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A Course in Convexity
About this Title
Alexander Barvinok, University of Michigan, Ann Arbor, Ann Arbor, MI
Publication: Graduate Studies in Mathematics
Publication Year 2002: Volume 54
ISBNs: 978-0-8218-2968-4 (print); 978-1-4704-1792-5 (online)
MathSciNet review: MR1940576
MSC: Primary 52-02; Secondary 49N15, 52-01, 90-02, 90C05, 90C22, 90C25
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.
Advanced undergraduates, graduate students, and researchers interested in mathematical methods, computer science, electrical engineering, and operations research.
Table of Contents
- 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