Read e-book online A Mathematician's Miscellany 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 predicament OF likelihood THEORY
FROM FERMAT'S final THEOREM TO THE ABOLITION OF CAPITAL PUNISHMENT
A MATHEMATICAL EDUCATION
REVIEW OF RAMANUJAN'S accrued 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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Perpendicular 60. My dear Sir, absolutely perpendicular Overhanging 70 65. I read in the proof-sheets of Hardy on Ramanujan ' : as said, each of the positive integers was one of his " '. friends My reaction was, I wonder who said personal that I wish I had ". '. now stands), it was Littlewood who said had was that received the had Hardy [What happened I and it off as and with wrote remark in silence poker face, with habit this on which he a dud. I later taxed Hardy " Well, what is one to do, is one always to be saying replied damned good ?

Let D be any closed bounded domain. Is it the case that T n P converges uniformly into A+ for all FIG. e. T n 5 C A + for n>n (D)) ? Everyone's first guess the yes (and corresponding thing is true in 1 dimensions), is in fact no. For this Miss Cartwright and I but the answer found the example of Fig. 14. ) which leaves the hedgehog (the figure of full lines) invariant as a whole, but transforms each spine into the next one to the right, and further imposes a general contraction of outside points towards the boundary of the hedgehog.

If f'^o(l) the graph y=f'(x) will for some arbitrarily large x have peaks (above or below y=0) enclosing triangles like PQR, the height of P not small, the slopes of PQ, PR not large, and so the area PQR not small. Thenf(Q)f(R) is not small, contradicting /=o(l). This is rigorous (and printable), in the sense that : ' c R Q FIG. 8 symbols no step occurs that is not For myself I think like this both unequivocal and trivial. wherever the subject matter permits. Probably the best of pictorial arguments is a proof of Let f(x) be the fixed point theorem in 1 dimensions in translating into ' ' : continuous and increasing in 0

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A Mathematician's Miscellany by JE Littlewood


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