A Mathematician's Miscellany by JE Littlewood PDF

By JE Littlewood

CONTENTS
========

MATHEMATICS WITH minimal uncooked MATERIAL
FROM THE MATHEMATICAL TRIPOS
CROSS-PURPOSES, subconscious ASSUMPTIONS, HOWLERS, MISPRINTS, ETC.
THE ZOO
BALLISTICS
THE obstacle OF likelihood THEORY
FROM FERMAT'S final THEOREM TO THE ABOLITION OF CAPITAL PUNISHMENT
A MATHEMATICAL EDUCATION
REVIEW OF RAMANUJAN'S amassed PAPERS
THREE REVIEWS
NEWTON AND THE allure OF A SPHERE
LARGE NUMBERS
THE DISCOVERY OF NEPTUNE
THE ADAMS-AIRY AFFAIR
'LION AND guy'

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Told impossible mathematically is a mathematical symbol name of a ' sum-class why : ' ; A * ? ) A recent (published) paper had near the beginning the passage the object of this paper is to prove [something * very important] '. It transpired with great difficulty, and not till near the end, that the object was an unachieved ' ' one. ' 2 From an ' book on Astronomy. ' complex of horrors repays analysis. Roughly spirals illegitimate combination of the correct due to the and the lines inpresence bright [This rich it ' an is show correct absence ' .

Is the probSubject always to E's holding no ace, ability of holding S ace only, divided by the probability of his holding at least S ace is the probability of his Iq W ; holding 1 at least 1 1 ~p _ 1 q \p by the probability of his holding 2nd numerator is 4 times the 1st. Hence ace only, divided ace. The (probability of 8 ace at least) 4- -f (probability of C ace at least) (probability of 1 ace at least) Since the contingencies in the numerator overlap, this ratio greater than 1. is A MATHEMATICIAN'S 28 * MISCELLANY ' ' W has an The fallacy p=q arises by the argument But there is no such we may suppose it is the spade ace if has more than one the informer has thing as it it The situation becomes clearer to choose one to be when a hand of 2 cards is dealt from the 3 cards, S ace, H ace, C 2.

17). The time be equated to the corresponding ch}^ for p. We are to take the FIG. 17 tend to (A *0 is not necessary) (or r) and means inter alia that we can ignore all terms involving Then approximately limit as this 2 /A . - ju, ; At time r we have, writing y, a for cos n 4 4 (<~f a), sin ~~ w rJ n) r n y by straightforward there is The no terra in r right hand calculation, ignoring 3 . side is r~C\ in to be equal to fVir> lirnif !

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A Mathematician's Miscellany by JE Littlewood


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