Galois Theories

Author: Francis Borceux,George Janelidze

Publisher: Cambridge University Press

ISBN: 9780521803090

Category: Mathematics

Page: 341

View: 8675

Develops Galois theory in a more general context, emphasizing category theory.

Galois Theory, Hopf Algebras, and Semiabelian Categories

Author: George Janelidze

Publisher: American Mathematical Soc.

ISBN: 0821832905

Category: Mathematics

Page: 570

View: 5816

This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabelian categories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers, specifically those interested in Galois theory and Hopf algebras and their categorical unification.

Galois Groups and Fundamental Groups

Author: Tamás Szamuely

Publisher: Cambridge University Press

ISBN: 0521888506

Category: Mathematics

Page: 270

View: 666

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Groups as Galois Groups

An Introduction

Author: Helmut Volklein

Publisher: Cambridge University Press

ISBN: 9780521562805

Category: Mathematics

Page: 248

View: 1200

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

Central Simple Algebras and Galois Cohomology

Author: Philippe Gille,Tamás Szamuely

Publisher: Cambridge University Press

ISBN: 1107156378

Category: Mathematics

Page: 418

View: 4952

The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.

p-adic Differential Equations

Author: Kiran S. Kedlaya

Publisher: Cambridge University Press

ISBN: 1139489208

Category: Mathematics

Page: N.A

View: 7632

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.

Modular Forms and Galois Cohomology

Author: Haruzo Hida,Professor Haruzo Hida

Publisher: Cambridge University Press

ISBN: 9780521770361

Category: Mathematics

Page: 343

View: 3192

Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

Algebra für Einsteiger

Von der Gleichungsauflösung zur Galois-Theorie

Author: Jörg Bewersdorff

Publisher: Springer-Verlag

ISBN: 3658022620

Category: Mathematics

Page: 214

View: 4970

Dieses Buch ist eine leicht verständliche Einführung in die Algebra, die den historischen und konkreten Aspekt in den Vordergrund rückt. Der rote Faden ist eines der klassischen und fundamentalen Probleme der Algebra: Nachdem im 16. Jahrhundert allgemeine Lösungsformeln für Gleichungen dritten und vierten Grades gefunden wurden, schlugen entsprechende Bemühungen für Gleichungen fünften Grades fehl. Nach fast dreihundertjähriger Suche führte dies schließlich zur Begründung der so genannten Galois-Theorie: Mit ihrer Hilfe kann festgestellt werden, ob eine Gleichung mittels geschachtelter Wurzelausdrücke lösbar ist. Das Buch liefert eine gute Motivation für die moderne Galois-Theorie, die den Studierenden oft so abstrakt und schwer erscheint. In dieser Auflage wurde ein Kapitel ergänzt, in dem ein alternativer, auf Emil Artin zurückgehender Beweis des Hauptsatzes der Galois-Theorie wiedergegeben wird. Dieses Kapitel kann fast unabhängig von den anderen Kapiteln gelesen werden.

Algebraic Number Theory

Author: A. Fröhlich,M. J. Taylor,Martin J. Taylor

Publisher: Cambridge University Press

ISBN: 9780521438346

Category: Mathematics

Page: 355

View: 2665

This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.

Character Theory and the McKay Conjecture

Author: Gabriel Navarro

Publisher: Cambridge University Press

ISBN: 1108428444

Category: Mathematics

Page: 250

View: 3715

Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

Finite Group Theory

Author: M. Aschbacher

Publisher: Cambridge University Press

ISBN: 9780521786751

Category: Mathematics

Page: 304

View: 4928

The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.

Galois Representations and (Phi, Gamma)-Modules

Author: Peter Schneider

Publisher: Cambridge University Press

ISBN: 110718858X

Category: Mathematics

Page: 156

View: 6753

A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969

Author: Donald G. Babbitt,Jane E. Kister

Publisher: American Mathematical Soc.

ISBN: 9780821896709

Category: Mathematics

Page: 541

View: 9702

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 6381

Exploratory Galois Theory

Author: John Swallow

Publisher: Cambridge University Press

ISBN: 9780521544993

Category: Computers

Page: 208

View: 3983

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

Author: D. J. Benson

Publisher: Cambridge University Press

ISBN: 9780521636537

Category: Mathematics

Page: 260

View: 2361

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 4473

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.