Michael Artin's Books

Introduction To Commutative Algebra

By: Michael F. Atiyah,I.G. MacDonald

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Introduction To Commutative Algebra

By: Michael F. Atiyah,I.G. MacDonald

First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

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140

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CRC Press

Published Date

ISBN 10

0429973268

ISBN 13

9780429973260

Number Theory in Function Fields

By: Michael Rosen

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Number Theory in Function Fields

By: Michael Rosen

Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

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355

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Springer Science & Business Media

Published Date

ISBN 10

1475760469

ISBN 13

9781475760460

Field Arithmetic

By: Michael D. Fried,Moshe Jarden

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Field Arithmetic

By: Michael D. Fried,Moshe Jarden

This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.

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839

Publisher

Springer Nature

Published Date

ISBN 10

3031280202

ISBN 13

9783031280207

Algebraic Geometry Codes: Advanced Chapters

By: Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin

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Algebraic Geometry Codes: Advanced Chapters

By: Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin

Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.

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466

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American Mathematical Soc.

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ISBN 10

1470448653

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9781470448653

Ramified Surfaces

On Branch Curves and Algebraic Geometry in the 20th Century

By: Michael Friedman

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Ramified Surfaces

On Branch Curves and Algebraic Geometry in the 20th Century

By: Michael Friedman

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.

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258

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Springer Nature

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ISBN 10

3031057201

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9783031057205

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

By: Vlastimil Dlab,Claus Michael Ringel

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Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

By: Vlastimil Dlab,Claus Michael Ringel

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

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502

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American Mathematical Soc.

Published Date

ISBN 10

0821834169

ISBN 13

9780821834169

Arthur E. Haas - The Hidden Pioneer of Quantum Mechanics

A Biography

By: Michael Wiescher

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Arthur E. Haas - The Hidden Pioneer of Quantum Mechanics

A Biography

By: Michael Wiescher

The book highlights the personal and scientific struggles of Arthur Erich Haas (1884-1941), an Austrian Physicist from a wealthy Jewish middle-class family, whose remarkable accomplishments in a politically hostile but scientifically rewarding environment deserve greater recognition. Haas was a fellow student of both Lise Meitner and Erwin Schrödinger and was also one of the last doctoral students of Ludwig Boltzmann. Following Boltzmann's suicide, Haas was forced to submit a more independent doctoral thesis in which he postulated new approaches in early quantum theory, actually introducing the idea of the Bohr radius before Niels Bohr. It is the lost story of a trailblazer in the fields of quantum mechanics and cosmology, a herald of nuclear energy and applications of modern science. This biography of Haas is based on new and previously unpublished family records and archived material from the Vienna Academy of Science and the University of Notre Dame, which the author has collected over many years. From his analysis of the letters, documents, and photos that rested for nearly a century in family attics and academic archives, Michael Wiescher provides a unique and detailed insight into the life of a gifted Jewish physicist during the first half of the twentieth century. It also sheds light on the scientific developments and thinking of the time. It appeals not only to historians and physicists, but also general readers. All appreciate the record of Haas’ interactions with many of the key figures who helped to found modern physics.

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558

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Springer Nature

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ISBN 10

3030806065

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9783030806064

Equivariant Cohomology of Configuration Spaces Mod 2

The State of the Art

By: Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler

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Equivariant Cohomology of Configuration Spaces Mod 2

The State of the Art

By: Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(R^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and l-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.

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217

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Springer Nature

Published Date

ISBN 10

3030841383

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9783030841386

Noncommutative Algebraic Geometry

By: Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss

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Noncommutative Algebraic Geometry

By: Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

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367

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Cambridge University Press

Published Date

ISBN 10

1107129540

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9781107129542

A Classical Introduction to Modern Number Theory

By: Kenneth Ireland,Michael Rosen

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A Classical Introduction to Modern Number Theory

By: Kenneth Ireland,Michael Rosen

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

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406

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Springer Science & Business Media

Published Date

ISBN 10

147572103X

ISBN 13

9781475721034

Infinite Group Actions on Polyhedra

By: MICHAEL W. DAVIS

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Infinite Group Actions on Polyhedra

By: MICHAEL W. DAVIS

In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory. Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings. Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.

