Lectures on Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Polytopes write by Günter M. Ziegler. This book was released on 2012-05-03. Lectures on Polytopes available in PDF, EPUB and Kindle. Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Lectures on Polytopes
Lectures on Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Polytopes write by Günter M. Ziegler. This book was released on 2012-05-03. Lectures on Polytopes available in PDF, EPUB and Kindle. Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Lectures on Discrete Geometry
Lectures on Discrete Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Discrete Geometry write by Jiri Matousek. This book was released on 2013-12-01. Lectures on Discrete Geometry available in PDF, EPUB and Kindle. The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Grobner Bases and Convex Polytopes
Grobner Bases and Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grobner Bases and Convex Polytopes write by Bernd Sturmfels. This book was released on 1996. Grobner Bases and Convex Polytopes available in PDF, EPUB and Kindle. This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.
Lectures in Geometric Combinatorics
Lectures in Geometric Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures in Geometric Combinatorics write by Rekha R. Thomas. This book was released on 2006. Lectures in Geometric Combinatorics available in PDF, EPUB and Kindle. 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 statepolytope 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 Grobner bases of toric ideals and other methods fromcommutative 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.
