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Ordered Fields And Real Algebraic Geometry
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Book Synopsis Ordered Fields and Real Algebraic Geometry by : American Mathematical Society. Meeting
Download or read book Ordered Fields and Real Algebraic Geometry written by American Mathematical Society. Meeting and published by . This book was released on 1982 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Real Algebraic Geometry and Ordered Structures by : Charles N. Delzell
Download or read book Real Algebraic Geometry and Ordered Structures written by Charles N. Delzell and published by American Mathematical Soc.. This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
Author :Special Session on Ordered Fields and Real Algebraic Geometry... Publisher : ISBN 13 :9780608039732 Total Pages :368 pages Book Rating :4.0/5 (397 download)
Book Synopsis Ordered Fields and Real Algebraic Geometry by : Special Session on Ordered Fields and Real Algebraic Geometry...
Download or read book Ordered Fields and Real Algebraic Geometry written by Special Session on Ordered Fields and Real Algebraic Geometry... and published by . This book was released on 1982 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Super-real Fields by : Harold G. Dales
Download or read book Super-real Fields written by Harold G. Dales and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
Book Synopsis Recent Advances in Real Algebraic Geometry and Quadratic Forms by : Bill Jacob
Download or read book Recent Advances in Real Algebraic Geometry and Quadratic Forms written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1994 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected here present an up-to-date record of the current research developments in the fields of real algebraic geometry and quadratic forms. Articles range from the technical to the expository and there are also indications to new research directions.
Book Synopsis Spaces of Orderings and Abstract Real Spectra by : Murray A. Marshall
Download or read book Spaces of Orderings and Abstract Real Spectra written by Murray A. Marshall and published by Springer. This book was released on 2006-11-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.
Download or read book Real Algebra written by Manfred Knebusch and published by Springer Nature. This book was released on 2022-10-22 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dieses Buch will dem Leser eine Einführung in wichtige Techniken und Methoden der heutigen reellen Algebra und Geometrie vermitteln. An Voraussetzungen werden dabei nur Grundkenntnisse der Algebra erwartet, so daß das Buch für Studenten mittlerer Semester geeignet ist.Das erste Kapitel enthält zunächst grundlegende Fakten über angeordnete Körper und ihre reellen Abschlüsse und behandelt dann verschiedene Methoden zur Bestimmung der Anzahl reeller Nullstellen von Polynomen. Das zweite Kapitel befaßt sich mit reellen Stellen und gipfelt in Artins Lösung des 17. Hilbertschen Problems. Kapitel III schließlich ist dem noch jungen Begriff des reellen Spektrums und seinen Anwendungen gewidmet."Neben dem 1987 erschienenen "Géometrie algébrique réelle" von J. Bochnak-M. Coste- M. Roy stellt die vorliegende Monographie das erste Lehrbuch auf diesem Gebiet dar... Damit liegt eine sehr empfehlenswerte Einführung...vor..." (H. Mitsch, Monatshefte für Mathematik 3/111, 1991)
Book Synopsis Real Algebraic Geometry by : Michel Coste
Download or read book Real Algebraic Geometry written by Michel Coste and published by Springer. This book was released on 2006-11-15 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.
Book Synopsis Lectures on Formally Real Fields by : A. Prestel
Download or read book Lectures on Formally Real Fields written by A. Prestel and published by Springer. This book was released on 2007-01-05 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Book Synopsis Topology of Real Algebraic Sets by : Selman Akbulut
Download or read book Topology of Real Algebraic Sets written by Selman Akbulut and published by Springer. This book was released on 2011-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Fall of 1975 we started a joint project with the ultimate goal of topo logically classifying real algebraic sets. This has been a long happy collaboration (c.f., [K2)). In 1985 while visiting M.S.R.1. we organized and presented our classification results up to that point in the M.S.R.1. preprint series [AK14] -[AK17]. Since these results are interdependent and require some prerequisites as well as familiarity with real algebraic geometry, we decided to make them self contained by presenting them as a part of a book in real algebraic geometry. Even though we have not arrived to our final goal yet we feel that it is time to introduce them in a self contained coherent version and demonstrate their use by giving some applications. Chapter I gives the overview of the classification program. Chapter II has all the necessary background for the rest of the book, which therefore can be used as a course in real algebraic geometry. It starts with the elementary properties of real algebraic sets and ends with the recent solution of the Nash Conjecture. Chapter III and Chapter IV develop the theory of resolution towers. Resolution towers are basic topologically defined objects generalizing the notion of manifold.
Book Synopsis Real Algebraic Geometry and Optimization by : Thorsten Theobald
Download or read book Real Algebraic Geometry and Optimization written by Thorsten Theobald and published by American Mathematical Society. This book was released on 2024-04-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
Book Synopsis Partially Ordered Rings and Semi-Algebraic Geometry by : Gregory W. Brumfiel
Download or read book Partially Ordered Rings and Semi-Algebraic Geometry written by Gregory W. Brumfiel and published by Cambridge University Press. This book was released on 1979-12-20 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.
Book Synopsis Algorithms in Real Algebraic Geometry by : Saugata Basu
Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Book Synopsis Number Systems by : Sergei Ovchinnikov
Download or read book Number Systems written by Sergei Ovchinnikov and published by American Mathematical Soc.. This book was released on 2015-02-26 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
Book Synopsis Ordered Fields and Real Algebraic Geometry by : American Mathematical Society. Meeting
Download or read book Ordered Fields and Real Algebraic Geometry written by American Mathematical Society. Meeting and published by . This book was released on 1982 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: