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A Mathematician's Miscellany - download pdf or read online

By JE Littlewood

CONTENTS
========

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

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Extra resources for A Mathematician's Miscellany

Example text

6 In 1930, however, A. S. Besicovitch (Math. Zeit. 27 (1928), 312-320) showed that the answer is zero area (unattained) given an arbitrarily small e the area swept can be less than e. As e tends to the movements of the segment become : 1 In the usual sense : they may have different ages. MATHEMATICS WITH MINIMUM 'RAW MATERIAL' infinitely complicated and infinity in all directions. involve excursions 19 towards Crum's problem. What is the maximum number of convex polyhedra of which every pair have a face (or part of one) in common ?

A very important theorem For a, j3>0 let M a/3 (due to M. Riesz) be the least upper bound as follows. b. for short) of I L(x, y) to 2 a and varying complex complex a for constant = | a; , y v subject 1a Then A log M is a convex function of aft a, j8 (in a, j8>0). convex function of one variable has a graph in which * the wide sense) the arc is below the chord '. With several variables a, j3, the function is to be convex in a (in . a=a . .... For the purpose extended to a form, T for short, which has a different outward appearance and takes on any line I, -f Aja, j8=/?

T thus produces a high-brow result out of nothing we like intoxication of the the experience something early days p== I 1 ' ' ; method of projecting conies into circles. Until lately there was no proof of the theorem that a/5 was not very decidedly difficult. The one I now present is due to G. Thorin ( Convexity Theorems Communications du seminaire maihematique de VUniversite de Lund, 9). b. b. of something subject to a number of independent conditions on the variables we may take the conditions in any order (or functions is simultaneously).

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A Mathematician's Miscellany by JE Littlewood


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