A Course in Convexity

Alexander Barvinok (Autor)

Buch | Softcover

366 Seiten

2002
American Mathematical Society (Verlag)
978-1-4704-8062-2 (ISBN)

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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.

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

Erscheinungsdatum	25.10.2025
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-8062-X / 147048062X
ISBN-13	978-1-4704-8062-2 / 9781470480622
Zustand	Neuware