Model Theory And Algebraic Geometry

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Model Theory And Algebraic Geometry

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Author : Elisabeth Bouscaren
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-17

Model Theory And Algebraic Geometry written by Elisabeth Bouscaren 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 1998-09-17 with Mathematics categories.

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.

Model Theory In Algebra Analysis And Arithmetic

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Author : Lou van den Dries
language : en
Publisher: Springer
Release Date : 2014-10-02

Model Theory In Algebra Analysis And Arithmetic written by Lou van den Dries and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-02 with Mathematics categories.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Model Theory An Introduction

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Author : David Marker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

Model Theory An Introduction written by David Marker 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 2006-04-06 with Mathematics categories.

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

Model Theory And Algebraic Geometry

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Author : Elisabeth Bouscaren
language : en
Publisher: Springer
Release Date : 2009-03-14

Model Theory And Algebraic Geometry written by Elisabeth Bouscaren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-14 with Mathematics categories.

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.

Algebraic Geometry And Statistical Learning Theory

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Author : Sumio Watanabe
language : en
Publisher: Cambridge University Press
Release Date : 2009-08-13

Algebraic Geometry And Statistical Learning Theory written by Sumio Watanabe 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 2009-08-13 with Computers categories.

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory on algebraic varieties.

Representation Theory And Algebraic Geometry

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Author : A. Martsinkovsky
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-15

Representation Theory And Algebraic Geometry written by A. Martsinkovsky 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 1997-05-15 with Mathematics categories.

For any researcher working in representation theory, algebraic or arithmetic geometry.

Algebraic Models In Geometry

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Author : Yves Félix
language : en
Publisher: Oxford University Press
Release Date : 2008

Algebraic Models In Geometry written by Yves Félix and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.

A Shorter Model Theory

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Author : Wilfrid Hodges
language : en
Publisher: Cambridge University Press
Release Date : 1997-04-10

A Shorter Model Theory written by Wilfrid Hodges 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 1997-04-10 with Mathematics categories.

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

Algebraic Geometry For Scientists And Engineers

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Author : Shreeram Shankar Abhyankar
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Algebraic Geometry For Scientists And Engineers written by Shreeram Shankar Abhyankar 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 1990 with Mathematics categories.

Based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, this book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities.

Number Theory And Algebraic Geometry

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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 2003

Number Theory And Algebraic Geometry written by Miles Reid 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 2003 with Mathematics categories.

Sir Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume provides contemporary insight into several subjects in which Sir Peter's influence has been notable, and is dedicated to his 75th birthday. The opening section reviews some of his many remarkable contributions to mathematics and other fields. The remaining contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. The topics treated include: rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties.