Topology Illustrated

ISBN-13: 9781495188756
ISBN-10: 1495188752
Author: Peter Saveliev
Publication date: 2016
Publisher: Peter Saveliev
Format: Hardcover 664 pages
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Book details

ISBN-13: 9781495188756
ISBN-10: 1495188752
Author: Peter Saveliev
Publication date: 2016
Publisher: Peter Saveliev
Format: Hardcover 664 pages

Summary

Acknowledged authors Peter Saveliev wrote Topology Illustrated comprising 664 pages back in 2016. Textbook and eTextbook are published under ISBN 1495188752 and 9781495188756. Since then Topology Illustrated textbook was available to sell back to BooksRun online for the top buyback price of $ 25.37 or rent at the marketplace.

Description

Please click "Look inside" and read Section 1.1 Topology around us.
The book contains over 1000 color illustrations and over 1000 exercises.
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).
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
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