Topology Illustrated

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Topology Illustrated
Please click "Look inside" and read Section 1.1 Topology around us.

Algebraic topology is the main subject of this book that initially follows a two-semester first course in topology. It furthermore takes the reader to more advanced parts of algebraic topology as well as some applications: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, exchange economy. An overview of discrete calculus is also included (extended presentation in Calculus Illustrated. Volume 1: Precalculus). The book contains over 1000 color illustrations and over 1000 exercises. The spreadsheets for the simulations and other supplementary material are found at the author's website.

CONTENTS
- Chapter 1. Cycles
  - 1. Topology around us
  - 2. Homology classes
  - 3. Topology of graphs
  - 4. Homology groups of graphs
  - 5. Maps of graphs
  - 6. Binary calculus on graphs
- Chapter 2. Topologies
  - 1. A new look at continuity
  - 2. Neighborhoods and topologies
  - 3. Topological spaces
  - 4. Continuous functions
  - 5. Subspaces
- Chapter 3. Complexes
  - 1. The algebra of cells
  - 2. Cubical complexes
  - 3. The algebra of oriented cells
  - 4. Simplicial complexes
  - 5. Simplicial homology
  - 6. Simplicial maps
  - 7. Parametric complexes
- Chapter 4. Spaces
  - 1. Compacta
  - 2. Quotients
  - 3. Cell complexes
  - 4. Triangulations
  - 5. Manifolds
  - 6. Products
- Chapter 5. Maps
  - 1. Homotopy
  - 2. Cell maps
  - 3. Maps of polyhedra
  - 4. The Euler and Lefschetz numbers
  - 5. Set-valued maps
- Chapter 6. Forms
  - 1. Discrete forms and cochains
  - 2. Calculus on cubical complexes
  - 3. Cohomology
  - 4. Metric tensor
- Chapter 7. Flows
  - 1. Metric complexes
  - 2. ODEs
  - 3. PDEs
  - 4. Social choice

Country	USA
Author	Peter Saveliev
Binding	Hardcover
EAN	9781495188756
ISBN	1495188752
Label	Peter Saveliev
Manufacturer	Peter Saveliev
MPN	Illustrated
NumberOfItems	1
NumberOfPages	664
PartNumber	Illustrated
PublicationDate	2016-02-02
Publisher	Peter Saveliev
Studio	Peter Saveliev
ReleaseDate	0000-00-00

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