A First Course in Abstract Algebra With Applications 3/e (H) (絕)
- 20本以上，享 8.5折
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- 一般書籍
- ISBN：9780131862678
- 作者：Joseph J. Rotman
- 版次：3
- 年份：2006
- 出版商：Pearson Education
- 頁數/規格：642頁/精裝單色
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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.
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
New to This Edition
- 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
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
