185
3
Symmetry of States
188
2
Summary of Chapter Ten
190
1
Summary of Principles
191
2
Onward
193
2
Bibliography
195
10
Index
205