This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games; chance and choice; where does it end; automatic thinking; two-way stretch; rules of play; an accountant's nightmare; and double talk. Practical examples and problems are featured throughout.
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CHAPTER I MATHEMATICAL GAMES The fascination of ordinary numbers Why fifteen Fellows of the Royal Society? The scale of ten A problem involving ordinary numbers A very long division A much shorter solution of the digital problem "Sixteen months in the year, and their names" "The binary scale, or scale of two" A magic table of numbers The game of Nim As played by an electronic brain against humans The theory behind the game Winning positions in the game Punched cards and automatic rearrangement of twelve cards The twelve-coin problem Can it be done without the use of mathematics? "The ternary scale, or scale of three" A solution of the twelve-coin problem Weighing up to forty pounds with only four weights There is an infinity of prime numbers The square root of two is not a rational number CHAPTER II CHANCE AND CHOICE A coin is spun Dr. Joad and the law of averages Historical background to theory of probability What is random behaviour? Scattering seed at random Urns and dice Addition law of probabilities Multiplication law Errors of mathematicians Eliza Doolittle Odds that a head turns up in tossing a penny A problem of Samuel Pepys Two letters from Isaac Newton to Samuel Pepys Expectation of a prize in a football pool Expectation of eternal bliss The St. Petersburg problem Moral criticism of mathematical results "Buffon's test, using child labour" The courageous Bertrand Anything which can happen will happen Buffon's needle theorem and the evaluation of p The giddy Lazzerini Extra-sensory perception and psycho-kinesis Why does heads turn up when you pray for tails? CHAPTER III WHERE DOES IT END? Is infinity greater than infinity? Can you count? Definition of an infinite class Countable infinities The positive rationals can be counted The decimals greater than zero and less than one cannot be counted A great unsolved problem of mathematics The terrible Cantor CHAPTER IV AUTOMATIC THINKING Classes One class contained in another Syllogisms Socrates was mortal Universal class and null class Some laws are unsatisfactory Writers and Shakespeare Another Lewis Carroll teaser Algebra of classes and propositions "Alice, Brenda, Cissie and Doreen" Who won the scholarship? CHAPTER V TWO-WAY STRETCH Ballon d'essai Rubber-sheet geometry Topological transformation defined Deformations The escape-artist's trick Supplying three houses with main services Is topology worth while? Multiply-connected figures Sphere and torus The Moebius band "Fun with paper, gum and scissors" Rotating ring of tetrahedra Modern art and the Klein bottle Simple polyhedra and Euler's formula The four-colour theorem Can you prove it? Disdainful doggerel CHAPTER VI RULES OF PLAY Laws of addition A double negative gives a positive Additive groups "What every airman knows, or how to add vectors" Rotation is addition Finite groups How to multiply Rings (not of commercial firms) The Pascal triangle The binomial theorem "Perms. and combs., or how to arrange and select" No help with football-pools How to divide Why exclude division by zero? The group postulates Do you put your shirt on before your tie? A plane slides over itself Symmetry investigated Inkblots rationalised Rotational symmetry Ornaments Point-lattices and curtain materials The symmetries in Arabic art CHAPTER VII AN ACCOUNTANT'S NIGHTMARE The gullible Emperor A fable of a slowly but surely divergent series A well-behaved series Can you rub out this line? Decimals which come to an end Those which do not What kind of decimals arise from rational numbers The uniqueness of infinite decimals Irrational numbers The number p Shanks and p A mystic rhyme for p Why should seven suffer? "Sir your superior mathematics" Trouble with series Pinning them down More fuss and bother Safety first Achilles and the tortoise Is he still running? CHAPTER VIII DOUBLE TALK Mathematicians not logical The uncertainty of logic Paradoxes galore Class of all classes paradox A humble mathematician Mathematics not logic Infinite collections of shoes Of socks Can you choose? Intuitionism Law of the excluded middle Right or wrong? Formalist view No neurosis amongst mathematicians CHAPTER IX WHAT IS MATHEMATICS? What mathematicians do International conferences Mathematicians as human beings What mathematics is not Poincaré to the rescue
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Descrizione libro Dover Publications, 2012. Paperback. Condizione libro: New. Codice libro della libreria P110486229491
Descrizione libro Dover Publications, 2012. Paperback. Condizione libro: New. Codice libro della libreria DADAX0486229491
Descrizione libro Condizione libro: Brand New. Book Condition: Brand New. Codice libro della libreria 97804862294921.0