Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Lectures in Geometric Combinatorics
 
Rekha R. Thomas University of Washington, Seattle, WA
Front Cover for Lectures in Geometric Combinatorics
Available Formats:
Softcover ISBN: 978-0-8218-4140-2
Product Code: STML/33
List Price: $34.00
Individual Price: $27.20
Electronic ISBN: 978-1-4704-2144-1
Product Code: STML/33.E
List Price: $32.00
Individual Price: $25.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $51.00
Front Cover for Lectures in Geometric Combinatorics
Click above image for expanded view
  • Front Cover for Lectures in Geometric Combinatorics
  • Back Cover for Lectures in Geometric Combinatorics
Lectures in Geometric Combinatorics
Rekha R. Thomas University of Washington, Seattle, WA
Available Formats:
Softcover ISBN:  978-0-8218-4140-2
Product Code:  STML/33
List Price: $34.00
Individual Price: $27.20
Electronic ISBN:  978-1-4704-2144-1
Product Code:  STML/33.E
List Price: $32.00
Individual Price: $25.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $51.00
  • Book Details
     
     
    Student Mathematical Library
    IAS/Park City Mathematics Subseries
    Volume: 332006; 143 pp
    MSC: Primary 52; Secondary 13;

    This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gröbner bases of toric ideals and other methods from commutative algebra.

    The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

    This book is published in cooperation with IAS/Park City Mathematics Institute.
    Readership

    Undergraduate and graduate students interested in computational geometry and polytopes.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Abstract algebra: Groups, rings and fields
    • Chapter 2. Convex polytopes: Definitions and examples
    • Chapter 3. Faces of polytopes
    • Chapter 4. Schlegel diagrams
    • Chapter 5. Gale diagrams
    • Chapter 6. Bizarre polytopes
    • Chapter 7. Triangulations of point configurations
    • Chapter 8. The secondary polytope
    • Chapter 9. The permutahedron
    • Chapter 10. Abstract algebra: Polynomial rings
    • Chapter 11. Gröbner bases I
    • Chapter 12. Gröbner bases II
    • Chapter 13. Initial complexes of toric ideals
    • Chapter 14. State polytopes of toric ideals
  • Additional Material
     
     
  • Reviews
     
     
    • Undergraduates will find this a very friendly and stimulating introduction to creative mathematics in higher dimensions.

      CHOICE Magazine
  • Request Review Copy
  • Get Permissions
IAS/Park City Mathematics Subseries
Volume: 332006; 143 pp
MSC: Primary 52; Secondary 13;

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gröbner bases of toric ideals and other methods from commutative algebra.

The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

This book is published in cooperation with IAS/Park City Mathematics Institute.
Readership

Undergraduate and graduate students interested in computational geometry and polytopes.

  • Chapters
  • Chapter 1. Abstract algebra: Groups, rings and fields
  • Chapter 2. Convex polytopes: Definitions and examples
  • Chapter 3. Faces of polytopes
  • Chapter 4. Schlegel diagrams
  • Chapter 5. Gale diagrams
  • Chapter 6. Bizarre polytopes
  • Chapter 7. Triangulations of point configurations
  • Chapter 8. The secondary polytope
  • Chapter 9. The permutahedron
  • Chapter 10. Abstract algebra: Polynomial rings
  • Chapter 11. Gröbner bases I
  • Chapter 12. Gröbner bases II
  • Chapter 13. Initial complexes of toric ideals
  • Chapter 14. State polytopes of toric ideals
  • Undergraduates will find this a very friendly and stimulating introduction to creative mathematics in higher dimensions.

    CHOICE Magazine
You may be interested in...
Please select which format for which you are requesting permissions.