Lectures on Algebraic Model Theory PDF Download
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Author: Bradd T. Hart
Publisher: American Mathematical Soc.
ISBN: 0821827057
Category : Mathematics
Languages : en
Pages : 121
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Book Description
This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
Author: Bradd T. Hart
Publisher: American Mathematical Soc.
ISBN: 0821827057
Category : Mathematics
Languages : en
Pages : 121
Get Book Here
Book Description
This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
Author: Lou van den Dries
Publisher: Springer
ISBN: 3642549365
Category : Mathematics
Languages : en
Pages : 201
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Book Description
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.
Author: Shreeram Shankar Abhyankar
Publisher: World Scientific
ISBN: 9812568263
Category : Mathematics
Languages : en
Pages : 758
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Book Description
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.
Author: David Marker
Publisher: Springer Science & Business Media
ISBN: 0387227342
Category : Mathematics
Languages : en
Pages : 342
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Book Description
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
Author: E. T. Hecke
Publisher: Springer Science & Business Media
ISBN: 1475740921
Category : Mathematics
Languages : en
Pages : 251
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Book Description
. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
Author: Katrin Tent
Publisher: Cambridge University Press
ISBN: 052176324X
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Concise introduction to current topics in model theory, including simple and stable theories.
Author: Mathias Drton
Publisher: Springer Science & Business Media
ISBN: 3764389052
Category : Mathematics
Languages : en
Pages : 177
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Book Description
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
Author: Günter Harder
Publisher: Springer Science & Business Media
ISBN: 3834895016
Category : Mathematics
Languages : en
Pages : 301
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Book Description
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Author: Bradd T. Hart
Publisher: Springer Science & Business Media
ISBN: 9401589232
Category : Mathematics
Languages : en
Pages : 285
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Book Description
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.
Author: Ken Brown
Publisher: Birkhäuser
ISBN: 303488205X
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
