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.
FREE Two-Day Shipping for students on millions of items. Learn more |
Book Description
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
This course will aim at understanding convex polytopes, which are fundamental geometric objects in combinatorics, using techniques from algebra and discrete geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pointed secondary fan, refinement poset, inner normal cone, inner normal fan, secondary polytope, state polytope, polyhedral fan, face poset, toric ideal, face lattice, monomial ideal, cyclic polytope, polytope conv, polyhedral complex, regular triangulations, finite generating set, vector configuration, secondary cones, top facet, initial ideals, lex order, affine hull, linear ideal, regular subdivisions, ideal membership New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This course will aim at understanding convex polytopes, which are fundamental geometric objects in combinatorics, using techniques from algebra and discrete geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pointed secondary fan, refinement poset, inner normal cone, inner normal fan, secondary polytope, state polytope, polyhedral fan, face poset, toric ideal, face lattice, monomial ideal, cyclic polytope, polytope conv, polyhedral complex, regular triangulations, finite generating set, vector configuration, secondary cones, top facet, initial ideals, lex order, affine hull, linear ideal, regular subdivisions, ideal membership New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- Abstract Algebra, 3rd Edition by David S. Dummit in Back Matter
- Solving Systems of Polynomial Equations (CBMS Regional Conference Series in Mathematics) by Bernd Sturmfels in Back Matter
- A Singular Introduction to Commutative Algebra by Gert-Martin Greuel in Back Matter
- Using Algebraic Geometry by David A. Cox in Back Matter
- Lectures on Polytopes (Graduate Texts in Mathematics) by Gunter M. Ziegler in Back Matter
Books on Related Topics
(learn more)
|
|
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
