Abstract Algebra With Applications Rings And Fields
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Abstract Algebra With Applications
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Author : Karlheinz Spindler
language : en
Publisher: CRC Press
Release Date : 1993-10-18
Abstract Algebra With Applications written by Karlheinz Spindler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-18 with Mathematics categories.
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Abstract Algebra With Applications
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Author : Karlheinz Spindler
language : en
Publisher:
Release Date : 1994
Abstract Algebra With Applications written by Karlheinz Spindler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Abstract Algebra With Applications Rings And Fields
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Author : Karlheinz Spindler
language : en
Publisher:
Release Date : 1994
Abstract Algebra With Applications Rings And Fields written by Karlheinz Spindler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebra, Abstract categories.
Abstract Algebra Introduction To Groups Rings And Fields With Applications Second Edition
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Author : Clive Reis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-08-30
Abstract Algebra Introduction To Groups Rings And Fields With Applications Second Edition written by Clive Reis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-30 with Mathematics categories.
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Essentials Of Abstract Algebra
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Author : Sachin Nambeesan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Essentials Of Abstract Algebra written by Sachin Nambeesan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Essentials of Abstract Algebra" offers a deep exploration into the fundamental structures of algebraic systems. Authored by esteemed mathematicians, this comprehensive guide covers groups, rings, fields, and vector spaces, unraveling their intricate properties and interconnections. We introduce groups, exploring their diverse types, from finite to infinite and abelian to non-abelian, with concrete examples and rigorous proofs. Moving beyond groups, we delve into rings, explaining concepts like ideals, homomorphisms, and quotient rings. The text highlights the relevance of ring theory in number theory, algebraic geometry, and coding theory. We also navigate fields, discussing field extensions, Galois theory, and algebraic closures, and exploring connections between fields and polynomial equations. Additionally, we venture into vector spaces, examining subspaces, bases, dimension, and linear transformations. Throughout the book, we emphasize a rigorous mathematical foundation and intuitive understanding. Concrete examples, diagrams, and exercises enrich the learning experience, making abstract algebra accessible to students, mathematicians, and researchers. "Essentials of Abstract Algebra" is a timeless resource for mastering the beauty and power of algebraic structures.
Abstract Algebra
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Author : Clive Reis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-05-31
Abstract Algebra written by Clive Reis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-31 with Mathematics categories.
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Basic Algebra
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Author : Paul M. Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-12-01
Basic Algebra written by Paul M. Cohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-01 with Mathematics categories.
This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.
Introduction To Abstract Algebra
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Author : Dr. Kuldeep Singh
language : en
Publisher: Navi International Book Publication house
Release Date : 2024-10-19
Introduction To Abstract Algebra written by Dr. Kuldeep Singh and has been published by Navi International Book Publication house this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-19 with Mathematics categories.
Mathematicians who specialize in abstract algebra study algebraic structures like fields, rings, and groups. Abstract algebra investigates the fundamental ideas and patterns that underpin these procedures, as contrast to elementary algebra, which works with particular equations and operations on numbers. It is a fundamental topic with applications in computer science, cryptography, and physics. It also offers the theoretical basis for many other areas of mathematics. The idea of a group, which is a set with a single operation that meets axioms such as closure, associativity, the presence of an identity element, and the existence of inverses, is one of the fundamental ideas in abstract algebra. A common subject in the study of symmetry and transformations is groups. By adding new operations, including addition and multiplication, and examining their interactions, rings and fields expand on fundamental concepts. By studying abstract algebra, mathematicians may identify patterns and correlations that remain across many systems by moving from concrete numbers to more generalized things. This abstraction makes it possible to comprehend mathematical structures more deeply and inspires the creation of new ideas and instruments. As a field of study, abstract algebra serves as a doorway to more complicated mathematical analysis and as a potent language for characterizing intricate systems across a range of scientific fields. The importance of abstract algebra is not limited to mathematics alone; it also affects other practical disciplines. For example, in computer science, knowledge of abstract algebraic structures is essential to comprehending data structures, algorithms, and cryptographic systems. Group theory and field theory ideas play a major role in cryptography, which protects digital communications, in the creation and cracking of encryption systems. Similar to this, group theory's description of symmetry operations in physics aids in the explanation of key ideas in relativity and quantum mechanics. This field's intrinsic abstraction encourages other ways of thinking. It promotes the development of rigorous yet creative problem-solving abilities since it often calls for identifying patterns and generalizations that are not immediately apparent. This ability to think abstractly is useful not just in mathematics but also in other fields like economics, engineering, and biology that study complex systems. Because of its degree of abstraction and divergence from the arithmetic and algebraic intuition acquired in previous mathematics courses, abstract algebra may be difficult to understand in educational settings
Introduction To Abstract Algebra An Sets Groups Rings And Fields
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Author : Steven Howard Weintraub
language : en
Publisher: World Scientific
Release Date : 2022-05-25
Introduction To Abstract Algebra An Sets Groups Rings And Fields written by Steven Howard Weintraub and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-25 with Mathematics categories.
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
Modern Algebra With Applications
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Author : William J. Gilbert
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-30
Modern Algebra With Applications written by William J. Gilbert and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Mathematics categories.
Praise for the first edition "This book is clearly written and presents a large number ofexamples illustrating the theory . . . there is no other book ofcomparable content available. Because of its detailed coverage ofapplications generally neglected in the literature, it is adesirable if not essential addition to undergraduate mathematicsand computer science libraries." –CHOICE As a cornerstone of mathematical science, the importance ofmodern algebra and discrete structures to many areas of science andtechnology is apparent and growing–with extensive use incomputing science, physics, chemistry, and data communications aswell as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instructionof modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of thissubject–effectively holding your interest and creating a moreseamless method of instruction. Incorporating the applications of modern algebra throughout itsauthoritative treatment of the subject, this book covers the fullcomplement of group, ring, and field theory typically contained ina standard modern algebra course. Numerous examples are included ineach chapter, and answers to odd-numbered exercises are appended inthe back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares Pólya—Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updatedSecond Edition also contains new material on order of an elementand cyclic groups, more details about the lattice of divisors of aninteger, and new historical notes. Filled with in-depth insights and over 600 exercises of varyingdifficulty, Modern Algebra with Applications, Second Edition canhelp anyone appreciate and understand this subject.