By Timothy Y. Chow, Daniel C. Isaksen

This quantity includes the court cases of a convention held in July, 2007 on the college of Minnesota, Duluth, in honor of Joseph A. Gallian's sixty fifth birthday and the thirtieth anniversary of the Duluth examine event for Undergraduates. in accordance with Gallian's awesome expository skill and huge mathematical pursuits, the articles during this quantity span a wide selection of mathematical issues, together with algebraic topology, combinatorics, layout idea, forcing, video game conception, geometry, graph thought, team idea, optimization, and likelihood. a few of the papers are simply expository whereas others are examine articles. The papers are meant to be available to a common arithmetic viewers, together with first-year or second-year graduate scholars. This quantity may be specifically valuable for mathematicians looking a brand new study region, in addition to these trying to enhance themselves and their study courses through studying approximately difficulties and strategies utilized in different components of arithmetic

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**Extra resources for Communicating Mathematics: A Conference in Honor of Joseph A. Gallian's 65th Birthday, July 16-19, 2007, University of Minnesota, Duluth, Minnesota**

**Sample text**

The reader may still be bothered by the lingering feeling that the point of introducing ZFC is to “make set theory rigorous” or to examine the foundations of mathematics. While it is true that ZFC can be used as a tool for such philosophical investigations, we do not do so in this paper. Instead, we take for granted that ordinary mathematical reasoning—including reasoning about sets—is perfectly valid and does not suddenly become invalid when the object of study is ZFC. That is, we approach the study of ZFC and its models in the same way that one approaches the study of any other mathematical subject.

Math. 81 (1974), 315–329. [6] Paul J. Cohen, Set Theory and the Continuum Hypothesis, Addison-Wesley, 1966. [7] Paul J. Cohen, The discovery of forcing, Rocky Mountain J. Math. 32 (2002), 1071–1100. 2279. [9] Jan Kraj´ıˇ cek, Bounded Arithmetic, Propositional Logic, and Complexity Theory, Cambridge University Press, 1995. [10] Kenneth Kunen, Set Theory: An Introduction to Independence Proofs, North Holland, 1983. , A. K. Peters, 1998. [12] Saunders Mac Lane and Ieke Moerdijk, Sheaves in Geometry and Logic, Springer-Verlag, 1992.

I believe that it is an open exposition problem to explain forcing. Current treatments allow readers to verify the truth of the basic theorems, and to progress fairly rapidly to the point where they can use forcing to prove their own independence results (see [2] for a particularly nice explanation of how to use forcing as a 2000 Mathematics Subject Classiﬁcation. Primary 03E35; secondary 03E40, 00-01. c 0000 (copyright Society holder) c 2009 American Mathematical 1 25 26 2 TIMOTHY Y. CHOW black box to turn independence questions into concrete combinatorial problems).