Real Algebra
DOWNLOAD
Download Real Algebra PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Real Algebra book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Unknown Quantity
DOWNLOAD
Author : John Derbyshire
language : en
Publisher: National Academies Press
Release Date : 2006-05-02
Unknown Quantity written by John Derbyshire and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Science categories.
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
Algorithms In Real Algebraic Geometry
DOWNLOAD
Author : Saugata Basu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-21
Algorithms In Real Algebraic Geometry written by Saugata Basu 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 2007-04-21 with Mathematics categories.
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook the main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results, on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number.
Real Algebra
DOWNLOAD
Author : Manfred Knebusch
language : en
Publisher: Springer Nature
Release Date : 2022-10-22
Real Algebra written by Manfred Knebusch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-22 with Mathematics categories.
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)
Real Linear Algebra
DOWNLOAD
Author : Antal E. Fekete
language : en
Publisher: CRC Press
Release Date : 1985-01-25
Real Linear Algebra written by Antal E. Fekete and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-25 with Mathematics categories.
Real Algebraic Varieties
DOWNLOAD
Author : Frédéric Mangolte
language : en
Publisher: Springer Nature
Release Date : 2020-09-21
Real Algebraic Varieties written by Frédéric Mangolte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.
This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.
Math For Real Life
DOWNLOAD
Author : Jim Libby
language : en
Publisher: McFarland
Release Date : 2017-01-19
Math For Real Life written by Jim Libby and has been published by McFarland this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-19 with Education categories.
"Where are we ever going to use this?" Every high school math student has asked this question. Often teachers themselves aren't sure how to respond. One answer is that higher mathematics learned in high school will be essential to learning yet more at the college level. A more satisfactory answer calls for an awareness of how math is applied in many specific areas. Written primarily for teachers, this book presents hundreds of practical applications for mathematics--from baseball statistics to the theory of relativity--that can be understood by anyone with a knowledge of high school algebra, geometry and trigonometry.
Positive Polynomials
DOWNLOAD
Author : Alexander Prestel
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-24
Positive Polynomials written by Alexander Prestel 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 2001-04-24 with Mathematics categories.
Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
Algorithmic Algebra
DOWNLOAD
Author : Bhubaneswar Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algorithmic Algebra written by Bhubaneswar Mishra 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 Computers categories.
Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics
DOWNLOAD
Author : D.H. Sattinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics written by D.H. Sattinger 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 2013-11-11 with Mathematics categories.
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Introduction To Lie Algebras
DOWNLOAD
Author : J. I. Hall
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-03
Introduction To Lie Algebras written by J. I. Hall and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-03 with Mathematics categories.
Being both a beautiful theory and a valuable tool, Lie algebras form a very important area of mathematics. This modern introduction targets entry-level graduate students. It might also be of interest to those wanting to refresh their knowledge of the area and be introduced to newer material. Infinite dimensional algebras are treated extensively along with the finite dimensional ones. After some motivation, the text gives a detailed and concise treatment of the Killing–Cartan classification of finite dimensional semisimple algebras over algebraically closed fields of characteristic 0. Important constructions such as Chevalley bases follow. The second half of the book serves as a broad introduction to algebras of arbitrary dimension, including Kac–Moody (KM), loop, and affine KM algebras. Finite dimensional semisimple algebras are viewed as KM algebras of finite dimension, their representation and character theory developed in terms of integrable representations. The text also covers triangular decomposition (after Moody and Pianzola) and the BGG category $mathcal{O}$. A lengthy chapter discusses the Virasoro algebra and its representations. Several applications to physics are touched on via differential equations, Lie groups, superalgebras, and vertex operator algebras. Each chapter concludes with a problem section and a section on context and history. There is an extensive bibliography, and appendices present some algebraic results used in the book.