1,595 research outputs found
Popularizing mathematics: from eight to infinity
It is rare to succeed in getting mathematics into ordinary conversation
without meeting all kinds of reservations. In order to raise public awareness
of mathematics effectively, it is necessary to modify such attitudes. In this
paper, we point to some possible topics for general mathematical conversation
A Note on Powers in Finite Fields
The study of solutions to polynomial equations over finite fields has a long
history in mathematics and is an interesting area of contemporary research. In
recent years the subject has found important applications in the modelling of
problems from applied mathematical fields such as signal analysis, system
theory, coding theory and cryptology. In this connection it is of interest to
know criteria for the existence of squares and other powers in arbitrary finite
fields. Making good use of polynomial division in polynomial rings over finite
fields, we have examined a classical criterion of Euler for squares in odd
prime fields, giving it a formulation which is apt for generalization to
arbitrary finite fields and powers. Our proof uses algebra rather than
classical number theory, which makes it convenient when presenting basic
methods of applied algebra in the classroom.Comment: 4 page
Circle maps and C*-algebras
We consider a construction of C*-algebras from continuous piecewise monotone
maps on the circle which generalizes the crossed product construction for
homeomorphisms and more generally the construction of Renault, Deaconu and
Anantharaman-Delaroche for local homeomorphisms. Assuming that the map is
surjective and not locally injective we give necessary and sufficient
conditions for the simplicity of the C*-algebra and show that it is then a
Kirchberg algebra. We provide tools for the calculation of the K-theory groups
and turn them into an algorithmic method for Markov maps.Comment: 37 pages, 4 figure
Fathers and Sons:an attempt to make some loving sense of Johannes de Silentio’s Fear and Trembling
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