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# ðŸ“™ A course in convexity by Alexander Barvinok â€” download pdf

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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. ## About book:

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The notion of convexity comes from geometry. Barvinok describes here its geometric aspects, yet he focuses on applications of convexity rather than on convexity for its own sake. Mathematical applications range from analysis and probability to algebra to combinatorics to number theory. Several important areas are covered, including topological vector spaces, linear programming, ellipsoids, and lattices. Specific topics of note are optimal control, sphere packings, rational approximations, numerical integration, graph theory, and more. And of course, there is much to say about applying convexity theory to the study of faces of polytopes, lattices and polyhedra, and lattices and convex bodies.

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

- Series:
**Graduate Studies in Mathematics 054** - Author:
**Alexander Barvinok** - Year:
**2002** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0-8218-2968-8,9780821829684**

- File size:
**2 067 233** - Format:
**pdf**

Security code:

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...

This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-poi...

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching...

Professors Kurdila and Zabarankin have done a great job putting together several topics of functional analysis, measure theory, convex analysis and optimization. However, although this book was prepared following the idea to provide the minimum of the the...

The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Ga...

This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating genera...

Convex Optimization & Euclidean Distance Geometry I thought I'd use this book as a reference since the unusually large Index is a good place to locate the definitions. Dattorro starts from the basic premises and works through the algebra with many examp...

During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these new developments, but at the s...

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the ...

Amartya Sen was awarded the Nobel Memorial Prize in Economics in 1998 "for his contributions in welfare economics." Although his primary academic appointments have been mostly in economics, Sen is also an important and influential social theorist and phil...

This volume appraises the major philosophical contributions of Hilary Putnam (b. 1926) to the theory of meaning, philosophy of mind, philosophy of science and mathematics, and moral theory. Concerned not only with the broad spectrum of problems addressed,...

Measuring Computer Performance sets out the fundamental techniques used in analyzing and understanding the performance of computer systems. The emphasis is on practical methods of measurement, simulation, and analytical modeling. David Lilja discusses per...

With his new book, More Process Patterns, Scott Ambler picks up where Process Patterns left off. Here, the author presents process patterns for the second half of the development lifecycle. He covers the Deliver phase and the Maintain and Support phases o...

Middle-aged women are often overlooked by medical practitioners even though their health needs are complex and changing, from the end of childbearing to old age, approximately ages 40 to 65. This book highlights the needs and healthcare concerns of women ...