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Michael Vogelius, Director of the Division of Mathematical Sciences, National Science FoundationMichael Vogelius, Director of the Division of Mathematical Sciences, National Science FoundationGore 104Small inhomogeneities and uniform expansions applications to enhanced detectability and approximate invisibility. <br><br> In this talk I shall give a survey of some older results and a discussion of some newer results concerning the perturbative effects of small inhomogeneities on the electromagnetic fields. I shall relate these results to enhanced imaging as well as to approximate cloaking, the latter by use of so-called (singular) mapping techniques. 3/17/2017 7:30:00 PM3/17/2017 9:30:00 PMFalse
Jungeun ParkJungeun ParkGore 104Examining Teaching and Learning of Calculus through Student and Expert Discourse </br></br> This talk will take a comprehensive look at how the derivative is addressed in University calculus courses by examining how it is presented and discussed by textbooks, instructors, and students. Taking a Sfardian approach, we will examine how words and visuals are used by these three different groups when discusisng the derivative. This will give us a detailed view of how students think about the derivative and how this differs from how experts discuss the concept. Furthermore, our analysis will show that instructors and textbooks do not explicitly address mathematical aspects of the derivative that students have difficulty understanding. For example, we will see that students have difficulties appreciating the relation between the derivative at a point and the derivative as a function on an interval while instructors and textbooks often leave the transition implicit and do not provide visuals to help students think about the relation. </br></br> Reception to follow in Ewing 536 at 4:30 p.m.2/17/2017 8:30:00 PM2/17/2017 9:30:00 PMFalse
David Bellamy, University of DelawareDavid Bellamy, University of Delaware103 Gore Hall <div dir="LTR"><font color="#282828" face="Arial">Title:</font><font color="#282828" face="Arial"> </font><font color="#282828" face="Arial">Tree-Likeness and the Fixed Point Property</font><font color="#282828" face="Arial"> </font></div> <div dir="LTR"><br> <font color="#282828" face="Arial">Abstract:</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">I am going to discuss briefly the historical context of the relationship between tree-likeness of compact metric continua and the fixed point property. This was mostly attempts to prove the conjecture that tree-like continua have the fixed point property. The beginnings go back to the 1930's, at least.Several special cases were proven over the years, narrowing the possibilities for what a counterexample would have to look like.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">Then I will discuss, in outline at least, the first counterexample to this conjecture which I constructed in the late 1970's. Pictures, which may be helpful, will be included.</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">If time and audience interest permit, I will describe a little of what others have done since.</font><font color="#282828" face="Arial"> </font></div> 12/2/2016 8:30:00 PM12/2/2016 9:30:00 PMFalse
Avi Wigderson Professor, School of Mathematics, Institute for Advanced Study, Princeton Avi Wigderson Professor, School of Mathematics, Institute for Advanced Study, Princeton 103 Gore Hall <div dir="LTR"><font color="#282828" face="Arial">Title: Randomness</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">Abstract:</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">Is the universe inherently deterministic or probabilistic? Perhaps more</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">importantly - can we tell the difference between the two?</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">Humanity has pondered the meaning and utility of randomness for millennia.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">There is a remarkable variety of ways in which we utilize perfect coin</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">tosses to our advantage: in statistics, cryptography, game theory,</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">algorithms, gambling... Indeed, randomness seems indispensable! Which of</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">these applications survive if the universe had no randomness in it at all?</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">Which of them survive if only poor quality randomness is available, e.g.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">that arises from "unpredictable" phenomena like the weather or the stock</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">market?</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">A computational theory of randomness, developed in the past three decades,</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">reveals (perhaps counter-intuitively) that very little is lost in such</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">deterministic or weakly random worlds. In the talk I'll explain the main</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">ideas and results of this theory.</font><font color="#282828" face="Arial"> </font><br> <br> <font color="#282828" face="Arial">The talk is aimed at a general scientific audience.</font><font color="#282828" face="Arial"> </font></div> 10/21/2016 7:30:00 PM10/21/2016 8:30:00 PMFalse

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