Abstract Algebra: An Interactive Approach

William Paulsen, William Paulsen

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July 29, 2009 by CRC Press
Textbook - 560 Pages - 34 B/W Illustrations
ISBN 9781420094527 - CAT# C4521
Series: Textbooks in Mathematics

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Features

  • Offers the option of using technology in the classroom by incorporating GAP and Mathematica commands
  • Discusses topics not covered in similar texts, such as semi-direct products and skew fields
  • Includes many diagrams produced by Mathematica to help students visualize difficult concepts, such as homomorphisms and permutations
  • Contains numerous homework problems of both the interactive and standard types
  • Provides a CD-ROM with GAP packages and Mathematica notebooks

Solutions manual available for qualifying instructors

Summary

By integrating the use of GAP and Mathematica®, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several interactive computer problems that utilize GAP and Mathematica to explore groups and rings.

Although the book gives the option to use technology in the classroom, it does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many graduate-level 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. He also incorporates problem sequences that allow students to delve into interesting topics in depth, including Fermat’s two square theorem.

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.