Advanced Modern Algebra
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Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-08-11
Advanced Modern Algebra written by Joseph J. Rotman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-11 with Mathematics categories.
"This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gr'obner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic K-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization."--Publisher's description.
Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher: American Mathematical Society
Release Date : 2025-06-25
Advanced Modern Algebra written by Joseph J. Rotman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Mathematics categories.
This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.
Learning Modern Algebra
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Author : Albert Cuoco
language : en
Publisher: MAA
Release Date : 2013
Learning Modern Algebra written by Albert Cuoco and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Much of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.
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 : Derek J.S. Robinson
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-02-07
Abstract Algebra written by Derek J.S. Robinson and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and the information and physical sciences. In addition to introducing the main concepts of modern algebra – groups, rings, modules and fields – the book contains numerous applications, which are intended to illustrate the concepts and to show the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems, error correcting codes and economics are described. There is ample material here for a two semester course in abstract algebra. Proofs of almost all results are given. The reader led through the proofs in gentle stages. There are more than 500 problems, of varying degrees of diffi culty. The book should be suitable for advanced undergraduate students in their fi nal year of study and for fi rst or second year graduate students at a university in Europe or North America. In this third edition three new chapters have been added: an introduction to the representation theory of fi nite groups, free groups and presentations of groups, an introduction to category theory.
Studyguide For Advanced Modern Algebra By Rotman Joseph J Isbn 9780821847411
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Author : Cram101 Textbook Reviews
language : en
Publisher: Cram101
Release Date : 2013-08
Studyguide For Advanced Modern Algebra By Rotman Joseph J Isbn 9780821847411 written by Cram101 Textbook Reviews and has been published by Cram101 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08 with categories.
Never HIGHLIGHT a Book Again! Includes all testable terms, concepts, persons, places, and events. Cram101 Just the FACTS101 studyguides gives all of the outlines, highlights, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanies: 9780821847411. This item is printed on demand.
A History Of Abstract Algebra
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Author : Israel Kleiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-02
A History Of Abstract Algebra written by Israel Kleiner 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 2007-10-02 with Mathematics categories.
This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Problems In Abstract Algebra
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Author : A. R. Wadsworth
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-10
Problems In Abstract Algebra written by A. R. Wadsworth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-10 with Mathematics categories.
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Advanced Linear Algebra
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Advanced Linear Algebra written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author begins with chapters introducing basic notation for vector spaces, permutations, polynomials, and other algebraic structures. The following chapters are designed to be mostly independent of each other so that readers with different interests can jump directly to the topic they want. This is an unusual organization compared to many abstract algebra textbooks, which require readers to follow the order of chapters. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint, while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. A wide array of topics is included, ranging from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra). The book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.
Introduction To Modern Algebra
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Author : Neal Henry McCoy
language : en
Publisher: WCB/McGraw-Hill
Release Date : 1992
Introduction To Modern Algebra written by Neal Henry McCoy and has been published by WCB/McGraw-Hill this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.