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273

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Springer Nature

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ISBN 10

3031484436

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9783031484438

Algebraic K-theory and Algebraic Number Theory

Proceedings of a Seminar Held January 12-16, 1987, with Support from the National Science Foundation and Japan Society for the Promotion of Science

By: Michael R. Stein,R. Keith Dennis

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Algebraic K-theory and Algebraic Number Theory

Proceedings of a Seminar Held January 12-16, 1987, with Support from the National Science Foundation and Japan Society for the Promotion of Science

By: Michael R. Stein,R. Keith Dennis

This volume contains the proceedings of a seminar on Algebraic $K$-theory and Algebraic Number Theory, held at the East-West Center in Honolulu in January 1987. The seminar, which hosted nearly 40 experts from the U.S. and Japan, was motivated by the wide range of connections between the two topics, as exemplified in the work of Merkurjev, Suslin, Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, Thomason, and Ihara. As is evident from the diversity of topics represented in these proceedings, the seminar provided an opportunity for mathematicians from both areas to initiate further interactions between these two areas.

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506

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821850903

ISBN 13

9780821850909

Algebraic Geometric Codes: Basic Notions

By: Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin

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Algebraic Geometric Codes: Basic Notions

By: Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin

The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.

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338

Publisher

American Mathematical Society

Published Date

ISBN 10

1470470071

ISBN 13

9781470470074

Infinite Length Modules

By: Henning Krause,Claus Michael Ringel

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Infinite Length Modules

By: Henning Krause,Claus Michael Ringel

This book is concerned with the role played by modules of infinite length when dealing with problems in the representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing interplay between finite and infinite length modules. The volume presents the invited lectures of a conference devoted to 'Infinite Length Modules', held at Bielefeld in September 1998, which brought together experts from quite different schools in order to survey surprising relations between algebra, topology and geometry. Some additional reports have been included in order to establish a unified picture. The collection of articles, written by well-known experts from all parts of the world, is conceived as a sort of handbook which provides an easy access to the present state of knowledge and its aim is to stimulate further development.

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776

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Springer Science & Business Media

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ISBN 10

3764364130

ISBN 13

9783764364137

The Fourier-Analytic Proof of Quadratic Reciprocity

By: Michael C. Berg

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The Fourier-Analytic Proof of Quadratic Reciprocity

By: Michael C. Berg

A unique synthesis of the three existing Fourier-analytictreatments of quadratic reciprocity. The relative quadratic case was first settled by Hecke in 1923,then recast by Weil in 1964 into the language of unitary grouprepresentations. The analytic proof of the general n-th order caseis still an open problem today, going back to the end of Hecke'sfamous treatise of 1923. The Fourier-Analytic Proof of QuadraticReciprocity provides number theorists interested in analyticmethods applied to reciprocity laws with a unique opportunity toexplore the works of Hecke, Weil, and Kubota. This work brings together for the first time in a single volume thethree existing formulations of the Fourier-analytic proof ofquadratic reciprocity. It shows how Weil's groundbreakingrepresentation-theoretic treatment is in fact equivalent to Hecke'sclassical approach, then goes a step further, presenting Kubota'salgebraic reformulation of the Hecke-Weil proof. Extensivecommutative diagrams for comparing the Weil and Kubotaarchitectures are also featured. The author clearly demonstrates the value of the analytic approach,incorporating some of the most powerful tools of modern numbertheory, including adèles, metaplectric groups, andrepresentations. Finally, he points out that the critical commonfactor among the three proofs is Poisson summation, whosegeneralization may ultimately provide the resolution for Hecke'sopen problem.

