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Page 2
... Solution to a Nonlinear , Many - Particle System Problem 2. Geometry , Invariant Measures , and Dynamical Systems Poincaré's Proof of the Recurrence Theorem PHYSICS 6 23 33 36 39 52 Problem 3. Random Homeomorphisms Iteration of Maps ...
... Solution to a Nonlinear , Many - Particle System Problem 2. Geometry , Invariant Measures , and Dynamical Systems Poincaré's Proof of the Recurrence Theorem PHYSICS 6 23 33 36 39 52 Problem 3. Random Homeomorphisms Iteration of Maps ...
Page 40
... solution ( Hawkins and Ulam 1944 ) . A lot of algebraic solvent evaporated and left behind an unexpected little crystal of a formula , the sort of outcome that makes you ask why it hadn't been obvious all along . Let f ( x ) be the ...
... solution ( Hawkins and Ulam 1944 ) . A lot of algebraic solvent evaporated and left behind an unexpected little crystal of a formula , the sort of outcome that makes you ask why it hadn't been obvious all along . Let f ( x ) be the ...
Page 44
... solutions by playing the game repeatedly on a high - speed computer . But Monte Carlo is not my topic , except again as it affects my picture of Stan Ulam , teacher . One of the topics we got on to later was a Monte Carlo approach to ...
... solutions by playing the game repeatedly on a high - speed computer . But Monte Carlo is not my topic , except again as it affects my picture of Stan Ulam , teacher . One of the topics we got on to later was a Monte Carlo approach to ...
Page 54
... solutions to the problems , Part II provides a tutorial on that subject , which starts with a bit of his- tory and concludes with several profound and useful theorems . Fortunately Mark Kac and Stan Ulam gave a very insightful summary ...
... solutions to the problems , Part II provides a tutorial on that subject , which starts with a bit of his- tory and concludes with several profound and useful theorems . Fortunately Mark Kac and Stan Ulam gave a very insightful summary ...
Page 55
... solutions . The line segment rotates within the curve , and in each position cuts off half the area and half the perimeter . 153 MAZUR PRIZE : A live goose November 6 , 1936 43 MAZUR PRIZE : One bottle of wine , S. ULAM Definition of a ...
... solutions . The line segment rotates within the curve , and in each position cuts off half the area and half the perimeter . 153 MAZUR PRIZE : A live goose November 6 , 1936 43 MAZUR PRIZE : One bottle of wine , S. ULAM Definition of a ...
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Popular passages
Page 299 - Talibus orabat dictis, arasque tenebat, cum sic orsa loqui vates : ' Sate sanguine divom, 125 Tros Anchisiade, facilis descensus Averno ; noctes atque dies patet atri janua Ditis ; sed revocare gradum superasque evadere ad auras, hoc opus, hie labor est.
Page 231 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.
Page 210 - The low-velocity equation of state for a lattice gas can be written as p - ^p (l - |v2), where p is the pressure, p is the density, and v is the flow speed.
Page 316 - Southeastern Conference on Combinatorics. Graph Theory, and Computing (Florida Atlantic University, Boca Raton, Florida, April 2-6, 1979), 3-18.
Page 121 - He is a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Physical Society and the American Association for the Advancement of Science.
Page 231 - A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws...
Page 224 - Instead, we conclude by remarking that really efficient high-speed computing devices may, in the field of non-linear partial differential equations as well as in many other fields, which are now difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress.
Page 272 - Let us say here that the results of our computations show features which were, from the beginning, surprising to us. Instead of a gradual, continuous flow of energy from the first mode to the higher modes, all of the problems show an entirely different behavior.
Page 58 - That was dramatized by Bertrand, who considered the problem of finding the probability that a chord of a circle chosen "at random" be longer than the side of an equilateral triangle inscribed in the circle.