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Topology Illustrated

Topology Illustrated

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Product Description

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

Technical Specifications

Country
USA
Brand
Peter Saveliev
Manufacturer
Peter Saveliev
Binding
Hardcover
PartNumber
Illustrated
Height
10
Length
7
Weight
2.98946827272
Width
1.44
NumberOfItems
1

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