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118

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118031199

ISBN 13

9781118031193

Passage to Ararat

By: Michael J. Arlen

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Passage to Ararat

By: Michael J. Arlen

In Passage to Ararat, which received the National Book Award in 1976, Michael J. Arlen goes beyond the portrait of his father, the famous Anglo-Armenian novelist of the 1920s, that he created in Exiles to try to discover what his father had tried to forget: Armenia and what it meant to be an Armenian, a descendant of a proud people whom conquerors had for centuries tried to exterminate. But perhaps most affectingly, Arlen tells a story as large as a whole people yet as personal as the uneasy bond between a father and a son, offering a masterful account of the affirmation and pain of kinship.

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307

Publisher

Macmillan

Published Date

ISBN 10

0374530122

ISBN 13

9780374530129

Geometry, Spectral Theory, Groups, and Dynamics

Proceedings in Memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel

By: Robert Brooks,Michael Entov,Yehuda Pinchover,Michah Sageev

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Geometry, Spectral Theory, Groups, and Dynamics

Proceedings in Memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel

By: Robert Brooks,Michael Entov,Yehuda Pinchover,Michah Sageev

This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952 - 2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and numbertheory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szego's theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate studentsand researchers interested in various aspects of geometry and global analysis.

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298

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821837109

ISBN 13

9780821837108

Period Domains over Finite and p-adic Fields

By: Jean-François Dat,Sascha Orlik,Michael Rapoport

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Period Domains over Finite and p-adic Fields

By: Jean-François Dat,Sascha Orlik,Michael Rapoport

This book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.

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395

Publisher

Cambridge University Press

Published Date

ISBN 10

1139488341

ISBN 13

9781139488341

Applications of Curves over Finite Fields

1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves Over Finite Fields, July 27-31, 1997, University of Washington, Seattle

By: Michael D. Fried

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Applications of Curves over Finite Fields

1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves Over Finite Fields, July 27-31, 1997, University of Washington, Seattle

By: Michael D. Fried

This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: 1. Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves. 2. Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus 0 covers, reductions of covers, and explicit computation of monodromy groups over finite fields. 3. Zeta functions and trace formulas. To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and L-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate the material presented in the book.

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254

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809253

ISBN 13

9780821809259

Portrait of a Greek Imagination

An Ethnographic Biography of Andreas Nenedakis

By: Michael Herzfeld

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Portrait of a Greek Imagination

An Ethnographic Biography of Andreas Nenedakis

By: Michael Herzfeld

In Portrait of a Greek Imagination, Michael Hetzfeld succeeds in telling the life history of Andreas Nenedakis in a way that beautifully connects autobiographic and ethnographic levels of understanding. One learns a great deal about Nenedakis as a writer and a person while acquiring new knowledge and insight into the spirals of history that have drawn together Cretan, Greek, and European society during the twentieth century. It is an important contribution to the current discussions about the intersection of anthropology and literature.

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352

Publisher

University of Chicago Press

Published Date

ISBN 10

0226329097

ISBN 13

9780226329093

The Geometry and Topology of Coxeter Groups. (LMS-32)

By: Michael W. Davis

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The Geometry and Topology of Coxeter Groups. (LMS-32)

By: Michael W. Davis

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

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601

Publisher

Princeton University Press

Published Date

ISBN 10

1400845947

ISBN 13

9781400845941

Geometric Group Theory

By: Cornelia Druţu,Michael Kapovich

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Geometric Group Theory

By: Cornelia Druţu,Michael Kapovich

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

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Page Count

841

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470411040

ISBN 13

9781470411046

Solving the Pell Equation

By: Michael Jacobson,Hugh Williams

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Solving the Pell Equation

By: Michael Jacobson,Hugh Williams

Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.

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504

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Springer Science & Business Media

Published Date

ISBN 10

0387849238

ISBN 13

9780387849232

Knots

By: Gerhard Burde,Heiner Zieschang,Michael Heusener

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Knots

By: Gerhard Burde,Heiner Zieschang,Michael Heusener

This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.

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432

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110270781

ISBN 13

9783110270785

Number Theory Through Inquiry

By: David C. Marshall,Edward Odell,Michael Starbird

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Number Theory Through Inquiry

By: David C. Marshall,Edward Odell,Michael Starbird

Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

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140

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470461595

ISBN 13

9781470461591

The Story of the St. Louis Cardinals

By: Michael O'Hearn

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The Story of the St. Louis Cardinals

By: Michael O'Hearn

Examines the history, players, and future of the St. Louis Cardinals baseball team.

