Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.
Rezensionen / Stimmen
An excellent choice of textbook for a geometry course ... Everything the reader needs is defined in the book ... The chapters are well integrated ... I enthusiastically recommend [the book]. It effectively demonstrates how convexity connects with just about all branches of mathematics. The book is well illustrated and well written ... In reading it, I get the sense of how enjoyable it would be to hear Barvinok lecture on the material. I hope that it will attract many students to this branch of geometry."" - MAA Monthly
""My impression is that the book would be fine to teach from ... it contains many useful diagrams. The test is well written, and everything is clearly explained ... wealth of material that it contains and the excellence of its treatment would make this book a desirable addition to one's library. I recommend it highly."" - Bulletin of the LMS
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Verlagsort
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ISBN-13
978-1-4704-8062-2 (9781470480622)
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Schweitzer Klassifikation
Alexander Barvinok, University of Michigan, Ann Arbor, MI.
Chapters
Chapter 1. Convex sets at large
Chapter 2. Faces and extreme points
Chapter 3. Convex sets in topological vector spaces
Chapter 4. Polarity, duality and linear programming
Chapter 5. Convex bodies and ellipsoids
Chapter 6. Faces of polytopes
Chapter 7. Lattices and convex bodies
Chapter 8. Lattice points and polyhedra
