Mathematics Colloquia
Below are the scheduled colloquia for the current semester. In general, the colloquia, seminars, and other talks are always aimed at a wide audience, and undergraduates should consider attending these talks. In particular, these are for anyone interested in mathematics, which includes mathematics undergraduates, graduate students, and faculty.
For details on colloquia from previous semesters, visit our archive.
Organizer(s): Dr. Mahboub Baccouch
Tuesday January 29 2013, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Neal Grandgenett Haddix Community Chair of STEM Education, University of Nebraska at Omaha
Five Minute Challenges for Reinforcing Mathematical Topics
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Sometimes it is nice to do a quick five minute activity to introduce or reinforce mathematical topics in algebra, geometry, probability, statistics, or calculus, as well to illustrate mathematical connections to other disciplines. Simple activities such as envelope cutting, paper folding, yarn knots, and mirror reflections actually have lots of underlying mathematical connections, and can build significant student interest across science, technology, engineering, and mathematics (STEM). This cool math talk will illustrate some of these quick mathematical challenges and strategies, that are useful in a wide range of K16 mathematics courses. Dr. Neal Grandgenett, the Haddix Community Chair of STEM Education at UNO will demonstrate (and distribute) some of these quick five minute challenges to help build student mathematical interest.
Tuesday February 26 2013, 2:30pm - 3:30pm, Location 116 DSC
Karen Rhea, University of Michigan
Student-Centered Coursework
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When thinking about inquiry-based learning (IBL), there are many things to consider: the necessary syllabus of the courses, the expertise and training of instructors, the goals and expectations of the students, and the institution. In this talk, we will explore a class model that has shown to successfully encourage an interactive-engaged classroom. We will discuss how the style is supported and the reasons why we believe that model is an important support for the goals of our courses. This talk is intended for a variety of audiences including pre-service teachers, university instructors (both experienced and novice to IBL), and people interested in learning more about IBL.
Speaker Biography
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Karen Rhea is a • Lecturer Emeritus at the University of Michigan and she was named the Patricia Shure Collegiate Lecturer in 2012 for her contributions to U of M education. In 2011, she was the recipient of the MAA’s Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics for her contributions to changes in the calculus curriculum nationally and for her work developing other outstanding teachers. In 2010 she was the recipient of the Matthews Underclass Teaching Award from the College of Literature, Science, and Arts for her distinctive contribution to teaching in courses in first- or second-year level math courses and her enthusiasm and dedication to undergraduate education
Friday March 8 2013, 2:30pm - 3:30pm, Location 116 DSC
Dr. George Avalos, Professor, University of Nebraska-Lincoln
Concerning Rational Decay Properties of Certain Coupled PDE Systems
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In this talk, we shall demonstrate how delicate frequency domain relations and estimates, derived for certain coupled systems of partial differential equation models (PDE's), may be exploited so as to establish results of uniform and rational decay. In particular, our focus will be upon decay properties of coupled PDE systems of different characteristics; e.g., hyperbolic versus parabolic characteristics. For such PDE systems of contrasting dynamics, the attainment of explicit decay rates is known to be a difficult problem, inasmuch as there has not been an established methodology to handle hyperbolic-parabolic systems. For uncoupled wave equations or uncoupled heat equations, there are specific Carleman's multiplier methods in the time domain, wherein the exponential weights in each Carleman's multiplier carefully take into account the particular dynamics involved, be it hyperbolic or parabolic. But for coupled PDE systems which involve hyperbolic dynamics interacting with parabolic dynamics, typically across some boundary interface, Carleman's multipliers are not readily applicable. Given that such coupled PDE systems occur frequently in nature and in engineering applications; e.g., fluid-structure and structural acoustic interactions, there is a patent need to devise broadly implementable techniques by which one can infer uniform decay for a given PDE system. In this connection, our talk shall center on a novel frequency domain methodology.
Speaker Biography
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George Avalos received the Ph.D. in Applied Mathematics from the University of Virginia. He is currently a Professor at the University of Nebraska-Lincoln. His research interests include Control Theory for Partial Differential Equations.
Tuesday March 26 2013, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Ron Taylor, Berry College
An introduction to the mathematical theory of knots
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Knot theory was born out of an interest in cataloging the elements and was derailed by the discovery of the speed of light. Subsequently it was revived both as an area of mathematics, but one with scientific implications. In this talk we will discuss the history of knot theory along with some interesting results and applications.
Friday March 29 2013, 2:30pm - 3:30pm, Location 116 DSC
Jun Kawabe, Faculty of Engineering, Shinshu University
The study of Riesz space-valued nonadditive measures
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In 1974, Sugeno [2] introduced the notion of fuzzy measures and integrals to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov [1] independently introduced the notion of submeasures to refine measure theory further. Both fuzzy measures and submeasures are special kinds of nonadditive measures, and their studies have stimulated engineers’ and mathematicians’ interest in nonadditive measure theory; see Wang and Klir [3].