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The Creative Company

Published Date

ISBN 10

1583415513

ISBN 13

9781583415511

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

By: J. Michael Steele

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The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

By: J. Michael Steele

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

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320

Publisher

Cambridge University Press

Published Date

ISBN 10

052154677X

ISBN 13

9780521546775

Riemann, Topology, and Physics

By: Michael I. Monastyrsky

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Riemann, Topology, and Physics

By: Michael I. Monastyrsky

The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.

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220

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Springer Science & Business Media

Published Date

ISBN 10

0817647791

ISBN 13

9780817647797

Inside Stories

Writing about Home

By: Michael Huey

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Inside Stories

Writing about Home

By: Michael Huey

Art historian and conceptual artist Michael Huey returns again and again to the topics loss, legacy, and the archive in his work, including that of a journalist covering historical architecture in central Europe and beyond. In search of a variety of expressions of life and passion, he has for more than 30 years written about interiors—home, in the broadest sense—for newspapers and magazines, starting with The Home Forum, the arts and letters page of The Christian Science Monitor, and continuing for The World of Interiors, German AD, nest, and Cabana. This book contains a selection of Michael Huey’s very best stories, comprising over 70 superb articles accompanied by the author’s inspiring photographs. Through this lens we travel from hidden gems of the Baroque to forgotten places of the 19th century, to Vienna’s Art Nouveau, and on to recent times. But always he shows us homes, interiors, and people lovingly interwoven with art.

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215

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ALBUM VERLAG

Published Date

ISBN 10

3851641973

ISBN 13

9783851641974

Algebraic Geometry

Notes on a Course

By: Michael Artin

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Algebraic Geometry

Notes on a Course

By: Michael Artin

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.

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332

Publisher

American Mathematical Society

Published Date

ISBN 10

1470468484

ISBN 13

9781470468484

Lockdown

THE VIRUS WAS NOT THE CAUSE

By: Michael Morris

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Lockdown

THE VIRUS WAS NOT THE CAUSE

By: Michael Morris

There is no going back to the old "normal". What you used to know as "your life" is no more. This rebuilding phase, disguised as a "pandemic", has been well prepared and none of this has to do with a virus or a health hazard. In 2019, a great reset of the monetary, economic and political system was long overdue. The tension could be felt everywhere. The elite, the "Secret World Government" finally wanted to implement their "New World Order". They were tired of the delusion of free elections, individual rights and self-realization. As long as we were needed as work force they played along, but now that robots and AI are better and faster than us we became dispensable. However, neither those responsible for the old system nor their puppets in politics and the media were willing to take the blame for a major system crash. They feared the rage of the masses. What they needed was a scapegoat, something or someone to be held responsible for the great reset, a complete redesign of our way of living and for many of us the right for living. And then the Chinese presented the perfect way out of their dilemma: an enemy that nobody can see or fight or even understand. SARS-COV-2 is a political virus, designed in a lab in China with Western support and knowing. This is a proven fact. This common cold virus did not come unforeseen. There was a clear build-up of events in 2019 that led to the worldwide lockdown with all its consequences, ranging from intelligence reports to Bill Gates' Event 201 to a Climate Emergency in Europe after faked elections. Even with the easing of lockdown measures in some areas or countries this experiment is far from over. It has just begun. Do you think that politicians or so-called "scientists" and "journalists" will voluntarily renounce their newly gained powers and the attention that they so enjoy? This is a serious political, social, economical and spiritual crisis. This is as serious as it can get. This is Huxley's Brave New World and Orwell's 1984 all combined. This is the ultimate fight "Good" versus "Evil". What do you want this world to be, for yourself and for your descendants: fearful and oppressive or loving and creative? Find out what lies behind it and get ready to act.

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Page Count

405

Publisher

Amadeus Verlag

Published Date

ISBN 10

3938656735

ISBN 13

9783938656730

Book's by Michael Artin

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