Convexity From The Geometric Point Of View
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Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Convexity From The Geometric Point Of View Exercises And Solutions
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2025-08-04
Convexity From The Geometric Point Of View Exercises And Solutions written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-04 with Mathematics categories.
This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View, published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding solutions follow each exercise. Besides the discussion of all solutions, some additional facts about the main text are sprinkled throughout. Sections of further reading are posted to the ends of each chapter supplying the reader with background literature to selected notions and tools that play a role in the exercises and/or solutions to the chapter. The original text gives a comprehensive introduction to the “common core” of convex geometry and is suitable as a primary text for courses in convex geometry and in discrete geometry (including polytopes). Additionally, it can be used as a single reference for a complete introduction to convex geometry. The content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field, various subfields, and interesting connections to neighboring disciplines. Mainly directed to graduate and advanced undergraduates, the original text is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. The same is true for this book of solutions.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher:
Release Date : 2024
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.
Foundations Of Convex Geometry
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Author : W. A. Coppel
language : en
Publisher: Cambridge University Press
Release Date : 1998-03-05
Foundations Of Convex Geometry written by W. A. Coppel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-05 with Mathematics categories.
This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Bodies Of Constant Width
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Author : Horst Martini
language : en
Publisher: Springer
Release Date : 2019-03-16
Bodies Of Constant Width written by Horst Martini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-16 with Mathematics categories.
This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.
Combinatorial Convexity And Algebraic Geometry
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Author : Günter Ewald
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial Convexity And Algebraic Geometry written by Günter Ewald and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts.
Geometry Of Isotropic Convex Bodies
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Author : Silouanos Brazitikos
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-24
Geometry Of Isotropic Convex Bodies written by Silouanos Brazitikos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-24 with Mathematics categories.
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Handbook Of Convex Geometry
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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Handbook Of Convex Geometry written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.