University of Lethbridge > Faculty of Arts & Science > Mathematics & Computer Science > Research

Mathematics and Computer Science

FALL 2010

Friday, Dec. 03
in Room C674
Tim Trudgian

postdoctoral fellow
Ph.D. 2010, Oxford, UK
Some Mathematics in Music

This talk will explain some of the (elementary) mathematics behind musical harmonics:
why one combination of notes produces a pleasant sound, while another is abominable;
why, in Western music, there are twelve notes in a scale;
and the reasons that instruments can be tuned very accurately ``by ear'' alone.

Mathematics at a level beyond secondary school will not be assumed, nor will any music theory.

Friday, Oct. 29
in Room C674
Stephen Curran

Department of Mathematics
University of Pittsburgh at Johnstown
Johnstown, Pennsylvania, USA
Periodic Points of Continuous Functions

A continuous function f:R->R is said to have a periodic point of period k, if
for some real number x_0, k is the smallest positive integer that gives f^k(x_0)=x_0.

A theorem of Li and Yorke states that if f has a periodic point of period 3, then f has a periodic point of period k for all positive integers k.
A natural question arises: When does the existence of a periodic point of period k imply the existence of a periodic point of period l?
This question was answered by a theorem of Sharkovsky. One can interpret the search for periodic points of any period from the existence of a periodic point of a given period as the search for a closed walk of a given length in a digraph constructed from the function. This leads to a graph-theoretic proof of Sharkovsky's theorem.

Everybody is welcome !

Previous years:
2009-2010 - 2008-2009 - 2007-2008 - 2005 - 2004 - 2003 - 2002 - 2001
Student Seminar (Please email me to the above address if you wish to come visit us and give a talk).

Contact: Habiba Kadiri (