Natural Resources 101
ABSTRACT: The US Constitution assigns to each state a number of representatives (in the House) proportional to its population. Thus, if the US population is N, a state's population is p, and the total number of representatives (currently 435) is h, then the number of representatives assigned to that state is (p/N)h. The main problem for this simple formula is that (p/N)h is usually not a whole number, whereas we do not elect fractional representatives. So there is need for some kind of round-off convention. There are several distinct ways of doing this, and they confer very different kinds of advantages to different kinds of states in this very high stakes decision making. The debate over different models began with Jefferson, Hamilton, and Adams, and it has continued up to recent times. Professor Bass will offer a historical account of this problem, pointing out some of the mathematical issues and paradoxes involved.
ABSTRACT: In a finite connected graph, X, we consider closed edge-paths, without backtracking, and which are prime (not a repetition of such a path). There are only finitely many of these of a given length, and so we can "count" them using a suitable generating function, expressed as a power series. It is quite remarkable that this power series turns out in fact to be a polynomial, one whose roots capture significant geometric information about the graph. In this talk, Professor Bass will give a more or less self contained exposition of the formulation and proof of this theorem, and a few applications. The presentation should be accessible with only undergraduate mathematics (calculus and linear algebra).
*About Hyman Bass:
Hyman Bass is the Roger Lyndon Collegiate Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.
Prior to 1999 he was Adrain Professor of Mathematics at Columbia University. His mathematical research publications cover broad areas of algebra with connections to geometry, topology, and number theory. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Bass is president of the American Mathematical Society. He recently chaired the Mathematical Sciences Education Board at the National Research Council, and the Committee on Education of the American Mathematical Society; he is currently President of the International Commission on Mathematics Instruction.
During the past five years he has been collaborating with
Deborah Ball and her research group at the University of Michigan on the
mathematical knowledge and resources entailed in the teaching of mathematics
at the elementary level. He has helped to build bridges between diverse
professional communities, especially between mathematicians and other stakeholders
involved in mathematics education.