Advanced Modern Algebra

Advanced Modern Algebra

Author: Joseph J. Rotman

Publisher: American Mathematical Society

Published: 2023-02-22

Total Pages: 570

ISBN-13: 1470472759

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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 Algebra

Advanced Algebra

Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

Published: 2007-10-11

Total Pages: 757

ISBN-13: 0817646132

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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.


Discourses on Algebra

Discourses on Algebra

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 288

ISBN-13: 3642563252

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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.


Modern Algebra

Modern Algebra

Author: Seth Warner

Publisher: Courier Corporation

Published: 2012-08-29

Total Pages: 852

ISBN-13: 0486137090

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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.


A Book of Abstract Algebra

A Book of Abstract Algebra

Author: Charles C Pinter

Publisher: Courier Corporation

Published: 2010-01-14

Total Pages: 402

ISBN-13: 0486474178

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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.


A First Course in Abstract Algebra

A First Course in Abstract Algebra

Author: Joseph J. Rotman

Publisher:

Published: 2000

Total Pages: 552

ISBN-13:

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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.


Learning Modern Algebra

Learning Modern Algebra

Author: Albert Cuoco

Publisher: MAA

Published: 2013

Total Pages: 481

ISBN-13: 1939512018

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A guide to modern algebra for mathematics teachers. It makes explicit connections between abstract algebra and high-school mathematics.


Basic Algebra

Basic Algebra

Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

Published: 2007-07-28

Total Pages: 762

ISBN-13: 0817645292

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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. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.


Journey into Mathematics

Journey into Mathematics

Author: Joseph J. Rotman

Publisher: Courier Corporation

Published: 2013-01-18

Total Pages: 323

ISBN-13: 0486151689

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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.


Advanced Modern Algebra

Advanced Modern Algebra

Author: Joseph J. Rotman

Publisher: American Mathematical Soc.

Published: 2015-11-30

Total Pages: 722

ISBN-13: 1470415542

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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.