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The Pleasures of Counting

Book Description

What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. I: The uses of abstraction
    1. 1. Unfeeling statistics
      1. 1.1 Snow on cholera
      2. 1.2 An altar of pedantry
    2. 2. Prelude to a battle
      1. 2.1 The first great submarine war
      2. 2.2 The coming of convoy
      3. 2.3 The second submarine war
    3. 3. Blackett
      1. 3.1 Blackett at Jutland
      2. 3.2 Tizard and radar
      3. 3.3 The shortest wavelength will win the war
      4. 3.4 Blackett’s circus
    4. 4. Aircraft versus submarine
      1. 4.1 Twenty-five seconds
      2. 4.2 Let’s try the slide-rule for a change
      3. 4.3 The area rule
      4. 4.4 What can we learn?
      5. 4.5 Some problems
  8. II: Meditations on measurement
    1. 5. Biology in a darkened room
      1. 5.1 Galileo on falling bodies
      2. 5.2 The long and the short and the tall
    2. 6. Physics in a darkened room
      1. 6.1 The pyramid inch
      2. 6.2 A different age
    3. 7. Subtle is the Lord
      1. 7.1 Galileo and Einstein
      2. 7.2 The Lorentz transformation
      3. 7.3 What happened next?
      4. 7.4 Does the earth rotate?
    4. 8. A Quaker mathematician
      1. 8.1 Richardson
      2. 8.2 Richardson’s deferred approach to the limit
      3. 8.3 Does the wind have a velocity?
      4. 8.4 The four-thirds rule
    5. 9. Richardson on war
      1. 9.1 Arms and insecurity
      2. 9.2 Statistics of deadly quarrels
      3. 9.3 Richardson on frontiers
      4. 9.4 Why does a tree look like a tree?
  9. III: The pleasures of computation
    1. 10. Some classic algorithms
      1. 10.1 These twice five figures
      2. 10.2 The good old days
      3. 10.3 Euclid’s algorithm
      4. 10.4 How to count rabbits
    2. 11. Some modern algorithms
      1. 11.1 The railroad problem
      2. 11.2 Braess’s paradox
      3. 11.3 Finding the largest
      4. 11.4 How fast can we sort?
      5. 11.5 A letter of Lord Chesterfield
    3. 12. Deeper matters
      1. 12.1 How safe?
      2. 12.2 The problems of infinity
      3. 12.3 Turing’s theorem
  10. IV: Enigma variations
    1. 13. Enigma
      1. 13.1 Simple codes
      2. 13.2 Simple Enigmas
      3. 13.3 The plugboard
    2. 14. The Poles
      1. 14.1 The plugboard does not hide all finger-prints
      2. 14.2 Beautiful Polish females
      3. 14.3 Passing the torch
    3. 15. Bletchley
      1. 15.1 The Turing bombes
      2. 15.2 The bombes at work
      3. 15.3 SHARK
    4. 16. Echoes
      1. 16.1 Hard problems
      2. 16.2 Shannon’s theorem
  11. V: The pleasures of thought
    1. 17. Time and chance
      1. 17.1 Why are we not all called Smith?
      2. 17.2 Growth and decay
      3. 17.3 Species and speculation
      4. 17.4 Of microorganisms and men
    2. 18. Two mathematics lessons
      1. 18.1 A Greek mathematics lesson
      2. 18.2 A modern mathematics lesson I
      3. 18.3 A modern mathematics lesson II
      4. 18.4 A modern mathematics lesson III
      5. 18.5 A modern mathematics lesson IV
      6. 18.6 Epilogue
    3. 19. Last thoughts
      1. 19.1 A mathematical career
      2. 19.2 The pleasures of counting
  12. Appendix 1: Further reading
    1. A1.1 Some interesting books
    2. A1.2 Some hard but interesting books
  13. Appendix 2: Some notations
  14. Appendix 3: Sources
  15. Bibliography
  16. Index
  17. Acknowledgements