Adventures in Group Theory

Rubik's Cube, Merlin's Machine, and Other Mathematical Toys

Häftad, Engelska, 2009

383 kr

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Beskrivning

This updated and revised edition of David Joyner's entertaining "hands-on" tour of group theory and abstract algebra brings life, levity, and practicality to the topics through mathematical toys. Joyner uses permutation puzzles such as the Rubik's Cube and its variants, the 15 puzzle, the Rainbow Masterball, Merlin's Machine, the Pyraminx, and the Skewb to explain the basics of introductory algebra and group theory. Subjects covered include the Cayley graphs, symmetries, isomorphisms, wreath products, free groups, and finite fields of group theory, as well as algebraic matrices, combinatorics, and permutations. Featuring strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.

Produktinformation

Utgivningsdatum:2009-02-23
Mått:153 x 228 x 19 mm
Vikt:435 g
Format:Häftad
Språk:Engelska
Antal sidor:328
Upplaga:2
Förlag:Johns Hopkins University Press
ISBN:9780801890130

Utforska kategorier

Grupper och gruppteori inom Naturvetenskap och teknik

Mer om författaren

David Joyner is a professor of mathematics at the U.S. Naval Academy. He is coauthor of Applied Abstract Algebra, also published by Johns Hopkins, and editor of Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory.

Recensioner i media

"Adventures in Group Theory is a tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." - MAA Online "Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts." - Choice "Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book." - American Scientist"

Innehållsförteckning

PrefaceAcknowledgmentsWhere to Begin...1. Elementary, my dear Watson2. 'And you do addition?'3. Bell ringing and other permutations4. A procession of permutation puzzles5. What's commutative and purple?6. Welcome to the machine7. 'God's algorithm' and graphs8. Symmetry and the Platonic solids9. The illegal cube group10. Words which move11. The (legal) Rubik's Cube group12. Squares, two-faces, and other subgroups13. Other Rubik-like puzzle groups14. Crossing the Rubicon15. Some solution strategies16. Coda: Questions and other directionsBibliographyIndex