The classical theorems, such as the Egoroff theorem, the Alexandroff theorem, and some convergence theorems of integrals, are fundamental and important to develop measure theory. Therefore many researchers continue to try to obtain their successful analogues in nonadditive measure theory.
When we try to develop nonadditive measure theory in Riesz space, along with the nonadditivity of measures, we confront some tougher problems due to the epsilon-argument, which is useful in measure theory, not working well in a general Riesz space. In this talk, instead of the epsilon-argument, we introduce and impose some new smoothness conditions on a Riesz space (the asymptotic Egoroff property, the monotone function continuity property, and so on) to obtain successful analogues of some important results in real-valued nonadditive measure theory.
This work is supported by Grant-in-Aid for Scientific Research No. 20540163, Japan Society for the Promotion of Science (JSPS).
References
[1] I. Dobrakov, On submeasures I, Dissertationes Math. (Rozprawy Mat.) 112, Warszawa, 1974.
[2] M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974.
[3] Z. Wang, G.J. Klir, Generalized Measure Theory, Springer, Berlin Heidelberg, New York, 2009.
Speaker Biography
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Prof. Jun Kawabe received his PhD in Information Sciences, from Tokyo Institute of Technology, Tokyo, Japan, in 1986. Then he worked as a lecturer and associate professor in Shinshu University, Nagano, Japan. He has been serving as a full professor in Shinshu University since 2003. He was a visiting researcher in Massachusetts Institute of Technology in 1996 and 2005-06. Prof. Kawabe has published 48 research papers and 2 books. His research interests are: non-Additive Measure Theory, weak convergence of vector measures with values in Riesz space, fuzziness and uncertainty, fuzzy set, fuzzy number, and probability theory.
Wednesday April 3 2013, 2:30pm - 3:30pm, Location 116 DSC
Melanie DeVries, Graduate Student, UNL
Unknotting Mathematical Knots
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Knot theory is a subfield of mathematics that concentrates on objects called knots – embeddings of the circle in a 3-dimensional balls – which can be thought of as endlessly elastic and frictionless strings that are tangled around themselves before their ends are glued together. The main question of this field is when are two knots equivalent, a deceptively simple question that has spawned the study of several different intrinsic properties of knots. One we will look at in particular is the study of unknotting numbers, the number of times a move called an unknotting operation needs to be applied to untangle a knot. We will also look at unknotting operations and unknotting numbers in a generalization of knot theory – virtual knot theory – that looks at embeddings of knots in more complicated surfaces.
Friday April 5 2013, 1:00pm - 2:00pm, Location 401 RH (Cool Math Talk)
John Konvalina, Department of Mathematics, UNO
A Mathematical Adventure from Combinatorics to Fractal Geometry to Brain Tumor Growth
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This talk will take you on a quick journey in discovery and amazement of the power of mathematical thinking from a simple counting problem arising in mathematical biology to the emergence of a new fractal, and then, finally, coming back around to biology with an application to brain tumor growth.
Speaker Biography
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Dr. Konvalina is Professor and Chair of the Department of Mathematics. His interests are in combinatorics, number theory, mathematics education, fractals, chaos theory, mathematical biology, data science, math anxiety, and more! He has published three textbooks and dozens of papers in pure and applied mathematics.
Wednesday April 17 2013, 2:30pm - 3:30pm, Location 116 DSC
Ginger McKee, Wolfram Research, Inc
Mathematica 9 in Education and Research
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During this free seminar, we will explore Mathematica's use for a wide variety of practical and theoretical applications across a variety of disciplines. Attendees will not only see new features in Mathematica 9, but will also receive examples of this functionality to begin using immediately. No Mathematica experience is required, and students are encouraged to attend.
Speaker Biography
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To find out more, please contact Ginger McKee at ginger@wolfram.com or 1-800-965-3726 ext. 3492
Tuesday April 23 2013, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Dana Ernst, Assistant Professor, Department of Mathematics and Statistics, Northern Arizona University
Impartial Games for Generating Groups
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Given a single element from a group G, we can create new elements of the group by raising the element to various powers. Some finite number of elements will "generate" all of group G. In the game DO GENERATE, the goal is to generate the all of G. In DO NOT GENERATE, the loser is the player who generates all of G. In this talk, Dr. Dana Ernst will help us explore both games and discuss winning strategies. Time permitting, he will also relay some of the current research related to both games.
Speaker Biography
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- Assistant Professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ
- Special Projects Coordinator for the Academy of Inquiry-Based Learning
- Research interests include combinatorics, algebraic structures, inquiry-based learning, and the Moore method for teaching mathematics
