Abstract Algebra: An Interactive Approach
Abstract Algebra: An Interactive Approach (Textbooks in Mathematics) William Paulsen,
Publisher: CRC
ISBN: 1420094521
DDC: 512.02
Edition: Hardcover; 2009-07-29
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.
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