Abstract Algebra

An Interactive Approach, Second Edition

William Paulsen

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English

Chapman & Hall/CRC
14 October 2024

Algebra

Series: Textbooks in Mathematics

The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use.

This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered.

This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.

Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics.

This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.

By: William Paulsen
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.202kg
ISBN: 9781032917955
ISBN 10: 1032917954
Series: Textbooks in Mathematics
Pages: 650
Publication Date: 14 October 2024
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Paperback
Publisher's Status: Active

Preliminaries. Understanding the Group Concept. The Structure within a Group. Patterns within the Cosets of Groups. Mappings between Groups. Permutation Groups. Building Larger Groups from Smaller Groups. The Search for Normal Subgroups. Solvable and Insoluble Groups. Introduction to Rings. The Structure within Rings. Integral Domains and Fields. Unique Factorization. Finite Division Rings. The Theory of Fields. Galois Theory. Appendix: Sage vs. Mathematica®. Answers to Odd-Numbered Problems. Bibliography.

William Paulsen, PhD, professor of mathematics, Arkansas State University, USA

Reviews for Abstract Algebra: An Interactive Approach, Second Edition

Praise for previous editions: ""The textbook gives an introduction to algebra. The course includes the explanation on how to use the computer algebra systems GAP and Mathematica …The book can be used for an undergraduate-level course (chapter 1-4 and 9-12) or a second semester graduate-level course."" —Gerhard Pfister, Zentralblatt MATH