Author(s): Paul B. Yale
Publisher: Holden-Day
Year: 1968
Title page
Preface
Chapter 1: Algebraic and Combinatoric Preliminaries
1.1. Basic notions about sets and groups
1.2. The algebra of permutations and examples of groups
1.3. Homomorphisms and permutation representations of groups
1.4. Automorphisms of a group
1.5. Cosets and orbits, Lagrange's theorem
1.6. The Polya-Burnside theorem
Bibliography and suggestions for further reading
Chapter 2: Isometries and Similarities: An Intuitive Approach
2.1. Isometries and similarities
2.2. Involutions in S
2.3. The classification of isometries
2.4. Geometrie implications of conjugacy in S
2.5. An exercise: Isometries in the plane
2.6. Dilatations and spiral similarities
2.7. Automorphisms of E and S
2.8. Homomorphisms of E and S
Bibliography and suggestions for further reading
Review problems for Chapters 1 and 2
Chapter 3: An Introduction to Crystallography
3.1. Discrete groups of isometries
3.2. Finite groups of isometries
3.3. Lattices and lattice groups
3.4. Crystallographic point groups
3.5. The seven crystal systems
3.6. Crystallographic space groups
3.7. Generalizations
Bibliography and suggestions for further reading
Chapter 4: Fields and Vector Spaces: A Quick Review
4.1. Fields
4.2. Vector spaces, subspaces, echelon form
4.3. Linear transformations
4.4 Coordinate mappings, matrices for linear transformations
4.5. Similar matrices and commutative diagrams
4.6. Applications of matrix similarity
4.7. Symmetries of V_n(F), GL_n(F)
Bibliography and suggestions for further reading
Chapter 5: Affine Spaces
5.1. Axioms for affine spaces
5.2. Affine subspaces
5.3. Parallel and skew subspaces
5.4. Affine coordinates
5.5. Affine symmetries I: Dilatations
5.6. Affine symmetries II: Affine transformations
Term-paper topics
5.7. The analytic representation of affine transformations
5.8. Affine symmetries III: Collineations
5.9. Volume in real affine spaces
5.10. Lattices in real affine s paces
5.11. Collineations in real affine spaces
Bibliography and suggestions for further reading
Chapter 6: Projective Spaces
6.1. Extended affine spaces and collapsed vector spaces
6.2. Projective subspaces
6.3. Projective planes
6.4. Homogeneous coordinates
6.5. Projective symmetries I: Perspectivities
6.6. Projective symmetries II: Projective transformations
6.7. Projective symmetries III: Collineations
6.8. Dual spaces and the principle of duality
6.9. Correlations and semi-bilinear forms
6.10. Quadrics and polarities
6.11. Real projective spaces
6.12. Projective spaces over noncommutative fields
Bibliography and suggestions for further reading
Term-paper topics
Index
Index of notation
