John Horton Conway (1937–2020)

Indeholder "Preface", "Zeroth Part ... On Numbers", " Chapter 0: All Numbers Great and Small", " Chapter 1: The Class No is a Field", " Chapter 2: The Real and Ordinal Numbers", " Chapter 3: The Structure of the General Number", " Chapter 4: Algebra and Analysis of Numbers", " Chapter 5: Number Theory in the Land of Oz", " Chapter 6: The Curious Field On2", " Appendix to Part Zero", "First Part ... and Games", " Chapter 7: Playing Several Games at Once", " Chapter 8: Some Games are Already Numbers", " Chapter 9: On Games and Numbers", " Chapter 10: Simplifying Games", " Chapter 11: Impartial Games and the Game of Nim", " Chapter 12: How to Lose when you Must", " Chapter 13: Animated Functions, Welter's Game and Hackenbush Unrestrained", " Chapter 14: How to Play Several Games at Once in a Dozen Different Ways", " Chapter 15: Ups, Downs and Bynumbers", " Chapter 16: The Long and the Short and the Small", "Appendix", "Index".

"Preface" handler om ???
"Zeroth Part ... On Numbers" handler om ???
" Chapter 0: All Numbers Great and Small" handler om ???
" Chapter 1: The Class No is a Field" handler om ???
" Chapter 2: The Real and Ordinal Numbers" handler om ???
" Chapter 3: The Structure of the General Number" handler om ???
" Chapter 4: Algebra and Analysis of Numbers" handler om ???
" Chapter 5: Number Theory in the Land of Oz" handler om ???
" Chapter 6: The Curious Field On2" handler om ???
" Appendix to Part Zero" handler om ???
"First Part ... and Games" handler om ???
" Chapter 7: Playing Several Games at Once" handler om ???
" Chapter 8: Some Games are Already Numbers" handler om ???
" Chapter 9: On Games and Numbers" handler om ???
" Chapter 10: Simplifying Games" handler om ???
" Chapter 11: Impartial Games and the Game of Nim" handler om ???
" Chapter 12: How to Lose when you Must" handler om ???
" Chapter 13: Animated Functions, Welter's Game and Hackenbush Unrestrained" handler om ???
" Chapter 14: How to Play Several Games at Once in a Dozen Different Ways" handler om ???
" Chapter 15: Ups, Downs and Bynumbers" handler om ???
" Chapter 16: The Long and the Short and the Small" handler om ???
"Appendix" handler om ???
"Index" handler om ???

Conway, alias J. H. Conway alias John Horton Conway, er genial. Denne gamle bog fra 1976 er historien om hvordan man kan definere tal på en måde, så snart sagt alle mulige udvidelser springer frem af panden af sig selv. Surreal Numbers er et forsøg fra Donald Knuth på at lave en lille roman ud af disse tal.

Theorem 100: This is the last theorem in this book. (The proof is obvious).… (más)

Have you ever exploited symmetry in your own designs, proofs, or organizational solutions? Of course the answer is "yes": symmetry is one of the deepest principles of human mind. In the form of conservation laws, it literally provides the basis for much of modern physics. But don't worry, this book is not about physics! It is a heavily illustrated book about the math behind symmetry.

Conway has created a wonderful example of graphical clarity and geometric thinking about regular patterns and tilings. Don't be put off by his coinage of goofy terms; he successfully presents deep mathematics via purely visual proofs. Furthermore, he turns the old way of presenting symmetry on its head, starting with geometry and topology, and only later addressing group theory.

This book is highly recommended to anyone who is interested in how symmetry works. Some understanding of group theory would be helpful, but the graphics alone make perusing the book worthwhile.… (más)