Allison M. Pacelli

Mathematics and Politics: Strategy, Voting, Power and Proof.

This book teaches humanities majors the accessibility and beauty of discrete and deductive mathematics. It assumes no prior knowledge of either college-level mathematics or political science, and could be offered at the freshman or sophomore level. The book devotes one chapter each to a model of escalation, game-theoretic models of international conflict, political power, and social choice. The material progresses in level of difficulty as the book progresses.

Class groups of imaginary function fields: The inert case

Let F be a finite field and T a transcendental element over F. An imaginary function field is defined to be a function field such that the prime at infinity is inert or totally ramified. For the totally imaginary case, in a recent paper the second author constructed infinitely many function fields of any fixed degree over F(T) in which the prime at infinity is totally ramified and with ideal class numbers divisible by any given positive integer greater than 1. In this paper, we complete the imaginary case by proving the corresponding result for function fields in which the prime at infinity is inert. Specifically, we show that for relatively prime integers m and n, there are infinitely many function fields K of fixed degree m such that the class group of K contains a subgroup isomorphic to (Z/nZ) m-1 and the prime at infinity is inert.

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by n

In this paper,wefindalowerbound onthe numberofcyclic functionfields ofprime degree l whose class numbers are divisible by a given integer n. This generalizes a previous result of D. Cardon andR.Murtywhichgivesalowerboundonthenumberofquadratic functionfieldswithclassnumbers divisible by n.