Adventures in Group Theory

Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
2. Auflage 2008
ISBN: 978-0-8018-9013-0
Verlag: Johns Hopkins University Press

Buch, Englisch, 328 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 537 g

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.

Autoren/Hrsg.

Joyner, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Populäre Darstellungen der Mathematik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Preface
Acknowledgments
Where to Begin.
1. Elementary, my dear Watson
2. 'And you do addition?'
3. Bell ringing and other permutations
4. A procession of permutation puzzles
5. What's commutative and purple?
6. Welcome to the machine
7. 'God's algorithm' and graphs
8. Symmetry and the Platonic solids
9. The illegal cube group
10. Words which move
11. The (legal) Rubik's Cube group
12. Squares, two-faces, and other subgroups
13. Other Rubik-like puzzle groups
14. Crossing the Rubicon
15. Some solution strategies
16. Coda: Questions and other directions
Bibliography
Index

Über Autor(innen)

Joyner, David
David Joyner is a professor in the Mathematics Department at the U.S. Naval Academy. He is the author of Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, also published by Johns Hopkins.

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.