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A First Course in Abstract Algebra With Applications 3/e

作者：Joseph J. Rotman
原價：NT$ 1,190

ISBN：9789862800133
版次：3
年份：2006
出版商：Pearson Education
頁數/規格：644頁/平裝單色

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內容介紹本書特色目錄作者介紹

Description
This text introduces students to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

Features

Comprehensive coverage of abstract algebra – Includes discussions of the fundamental theorem of Galois theory; Jordan-Holder theorem; unitriangular groups; solvable groups; construction of free groups; von Dyck's theorem, and presentations of groups by generators and relations.

Significant applications for both group and commutative ring theories, especially with Gr o bner bases – Helps students see the immediate value of abstract algebra.

Flexible presentation – May be used to present both ring and group theory in one semester, or for two-semester course in abstract algebra.

Number theory – Presents concepts such as induction, factorization into primes, binomial coefficients and DeMoivre's Theorem, so students can learn to write proofs in a familiar context.

Section on Euclidean rings – Demonstrates that the quotient and remainder from the division algorithm in the Gaussian integers may not be unique. Also, Fermat's Two-Squares theorem is proved.

Sylow theorems – Discusses the existence of Sylow subgroups as well as conjugacy and the congruence condition on their number.

Fundamental theorem of finite abelian groups – Covers the basis theorem as well as the uniqueness to isomorphism

Extensive references and consistent numbering system for lemmas, theorems, propositions, corollaries, and examples – Clearly organized notations, hints, and appendices simplify student reference.

New to This Edition

Rewritten for smoother exposition – Makes challenging material more accessible to students.

Updated exercises – Features challenging new problems, with redesigned page and back references for easier access.

Extensively revised Ch. 2 (groups) and Ch. 3 (commutative rings ) – Makes chapters independent of one another, giving instructors increased flexibility in course design.

New coverage of codes – Includes 28-page introduction to codes, including a proof that Reed-Solomon codes can be decoded.

New section on canonical forms (Rational, Jordan, Smith) for matrices – Focuses on the definition and basic properties of exponentiation of complex matrices, and why such forms are valuable.

New classification of frieze groups – Discusses why viewing the plane as complex numbers allows one to describe all isometries with very simple formulas.

Expanded discussion of orthogonal Latin squares – Includes coverage of magic squares.

Special Notation section – References common symbols and the page on which they are introduced.

Table of Contents
Chapter 1: Number Theory
Chapter 2: Groups I
Chapter 3: Commutative Rings I
Chapter 4: Linear Algebra
Chapter 5: Fields
Chapter 6: Groups II
Chapter 7: Commutative Rings III

Joseph J. Rotman, University of Illinois

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