Topology Illustrated
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Topology Illustrated byPeter Saveliev
Contains 1000 illustrations.
Sold on Amazon.com . If you are an instructor considering using the book for your class, contact me about a copy.
Below are some sections of an early online draft (11/15/2015). Because of the extensive editing that had happened prior to publication, some of the sections had to be omitted.
A bird's-eye view of discrete calculus is given in Chapter 4. I recently created an article “Discrete calculus” for Wikipedia . It’ll need a lot of work.
If you have any questions, please email me or try the facebook page (until a better place is found).
CONTENTS
Preface 1
Chapter 1. Cycles
- Topology around us 13
- Homology classes 15
- Topology of graphs 12
- Homology groups of graphs 19
- Maps of graphs 19
- Binary calculus on graphs 11
Chapter 2. Topologies
- A new look at continuity 10
- Neighborhoods and topologies 13
- Topological spaces 15
- Continuous functions 24
- Subspaces 20
Chapter 3. Complexes
- The algebra of cells 19
- Cubical complexes 19
- The algebra of oriented cells 14
- Simplicial complexes 19
- Simplicial homology 19
- Simplicial maps 22
- Parametric complexes 14
Chapter 4. Spaces
- Compacta 12
- Quotients 20
- Cell complexes 24
- Triangulations 16
- Manifolds 29
- Products 29
Chapter 5. Maps
- Homotopy 27
- Cell maps 26
- Maps of polyhedra 29
- The Euler and Lefschetz numbers 18
- Set-valued maps 15
Chapter 6. Forms
- Discrete forms and cochains 21
- Calculus on cubical complexes 23
- Cohomology 25
- Metric tensor 27
Chapter 7. Flows
- Metric complexes 12
- ODEs 29
- PDEs 24
- Social choice 26
- Appendix:Notation 4
- Appendix: Student's guide to proof writing 3
- Index
- Link:Spreadsheets
- Link:Errata
- Link:Addenda
- Addendum: The political spectrum is a circle
- Addendum: Integer-valued calculus
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