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13 results

  • Point at infinity
  • Niel Shell
  • Journal: Bulletin of the Australian Mathematical Society / Volume 38 / Issue 3 / December 1988
  • Published online by Cambridge University Press: 17 April 2009, pp. 321-323
  • Print publication: December 1988
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    We adjoin a point at infinity to a field with a ring topology and extend the topology by taking complements of bounded sets as neighbourhoods of infinity. We note some elementary relations between the topology on the field and the topology on the field with infinity adjoined.

  • Bounded and relatively bounded sets
  • Niel Shell
  • Journal: Bulletin of the Australian Mathematical Society / Volume 36 / Issue 3 / December 1987
  • Published online by Cambridge University Press: 17 April 2009, pp. 493-498
  • Print publication: December 1987
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    All subsets of a field that are intersections of almost-orders of the field are characterised, and all ring topologies on a field which are not finer than any nontrivial locally bounded ring are characterised.

  • Preface
  • Compiled by Ralph A. Artino, The City College of New York, Anthony M. Gaglione, The U.S. Naval Academy, Niel Shell, The City College of New York
  • Book: The Contest Problem Book IV
  • Published by: Mathematical Association of America
  • Published online: 05 January 2012
  • Print publication: 01 June 1982, pp vii-x
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    Summary

    This volume contains the Annual High School Mathematics Examinations, given 1973 through 1982. It is a continuation of Contest Problem Books I, II, III, published as Volumes 5, 17, and 25 of the New Mathematical Library series and which contain the first twenty-three annual examinations. The Annual High School Mathematics Examinations (AHSME), it is hoped, provide challenging problems which teach, stimulate and provide enjoyment for not only the participants, but also the readers of these volumes.

    All high school students are eligible to participate in the Annual High School Mathematics Examinations. In 1982, over 418,000 students in the United States, Canada, Puerto Rico, Colombia, Jamaica, Australia, Italy, England, Hungary, Ireland, Israel, Finland, Belgium and Luxembourg participated in the examination. It was administered also in many APO/FPO and other schools abroad. Each year a Summary of Results and Awards is sent to all participating high schools (in the United States and Canada). The problems are designed so that they can be solved with a knowledge of only “pre-calculus” mathematics, with emphasis on intermediate algebra and plane geometry. The subject classification at the end of the volume indicates which questions are related to which topics.

    The problems on each examination become progressively more difficult, Between 1973 and 1977, the participants were given eighty minutes to complete the examination, and in subsequent years they were allowed ninety minutes.

The Contest Problem Book IV
  • The Contest Problem Book IV
  • Annual High School Examinations 1973-1982
  • Compiled by Ralph A. Artino, Anthony M. Gaglione, Niel Shell
  • Published by: Mathematical Association of America
  • Published online: 05 January 2012
  • Print publication: 01 June 1982
  • View description
    The Annual High School Mathematics Examination (AHSME) began as a local contest in New York City in 1950. By 1960, 150,000 students throughout the United States and Canada took the AHSME. The 1982 Examination was administered to 418,000 participants in the United States and Canada and to 20,000 students in various countries of other continents. In the United States and Canada, one use of AHSME is to select approximately one hundred participants in the U.S.A. Mathematical Olympiad, and the Olympiads are used in the selection of a student team to represent the United States in the International Mathematical Olympiad. Since the difficulty of problems appearing in the AHSME varies over a wide range, they are a valuable teaching aid for all high school students interested in mathematics.