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The Raven's Hat

Fallen Pictures, Rising Sequences, and Other Mathematical Games

Author Jonas Peters, Nicolai Meinshausen
Illustrated by Malte Meinshausen
Ebook (EPUB)
The MIT Press
On sale Feb 02, 2021 | 192 Pages | 9780262362689
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Games that show how mathematics can solve the apparently unsolvable.

This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.
Choice 2021 Outstanding Academic Title

“A book of intriguing problems that are simple to state and yet seem impossible to solve. Each problem has been carefully chosen to illustrate an important mathematical concept. The lucid explanations provide aha moments that connect the problems to key ideas in a wide variety of undergraduate courses. A wonderful book for someone who likes mathematics and likes to be challenged!” —Chris Bernhardt, author of Quantum Computing for Everyone
 
“This is a fantastic book! It’s full of clever and carefully constructed puzzles that will entertain any mathematically curious reader, from novice to expert.”
—Richard J. Samworth, Professor of Statistical Science, University of Cambridge
Jonas Peters is Professor of Statistics at the University of Copenhagen. Nicolai Meinshausen is Professor of Statistics at ETH (Swiss Federal Institute of Technology) in Zurich.
Jonas Peters View titles by Jonas Peters
Nicolai Meinshausen View titles by Nicolai Meinshausen
Malte Meinshausen View titles by Malte Meinshausen
1. HAT COLORS AND HAMMING CODES 1
2. TWENTY BOXES AND PERMUTATIONS 17
3. THE DOVETAIL TRICK AND RISING SEQUENCES 33
4. ANIMAL STICKERS AND CYCLIC GROUPS 55
5. OPERA SINGERS AND INFORMATION THEORY 73
6. ANIMAL MATCHING AND PROJECTIVE GEOMETRY 93 6
7. THE EARTH AND AN EIGENVALUE 109
8. THE FALLEN PICTURE AND ALGEBRAIC TOPOLOGY 123 
A. WHAT DO WE MEAN WHEN WE WRITE …? 139
B. WHAT IS … 143 
C. CHAPTER-SPECIFIC DETAILS 157 
REFERENCES 171
INDEX 175

About

Games that show how mathematics can solve the apparently unsolvable.

This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.

Reviews

Choice 2021 Outstanding Academic Title

“A book of intriguing problems that are simple to state and yet seem impossible to solve. Each problem has been carefully chosen to illustrate an important mathematical concept. The lucid explanations provide aha moments that connect the problems to key ideas in a wide variety of undergraduate courses. A wonderful book for someone who likes mathematics and likes to be challenged!” —Chris Bernhardt, author of Quantum Computing for Everyone
 
“This is a fantastic book! It’s full of clever and carefully constructed puzzles that will entertain any mathematically curious reader, from novice to expert.”
—Richard J. Samworth, Professor of Statistical Science, University of Cambridge

Author

Jonas Peters is Professor of Statistics at the University of Copenhagen. Nicolai Meinshausen is Professor of Statistics at ETH (Swiss Federal Institute of Technology) in Zurich.
Jonas Peters View titles by Jonas Peters
Nicolai Meinshausen View titles by Nicolai Meinshausen
Malte Meinshausen View titles by Malte Meinshausen

Table of Contents

1. HAT COLORS AND HAMMING CODES 1
2. TWENTY BOXES AND PERMUTATIONS 17
3. THE DOVETAIL TRICK AND RISING SEQUENCES 33
4. ANIMAL STICKERS AND CYCLIC GROUPS 55
5. OPERA SINGERS AND INFORMATION THEORY 73
6. ANIMAL MATCHING AND PROJECTIVE GEOMETRY 93 6
7. THE EARTH AND AN EIGENVALUE 109
8. THE FALLEN PICTURE AND ALGEBRAIC TOPOLOGY 123 
A. WHAT DO WE MEAN WHEN WE WRITE …? 139
B. WHAT IS … 143 
C. CHAPTER-SPECIFIC DETAILS 157 
REFERENCES 171
INDEX 175

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