Adventures in group theory : Rubik's cube, Merlin's machine, and other mathematical toys

著者

• Joyner, David

書誌事項

Adventures in group theory : Rubik's cube, Merlin's machine, and other mathematical toys

David Joyner

The Johns Hopkins University Press, c2008

2nd ed

• : pbk
• : hbk

注記

Includes bibliographical references and index

内容説明・目次

巻冊次

: hbk ISBN 9780801890123

内容説明

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.

目次

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

巻冊次

: pbk ISBN 9780801890130

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA8840836X
• ISBN:
  • 9780801890130
  • 9780801890123
• LCCN: 2008011322
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Baltimore, Md.
• ページ数/冊数: xv, 310 p.
• 大きさ: 25 cm