Advanced Abstract Algebra
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Discourses On Algebra
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Author : Igor R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discourses On Algebra written by Igor R. Shafarevich 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 2012-12-06 with Mathematics categories.
Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.
Advanced Abstract Algebra
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Author :
language : en
Publisher: Krishna Prakashan Media
Release Date :
Advanced Abstract Algebra written by and has been published by Krishna Prakashan Media this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Advanced Linear Algebra
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Advanced Linear Algebra written by Steven Roman 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 2007-12-31 with Mathematics categories.
Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Advanced Linear Algebra
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Author : Nicholas Loehr
language : en
Publisher: CRC Press
Release Date : 2014-04-10
Advanced Linear Algebra written by Nicholas 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 2014-04-10 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 book’s 20 chapters are grouped into six main areas: algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. The level of abstraction gradually increases as students proceed through the text, moving from matrices to vector spaces to modules. 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. Unlike similar advanced mathematical texts, this one minimizes the dependence of each chapter on material found in previous chapters so that students may immediately turn to the relevant chapter without first wading through pages of earlier material to access the necessary algebraic background and theorems. Chapter summaries contain a structured list of the principal definitions and results. End-of-chapter exercises aid students in digesting the material. Students are encouraged to use a computer algebra system to help solve computationally intensive exercises.
Abstract Algebra
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Author : Claudia Menini
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Abstract Algebra written by Claudia Menini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-22
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 2023-02-22 with Mathematics categories.
This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher:
Release Date : 2002
Advanced Modern Algebra written by Joseph J. Rotman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
For two-term undergraduate level courses in Algebra. This text's organizing principle is the interplay between groups and rings, where rings includes the ideas of modules. It contains basic definitions, complete and clear theorems and gives attention to the topics of algebraic geometry, computers, homology and representations. More than merely a succession of definition theorem proofs, this text puts results and ideas in context so that students can appreciate why a certain topic is being studied and where definitions originate. *Coverage of topics not usually found in other texts - e.g. inverse and direct limits: Euclidean rings; Grobner bases; Ext and tor; Schreier-Neilsen theorem (subgroups of free groups are free); simplicity of PSL (2, q). *Numerous exercises. *Many examples and counter-examples. *Serious treatment of set theory - Reminds students what functions really are. *Early presentation of the basis theorem for finite abelian groups - Makes the proof of the basis theorem for finitely generated modules over PID's more digestible, allowing students to then see how that proof is translated into the language of modules. *Transition - To make the step from an undergraduat
Basic Abstract Algebra
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Author : Robert B. Ash
language : en
Publisher: Courier Corporation
Release Date : 2013-06-17
Basic Abstract Algebra written by Robert B. Ash and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Mathematics categories.
Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher:
Release Date : 2017-08-30
Advanced Modern Algebra written by Joseph J. Rotman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with categories.
This new edition, now in two parts, has been significantly reorganised and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. The second part presents many topics mentioned in the first part in greater depth and in more detail.
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.
