William Paulsen, "Abstract Algebra: An Interactive Approach"
C.. Pr..s | 2009-07-29 | ISBN: 1420094521 | 560 pages | PDF | 2,5 MB
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.
"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 1173
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