|Friday, Dec. 03
in Room C674
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
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,
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 !
Student Seminar (Please email me to the above address if you wish to come visit us and give a talk).
Contact: Habiba Kadiri (firstname.lastname@example.org)