Sinossi
For advanced undergraduates or beginning graduate students, this volume covers the geometry of convex polytopes in arbitrary dimension. It contains lectures from the advanced undergraduate course in geometric combinatorics given at the Park City Mathematics Institute in July of 2004. The lectures aimed "to develop the theory of convex polytopes from a geometric viewpoint to lead up to recent developments centered around secondary and state polytopes arising from point configurations." The chapters also deal with the basics of polytope theory, Schlegel and Gale diagrams, the theory of Gröbner bases, toric ideals, triangulations, and polynomial rings. A background in basic linear algebra is required. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)
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Book by Rekha R Thomas
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Lectures in Geometric Combinatories
Editore:
American Mathematical Society, Providence RI, 2006
ISBN 10: 0821841408
ISBN 13: 9780821841402
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Lectures in Geometric Combinatorics
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American Mathematical Society, US, 2006
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ISBN 13: 9780821841402
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Paperback. Condizione: New. illustrated Edition. 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 Grobner 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. Codice articolo LU-9780821841402
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Lectures in Geometric Combinatorics (Student Mathematical Library)
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American Mathematical Society, 2006
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ISBN 13: 9780821841402
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Condizione: New. Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. Series: Student Mathematical Library. Num Pages: 143 pages. BIC Classification: PB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 214 x 133 x 8. Weight in Grams: 188. . 2006. illustrated. paperback. . . . . Codice articolo V9780821841402
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Lectures in Geometric Combinatorics (Student Mathematical Library)
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American Mathematical Society, 2006
ISBN 10: 0821841408
ISBN 13: 9780821841402
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Condizione: New. Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. Series: Student Mathematical Library. Num Pages: 143 pages. BIC Classification: PB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 214 x 133 x 8. Weight in Grams: 188. . 2006. illustrated. paperback. . . . . Books ship from the US and Ireland. Codice articolo V9780821841402
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Lectures in Geometric Combinatorics
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American Mathematical Society, 2006
ISBN 10: 0821841408
ISBN 13: 9780821841402
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Lectures in Geometric Combinatorics
Editore:
American Mathematical Society, US, 2006
ISBN 10: 0821841408
ISBN 13: 9780821841402
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Da: Rarewaves.com UK, London, Regno Unito
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Paperback. Condizione: New. illustrated Edition. 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 Grobner 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. Codice articolo LU-9780821841402
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