MTU Cork Library Catalogue

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The geometry of numbers / C.D. Olds, Anneli Lax and Giuliana P. Davidoff.

By: Olds, C. D. (Carl Douglas), 1912-.
Contributor(s): Lax, Anneli | Davidoff, Giuliana P.
Material type: materialTypeLabelBookSeries: Anneli Lax new mathematical library ; vol.41.Publisher: Washington, DC : Mathematical Association of America, 2000Description: xvi, 174 p. : ill. ; 23 cm + pbk.ISBN: 0883856433.Subject(s): Geometry of numbersDDC classification: 512.7
Contents:
Part I: Lattice points and number theory -- Lattice points and straight lines -- Counting Lattice points -- Lattice points and the area of polygons -- Lattice points in circles -- Part II: An introduction to the geometry of numbers -- Minkowski's fundamental theorem -- Applications of Minkowski's theorems -- Linear transformations and integral lattices -- Geometric interpretations of quadratic forms -- A new principle on the geometry of numbers -- A Minkowski theorem (optional).
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 512.7 (Browse shelf(Opens below)) 1 Available 00113689
General Lending MTU Bishopstown Library Lending 512.7 (Browse shelf(Opens below)) 1 Available 00082834
Total holds: 0

Enhanced descriptions from Syndetics:

This is a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice points on lines, circles and inside simple polygons in the plane. A minimum of mathematical expertise is required beyond an acquaintance with elementary geometry. The authors gradually lead up to the theorems of Minkowski and others who succeeded him. On the way the reader will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres.

Bibliography: (pages 169-171) and index.

Part I: Lattice points and number theory -- Lattice points and straight lines -- Counting Lattice points -- Lattice points and the area of polygons -- Lattice points in circles -- Part II: An introduction to the geometry of numbers -- Minkowski's fundamental theorem -- Applications of Minkowski's theorems -- Linear transformations and integral lattices -- Geometric interpretations of quadratic forms -- A new principle on the geometry of numbers -- A Minkowski theorem (optional).

Table of contents provided by Syndetics

  • 1 Geometry and algebra
  • 2 Trigonometry, calculus and analytic geometry
  • 3 Inequalities
  • 4 Integer sums
  • 5 Sequences and series

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