Author : Simeon Ivanov
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 42,51 MB
Release : 1992
Category : Mathematics
ISBN : 9780821831403
This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.
Author : Francis Borceux
Publisher : Cambridge University Press
Page : 360 pages
File Size : 21,18 MB
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521803090
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
Author : Victor Percy Snaith
Publisher : World Scientific
Page : 234 pages
File Size : 50,44 MB
Release : 2003
Category : Mathematics
ISBN : 9789812386007
This book is ideally suited for a two-term undergraduate algebra course culminating in a discussion on Galois theory. It provides an introduction to group theory and ring theory en route. In addition, there is a chapter on groups ? including applications to error-correcting codes and to solving Rubik's cube. The concise style of the book will facilitate student-instructor discussion, as will the selection of exercises with various levels of difficulty. For the second edition, two chapters on modules over principal ideal domains and Dedekind domains have been added, which are suitable for an advanced undergraduate reading course or a first-year graduate course.
Author : Celine Carstensen-Opitz
Publisher : Walter de Gruyter GmbH & Co KG
Page : 422 pages
File Size : 10,74 MB
Release : 2019-09-02
Category : Mathematics
ISBN : 3110603993
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.
Author : Thomas Judson
Publisher : Orthogonal Publishing L3c
Page : 0 pages
File Size : 25,20 MB
Release : 2023-08-11
Category :
ISBN : 9781944325190
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Author : V.B. Alekseev
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 23,80 MB
Release : 2007-05-08
Category : Mathematics
ISBN : 1402021879
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Author : Julio R. Bastida
Publisher : Cambridge University Press
Page : 354 pages
File Size : 30,31 MB
Release : 1984-12-28
Category : Mathematics
ISBN : 9780521302425
This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.
Author : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 24,45 MB
Release : 2017-09-21
Category : Mathematics
ISBN : 1107167485
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author : Jeremy Kepner
Publisher : SIAM
Page : 388 pages
File Size : 41,4 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719918
The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.
Author : William J Gilbert
Publisher : John Wiley & Sons
Page : 366 pages
File Size : 26,60 MB
Release : 2008-09
Category :
ISBN : 9788126518302
Market_Desc: Upper undergraduate and graduate level modern algebra courses Special Features: · Includes applications so students can see right away how to use the theory· This classic text has sold almost 12,000 units· Contains numerous examples· Includes chapters on Boolean Algebras, groups, quotient groups, symmetry groups in three dimensions, Polya-Burnside method of enumeration, monoids and machines, rings and fields, polynomial and Euclidean rings, quotient rings, field extensions, Latin squares, geometrical constructions, and error-correcting codes· Andwers to odd-numbered exercises so students can check their work About The Book: The book covers all the group, ring, and field theory that is usually contained in a standard modern algebra course; the exact sections containing this material are indicated in the Table of Contents. It stops short of the Sylow theorems and Galois theory. These topics could only be touched on in a first course, and the author feels that more time should be spent on them if they are to be appreciated.
