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Rational Points on Elliptic Curves

Posted By: AvaxGenius
Date: 23 Mar 2023 18:27:32
Rational Points on Elliptic Curves

Rational Points on Elliptic Curves by Joseph H. Silverman , John Tate
English | PDF | 1992| 292 Pages | ISBN : 0387978259 | 22.97 MB

In 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por­ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter­ est in the theory of elliptic curves for subjects ranging from cryptogra­ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience.
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Rational Algebraic Curves: A Computer Algebra Approach (Repost)

Posted By: AvaxGenius
Date: 23 Mar 2023 18:23:16
Rational Algebraic Curves: A Computer Algebra Approach (Repost)

Rational Algebraic Curves: A Computer Algebra Approach by J. Rafael Sendra , Franz Winkler , Sonia Pérez-Díaz
English | PDF (True) | 2008 | 273 Pages | ISBN : 3540737243 | 3.68 MB

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas- nating mathematical beauty with challenging computational complexity and wide spread practical applicability.
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Conjectures in Arithmetic Algebraic Geometry: A Survey

Posted By: AvaxGenius
Date: 23 Mar 2023 18:06:06
Conjectures in Arithmetic Algebraic Geometry: A Survey

Conjectures in Arithmetic Algebraic Geometry: A Survey by Wilfred W. J. Hulsbergen
English | PDF | 1992 | 246 Pages | ISBN : 3528064331 | 11.1 MB

In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro- duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich- let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions.
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Methods of Algebraic Geometry in Control Theory: Part II (Repost)

Posted By: AvaxGenius
Date: 23 Mar 2023 18:02:17
Methods of Algebraic Geometry in Control Theory: Part II (Repost)

Methods of Algebraic Geometry in Control Theory: Part II Multivariable Linear Systems and Projective Algebraic Geometry by Peter Falb
English | PDF | 1999 | 382 Pages | ISBN : 0817641130 | 24.1 MB

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry).
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Topological Methods in Algebraic Geometry: Reprint of the 1978 Edition

Posted By: AvaxGenius
Date: 23 Mar 2023 12:39:09
Topological Methods in Algebraic Geometry: Reprint of the 1978 Edition

Topological Methods in Algebraic Geometry: Reprint of the 1978 Edition by Friedrich Hirzebruch
English | PDF | 1995 | 244 Pages | ISBN : 3540586636 | 20.22 MB

In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for­ mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo­ morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success.
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Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

Posted By: AvaxGenius
Date: 23 Mar 2023 12:18:37
Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions by Michel L. Lapidus , Machiel Frankenhuysen
English | PDF | 2000 | 277 Pages | ISBN : 0817640983 | 21.76 MB

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string.
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G-Functions and Geometry: A Publication of the Max-Planck-Institut für Mathematik, Bonn

Posted By: AvaxGenius
Date: 22 Mar 2023 18:57:57
G-Functions and Geometry: A Publication of the Max-Planck-Institut für Mathematik, Bonn

G-Functions and Geometry: A Publication of the Max-Planck-Institut für Mathematik, Bonn by Yves André
Deutsch | PDF | 1989 | 245 Pages | ISBN : 3528063173 | 14.23 MB

This is an introduction to some geometrie aspects of G-function theory. Most of the results presented here appear in print for the flrst time; hence this text is something intermediate between a standard monograph and a research artic1e; it is not a complete survey of the topic. Except for geometrie chapters (I.3.3, II, IX, X), I have tried to keep it reasonably self­ contained; for instance, the second part may be used as an introduction to p-adic analysis, starting from a few basic facts wh ich are recalled in IV.l.l.
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Algebraic Geometry

Posted By: AvaxGenius
Date: 22 Mar 2023 18:47:58
Algebraic Geometry

Algebraic Geometry by Robin Hartshorne
English | PDF | 1977 | 511 Pages | ISBN : 0387902449 | 47.8 MB

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles.
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Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Repost)

Posted By: AvaxGenius
Date: 22 Mar 2023 18:24:03
Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Repost)

Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series by Robert Lazarsfeld
English | PDF | 2004 | 395 Pages | ISBN : 3540225331 | 2.5 MB

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.
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Introduction to Coding Theory and Algebraic Geometry

Posted By: AvaxGenius
Date: 21 Mar 2023 12:43:33
Introduction to Coding Theory and Algebraic Geometry

Introduction to Coding Theory and Algebraic Geometry by Jacobus H. Lint , Gerard Geer
English | PDF | 1988 | 82 Pages | ISBN : 3034899793 | 8.1 MB

These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational.
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Introduction to Coding Theory, Third Edition

Posted By: AvaxGenius
Date: 21 Mar 2023 09:26:55
Introduction to Coding Theory, Third Edition

Introduction to Coding Theory, Third Edition by J. H. Lint
English | PDF(True) | 1999 | 244 Pages | ISBN : 3540641335 | 26.17 MB

It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added.
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Introduction to Complex Analytic Geometry

Posted By: AvaxGenius
Date: 16 Feb 2023 19:53:25
Introduction to Complex Analytic Geometry

Introduction to Complex Analytic Geometry by Stanisław Łojasiewicz
English | PDF | 1991 | 535 Pages | ISBN : 303487619X | 23 MB

facts. An elementary acquaintance with topology, algebra, and analysis (in­ cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions.
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Commutative Algebra: Noetherian and Non-Noetherian Perspectives

Posted By: AvaxGenius
Date: 27 Jan 2023 17:54:47
Commutative Algebra: Noetherian and Non-Noetherian Perspectives

Commutative Algebra: Noetherian and Non-Noetherian Perspectives by Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson
English | PDF(True) | 2011 | 490 Pages | ISBN : 1441969896 | 4.5 MB

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.
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The Use of Ultraproducts in Commutative Algebra (Repost)

Posted By: AvaxGenius
Date: 27 Jan 2023 17:52:13
The Use of Ultraproducts in Commutative Algebra (Repost)

The Use of Ultraproducts in Commutative Algebra by Hans Schoutens
English | PDF | 2010 | 215 Pages | ISBN : 3642133673 | 2.6 MB

In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
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A Singular Introduction to Commutative Algebra, Second, Extended Edition (Repost)

Posted By: AvaxGenius
Date: 27 Jan 2023 17:48:21
A Singular Introduction to Commutative Algebra, Second, Extended Edition (Repost)

A Singular Introduction to Commutative Algebra, Second, Extended Edition by Gert-Martin Greuel , Gerhard Pfister
English | PDF(True) | 2008 | 703 Pages | ISBN : 3540735410 | 9.9 MB

From the reviews of the first edition:
"It is certainly no exaggeration to say that … A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra … . Among the great strengths and most distinctive features … is a new, completely unified treatment of the global and local theories. … making it one of the most flexible and most efficient systems of its type….another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic….Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike."
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