Cover -- Title -- Copyrights -- Contents -- Preface -- Acknowledgements -- Chapter One: Shannon's Free Lunch -- 1.1 The ISBN Code -- 1.2 Binary Channels -- 1.3 The Hunt for Good Codes -- 1.4 Parity-Check Construction -- 1.5 Decoding a Hamming Code -- 1.6 The Free Lunch Made Precise -- 1.7 Further Reading -- 1.8 Solutions -- Chapter Two: Counting Dots -- 2.1 Introduction -- 2.2 Why Is Pick's Theorem True? -- 2.3 An Interpretation -- 2.4 Pick's Theorem and Arithmetic -- 2.5 Further Reading -- 2.6 Solutions -- Chapter Three: Fermat's Little Theorem and Infinite Decimals -- 3.1 Introduction -- 3.2 The Prime Numbers -- 3.3 Decimal Expansions of Reciprocals of Primes -- 3.4 An Algebraic Description of the Period -- 3.5 The Period Is a Factor of p −1 -- 3.6 Fermat's Little Theorem -- 3.7 Further Reading -- 3.8 Solutions -- Chapter Four: Strange Curves -- 4.1 Introduction -- 4.2 A Curve Constructed Using Tiles -- 4.3 Is the Curve Continuous? -- 4.4 Does the Curve Cover the Square? -- 4.5 Hilbert's Construction and Peano's Original -- 4.6 A Computer Program -- 4.7 A Gothic Frieze -- 4.8 Further Reading -- 4.9 Solutions -- Chapter Five: Shared Birthdays, Normal Bells -- 5.1 Introduction -- 5.2 What Chance of a Match? -- 5.3 How Many Matches? -- 5.4 How Many People Share? -- 5.5 The Bell-Shaped Curve -- 5.6 The Area under a Normal Curve -- 5.7 Further Reading -- 5.8 Solutions -- Chapter Six: Stirling Works -- 6.1 Introduction -- 6.2 A First Estimate for n! -- 6.3 A Second Estimate for n! -- 6.4 A Limiting Ratio -- 6.5 Stirling's Formula -- 6.6 Further Reading -- 6.7 Solutions -- Chapter Seven: Spare Change, Pools of Blood -- 7.1 Introduction -- 7.2 The Coin-Weighing Problem -- 7.3 Back to Blood -- 7.4 The Binary Protocol for a Rare Abnormality -- 7.5 A Refined Binary Protocol -- 7.6 An Efficiency Estimate Using Telephones.

7.7 An Efficiency Estimate for Blood Pooling -- 7.8 A Precise Formula for the Binary Protocol -- 7.9 Further Reading -- 7.10 Solutions -- Chapter Eight: Fibonacci's Rabbits Revisited -- 8.1 Introduction -- 8.2 Fibonacci and the Golden Ratio -- 8.3 The Continued Fraction for the Golden Ratio -- 8.4 Best Approximations and the Fibonacci Hyperbola -- 8.5 Continued Fractions and Matrices -- 8.6 Skipping down the Fibonacci Numbers -- 8.7 The Prime Lucas Numbers -- 8.8 The Trace Problem -- 8.9 Further Reading -- 8.10 Solutions -- Chapter Nine: Chasing the Curve -- 9.1 Introduction -- 9.2 Approximation by Rational Functions -- 9.3 The Tangent -- 9.4 An Integral Formula -- 9.5 The Exponential -- 9.6 The Inverse Tangent -- 9.7 Further Reading -- 9.8 Solutions -- Chapter Ten: Rational and Irrational -- 10.1 Introduction -- 10.2 Fibonacci Revisited -- 10.3 The Square Root of d -- 10.4 The Box Principle -- 10.5 The Numbers e and π -- 10.6 The Irrationality of e -- 10.7 Euler's Argument -- 10.8 The Irrationality of π -- 10.9 Further Reading -- 10.10 Solutions -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- P -- Q -- R -- S -- T -- U -- V -- W.