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3264, the mathematical solution to a question concerning geometric figures.
Book Synopsis 3264 and All That by : David Eisenbud
Download or read book 3264 and All That written by David Eisenbud and published by Cambridge University Press. This book was released on 2016-04-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3264, the mathematical solution to a question concerning geometric figures.
From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.
Book Synopsis Intersection Theory by : W. Fulton
Download or read book Intersection Theory written by W. Fulton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Book Synopsis The Geometry of Schemes by : David Eisenbud
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
Book Synopsis A Second Course in Complex Analysis by : William A. Veech
Download or read book A Second Course in Complex Analysis written by William A. Veech and published by Courier Corporation. This book was released on 2014-08-04 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
Book Synopsis Deformation Theory by : Robin Hartshorne
Download or read book Deformation Theory written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2009-11-12 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
Book Synopsis Algebraic Geometry and Statistical Learning Theory by : Sumio Watanabe
Download or read book Algebraic Geometry and Statistical Learning Theory written by Sumio Watanabe and published by Cambridge University Press. This book was released on 2009-08-13 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Book Synopsis The Red Book of Varieties and Schemes by : David Mumford
Download or read book The Red Book of Varieties and Schemes written by David Mumford and published by Springer. This book was released on 2004-02-24 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
Book Synopsis Elementary Algebraic Geometry by : Klaus Hulek
Download or read book Elementary Algebraic Geometry written by Klaus Hulek and published by American Mathematical Soc.. This book was released on 2003 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.
Book Synopsis Algebraic Geometry I: Schemes by : Ulrich Görtz
Download or read book Algebraic Geometry I: Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2020-07-27 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.
The definitive, classic account of the fall of the House of Baring, the oldest merchant bank in London, in 1995 and the ultimate rogue trader, Nick Leeson, who brought down the venerable institution with speculative investing. John Gapper, associate editor of the Financial Times, and his coauthor Nicholas Denton, now founder of Gawker Media, interviewed all the major players involved in the collapse of one of England's oldest banks. All That Glitters reveals the Faustian deal struck between the whizz-kid derivatives traders who seemed to be bringing in huge profits and the old guard who were happy to pocket them without asking too many questions. Gapper and Denton present a thrilling, in-depth account of Nick Leeson's motives and methods for hiding the unauthorized speculative trading as well as the final days of Barings and the last-ditch attempts by politicians and bankers to save the bank.
Book Synopsis All That Glitters by : John Gapper
Download or read book All That Glitters written by John Gapper and published by Penguin. This book was released on 2011-12-01 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive, classic account of the fall of the House of Baring, the oldest merchant bank in London, in 1995 and the ultimate rogue trader, Nick Leeson, who brought down the venerable institution with speculative investing. John Gapper, associate editor of the Financial Times, and his coauthor Nicholas Denton, now founder of Gawker Media, interviewed all the major players involved in the collapse of one of England's oldest banks. All That Glitters reveals the Faustian deal struck between the whizz-kid derivatives traders who seemed to be bringing in huge profits and the old guard who were happy to pocket them without asking too many questions. Gapper and Denton present a thrilling, in-depth account of Nick Leeson's motives and methods for hiding the unauthorized speculative trading as well as the final days of Barings and the last-ditch attempts by politicians and bankers to save the bank.
