Advanced Modern Algebra
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Author |
: Joseph J. Rotman |
Publisher |
: American Mathematical Society |
Total Pages |
: 570 |
Release |
: 2023-02-22 |
ISBN-10 |
: 9781470472757 |
ISBN-13 |
: 1470472759 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Advanced Modern Algebra by : Joseph J. Rotman
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.
Author |
: Anthony W. Knapp |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 757 |
Release |
: 2007-10-11 |
ISBN-10 |
: 9780817646134 |
ISBN-13 |
: 0817646132 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Advanced Algebra by : Anthony W. Knapp
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
Author |
: Joseph J. Rotman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 722 |
Release |
: 2015-11-30 |
ISBN-10 |
: 9781470415549 |
ISBN-13 |
: 1470415542 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Advanced Modern Algebra by : Joseph J. Rotman
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.
Author |
: Igor R. Shafarevich |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 288 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642563256 |
ISBN-13 |
: 3642563252 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Discourses on Algebra by : Igor R. Shafarevich
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.
Author |
: Seth Warner |
Publisher |
: Courier Corporation |
Total Pages |
: 852 |
Release |
: 2012-08-29 |
ISBN-10 |
: 9780486137094 |
ISBN-13 |
: 0486137090 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Modern Algebra by : Seth Warner
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Author |
: Charles C Pinter |
Publisher |
: Courier Corporation |
Total Pages |
: 402 |
Release |
: 2010-01-14 |
ISBN-10 |
: 9780486474175 |
ISBN-13 |
: 0486474178 |
Rating |
: 4/5 (75 Downloads) |
Synopsis A Book of Abstract Algebra by : Charles C Pinter
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author |
: Joseph J. Rotman |
Publisher |
: |
Total Pages |
: 552 |
Release |
: 2000 |
ISBN-10 |
: STANFORD:36105028605132 |
ISBN-13 |
: |
Rating |
: 4/5 (32 Downloads) |
Synopsis A First Course in Abstract Algebra by : Joseph J. Rotman
For one-semester or two-semester undergraduate courses in Abstract Algebra. This new edition has been completely rewritten. The four chapters from the first edition are expanded, from 257 pages in first edition to 384 in the second. Two new chapters have been added: the first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester. The new Chapter 5, Groups II, contains the fundamental theorem of finite abelian groups, the Sylow theorems, the Jordan-Holder theorem and solvable groups, and presentations of groups (including a careful construction of free groups). The new Chapter 6, Commutative Rings II, introduces prime and maximal ideals, unique factorization in polynomial rings in several variables, noetherian rings and the Hilbert basis theorem, affine varieties (including a proof of Hilbert's Nullstellensatz over the complex numbers and irreducible components), and Grobner bases, including the generalized division algorithm and Buchberger's algorithm.
Author |
: Robert B. Ash |
Publisher |
: Courier Corporation |
Total Pages |
: 434 |
Release |
: 2013-06-17 |
ISBN-10 |
: 9780486318110 |
ISBN-13 |
: 0486318117 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Basic Abstract Algebra by : Robert B. Ash
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.
Author |
: Jonathan D. H. Smith |
Publisher |
: John Wiley & Sons |
Total Pages |
: 386 |
Release |
: 2011-09-30 |
ISBN-10 |
: 9781118030837 |
ISBN-13 |
: 1118030834 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Post-Modern Algebra by : Jonathan D. H. Smith
Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
Author |
: Joseph J. Rotman |
Publisher |
: Courier Corporation |
Total Pages |
: 323 |
Release |
: 2013-01-18 |
ISBN-10 |
: 9780486151687 |
ISBN-13 |
: 0486151689 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Journey into Mathematics by : Joseph J. Rotman
This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.