Maa Seaway Fall Meeting Suny Plattsburgh , 2010

S MAA SEAWAY FALL MEETING SUNY PLATTSBURGH, 2010 Friday night speaker Andrew Granville, University of Montreal The anatomy of integers and permutations Different mathematical subjects have different basic objects -for example, integers for numbers, permutations in combinatorics and group theory. At first sight these objects come from such different worlds that they seem to have very little in common -How can one even begin to compare them? In this talk we will show how, with a little detective work, we can find ways to compare and contrast, by studying their "anatomy", and we will try to express this out of the usual context. Saturday morning speakers 1. Frank Swenton, Middlebury College Animating Convergence The concept of convergence is the axis about which all of calculus spins the root of every other major definition, concept, and theorem in the subject. Unfortunately, the limitations of the chalkboard and static printed media have hindered the presentation of this very dynamic concept, forcing us all too often to suppress its subtleties and speak instead merely of limits. In this talk, we‟ll take a different approach to the concept of convergence, eschewing the limit and introducing a set of very visual objects of study that properly display the full logic of the concept. We‟ll be introduced to an array of interactive Flash animations that provide us with the opportunity to actively explore their every detail at our own pace, and finally, we‟ll move on to see the appearance of these objects throughout the calculus curriculum, from limits both of functions and of sequences to the derivative and the definite integral. 2. Polya Lecture: Louis Kauffman, University of Illinois at Chicago Introduction to Knot Theory This talk is an introduction to knots. Knot theory is a branch of topology that studies the way one topological space can be placed inside another topological space. Thus knot theory is a study of the relativity of form. The simplest and most vivid example is classical knot theory where we study how (usually) closed loops of rope can be placed in three dimensional space. A loop all by itself is very simple, just a circle or a tube. But such an entity can assume infinitely many knotted forms in the way it can be embedded in three dimensional space. This talk will discuss how we make mathematical models for knots and links in order to tell them apart, and how these models lead to relationships with molecular biology, physics and many other areas of science and mathematics. 3. Randolph Lecture: Kate Fowler, Clarkson University K12 Educational Outreach in Mathematics: What? Why? How! WOW! Outreach initiatives are examples of using government funds to create programs aimed at cultivating teacher leaders and increasing K-12 student achievement. Funding is especially available to support STEM (Science, Technology, Engineering, and Mathematics) disciplines by forming collaborations between universities and local school districts. As stated by the many funding agencies, our future workforce needs to be able to solve problems that are not yet even imaginable. In this talk we give motivation and an overview of some outreach activities that are focused on professional development and are student-driven. We discuss not only content, but challenges in recruiting help and implementing practices in the classroom. Ultimately, we hope to show that these activities enhance not hinder meeting state and national standards in mathematics while engaging students in integrated STEM curriculum. Saturday afternoon speakers 1. Anurag Agarwal, RIT Representation Numbers and Prague Dimension of Graphs For a finite graph G with r vertices, we say it has a representation modulo N if its vertices can be assigned distinct labels from the set {0,1,2,...,n-1} so that two vertices are adjacent if and only if the difference in their labels is relatively prime to N. The smallest such number N is called the representation number of the graph. We will discuss the representation numbers for some known graphs and show how graph theory, algebra and number theory combine in solving this problem for some graphs. 2. Lan Cheng, SUNY Fredonia & Xuguang Sheng, American University Combinations of “Combinations of Pvalues” We investigate the impact of uncertainty over the number of false null hypotheses on commonly used p-value combination methods. Some methods, for example, Tippett‟s and Simes‟ methods, are powerful when there is only one or a few false individual null hypotheses. Others, such as Fisher‟s and Stouffer‟s methods, are powerful when there are many false null hypotheses. Since it is a priori unknown whether a few or almost all individual null hypotheses are false, no uniformly most powerful p-value combination method exists. We develop a combination of “combinations of p-values” (CCP) test that maintains good power properties in the presence of such an uncertainty, while at the same time controls type I error. Our test is based on a simple union of rejections decision rule, whereas the joint null hypothesis is rejected at the significance level α if at least one of the two pvalue combination methods yields a rejection at the level γ. The value of γ depends on the significance level, sample size and the correlation of two pvalue combination methods. The proposed test has the added advantage of being easy to carry out.