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Volume 2 - 01 January 1959

Contents

Page 2 of 4

Research Article

  • A Property of Convex Pseudopolyhedra

  • Z.A. Melzak
  • Published online by Cambridge University Press:
    20 November 2018, pp. 31-32
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  • In this note we prove one theorem and make a few conjectures, all of which are connected with the following problem raised by S. Mazur [l]: does there exist a closed convex surface whose plane sections give all plane closed convex curves, up to affinities? For our purposes we define a convex pseudopolyhedron to be the closed convex hull of a countable bounded nonplanar sequence of points in E3 with exactly one limit point.

Notes on Number Theory I

  • On the Product of the Primes not Exceeding n

  • Leo Moser
  • Published online by Cambridge University Press:
    20 November 2018, pp. 119-121
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  • One of the most elegant results of the elementary theory of the distribution of primes is that

    1

    where the product runs over primes. A very simple proof of (1) has recently been given by Erdös and Kalmar [1], [2].

Research Article

  • Outline of an Introduction to Mathematical Logic IV

  • Abraham Robinson
  • Published online by Cambridge University Press:
    20 November 2018, pp. 33-42
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  • The extended completeness theorem of the predicate calculas of the first order. In section 12, we developed a deductive theory of the first order predicate calculus, while in section II we dealt with the semantic theory of that calculus. We now have to consider the connection between these two theories. We recall that a sentence X can be satisfied by a structure M only if X is defined in M. Given a sentence X (a set of sentences K) we shall say that the structure M is a model of X (of K) if X is (all the sentences of K are) satisfied by M.

Other

  • Problems for Solution

  • Published online by Cambridge University Press:
    01 April 2019, pp. 122-123
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Notes

  • On the Discriminants of a Bilinear Form

  • Wild Jonathan, Prince Albert, Sask
  • Published online by Cambridge University Press:
    20 November 2018, pp. 46-48
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Solutions

  • Solution by the proposers

  • Published online by Cambridge University Press:
    01 April 2019, pp. 44-45
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Other

  • Solutions

  • Published online by Cambridge University Press:
    01 April 2019, pp. 123-124
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Problems for Solution

  • P 14.

  • L. Moser
  • Published online by Cambridge University Press:
    01 April 2019, pp. 43-44
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Research Article

  • The Half-Baked Method for Cooking of Experimental Data

  • Ralph G. Stanton
  • Published online by Cambridge University Press:
    20 November 2018, pp. 125-131
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  • Students in Mathematics and Physics courses are commonly exposed to a method of treating data known as the "half-table method". The method is presented with encomiums by R. C. Dearle [1] and by Lucius Tuttle and John Satterly [2]. It can best be described by an illustration; since the determination of the period of a pendulum is one of the experiments most commonly used (and occurs in both [1] and [2]), let us borrow a set of data from [2] and some explanatory text from [1].

Problems for Solution

  • P 12.

  • P. Scherk
  • Published online by Cambridge University Press:
    01 April 2019, p. 43
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Book Reviews

Solutions

  • Solution by the proposer

  • Published online by Cambridge University Press:
    01 April 2019, pp. 45-46
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Book Reviews

Problems for Solution

  • P 13.

  • H. Helfenstein
  • Published online by Cambridge University Press:
    01 April 2019, p. 43
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Solutions

  • P 2.

  • J. C. Hayes, P. Scherk
  • Published online by Cambridge University Press:
    01 April 2019, p. 44
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Book Reviews

  • Circles, by D. Pedoe. Pergamon Press, New York-London-Paris, 1957. x + 78 pages.

  • Hans Zassenhaus
  • Published online by Cambridge University Press:
    01 April 2019, p. 134
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Problems for Solution

  • P 11.

  • P. Erdös, L. Moser
  • Published online by Cambridge University Press:
    01 April 2019, p. 43
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Solutions

  • P 3.

  • P. Scherk
  • Published online by Cambridge University Press:
    01 April 2019, p. 45
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Page 2 of 4