## Mathematics Awareness Month ** April 2007 **

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Opening Remarks: Liza Fiol-Matta, Dean of the William J. Maxwell College of Arts and Sciences The 9 AM Session ?Celebrating the 300th Birthday of Leonhard Euler" Presider: Sandra Caravella, NJCU Mathematics Department, scaravella@njcu.edu 9:10 a.m. Evan Siegel, NJCU Mathematics Department, esiegel@njcu.edu Euler: Big Function, Little Theorem Euler's function takes in a positive integer and gives the number of primes less than or equal to it. One of its many surprising applications is that if two numbers have no common factor, the first number raised to the Euler's function of the second is one more than some multiple of the second number. The proof shows the power of the element of surprise in attacking a mathematical problem. 9:25 a.m. Hannah Misir, NJCU Mathematics Graduate Student, hmisir@alumni.fandm.edu Graph Theory: A Tribute to Leonard Euler This talk will provide an overview of a famous problem concerning the bridges of Konigsberg, a city in Prussia. This problem was first solved by the prolific Swiss mathematician Leonhard Euler, who in the process of deriving his solution invented the branch of mathematics now known as graph theory. 9:40 a.m. Maria Alzugaray Rodriguez, Mathematics Department-Suffolk Community College, alzugam@sunysuffolk.edu How to Solve Certain Problems Related to the Euler Line The centroid, the orthocenter and the circumcenter of a triangle are aligned. The line passing through them is called the Euler line of this triangle. We will show constructions allowing us to obtain triangles with a given Euler line and other prescribed elements. These constructions can be carried out using only a ruler and a compass. _________________ The 10 AM Session Presider: Cindy Arrigo, NJCU Biology Department, carrigo@njcu.edu 10:00 a.m. James E. Lennon, NJCU Director of Educational and School Psychology Programs, jlennonD@njcu.edu Brain Function and Mathematics Abilities: Evidence for General and Specific Abilities This presentation will provide an overview of genetic, factor analytic, empirical studies of general and specific mathematics abilities. 10:15 a.m. Karen D. Ivy, NJCU Mathematics Department, kivy@njcu.edu Kolb?'s Learning Model from a Mathematical Perspective Decades of research in applied psychology strongly suggest that problem solving is best accomplished with a strategy-building approach. Perhaps the learning model most applicable to how students learn mathematics is Kolb?'s Learning Model. This talk provides an overview of Kolb?'s Learning Model and of how each learning style translates into mathematical learning styles. 10:30 a.m. Pangyen Weng, Ramapo College of New Jersey, pweng@ramapo.edu Seeing without Eyes: Mathematics and MRI Magnetic resonance imaging (MRI) is a non-invasive method often used to render images of the inside of brains. During the scanning process of an MRI, a gigantic amount of data will be recorded and analyzed by using mathematical and computational methods. We will demonstrate how mathematics is applied to imaging the brain and helps scientists visualize its internal structure. 10:45 a.m. Marion Cohen, University of Pennsylvania, Mathwoman199436@aol.com Crossing the Equal Sign I will read from my recent book, "Crossing the Equal Sign"? (Plain View Press, TX), poetry about the experience of mathematics that does much to represent the intersection of the right and left brain, as well as to describe the process that both sides go through in doing math research. My own experience has been as mathematician, professor, and most of all math-lover. The poems have also appealed to non-mathematicians and have appeared in literary as well as math journals. The 11 AM Session Presider: Zhixiong Chen, NJCU Mathematics Department, zchen@njcu.edu 11:00 a.m. Biyue Liu, Monmouth University, bliu@monmouth.edu Blood Flow Simulations in Curved Atherosclerotic Arteries A stroke occurs when the blood supply to a region of the brain is lost. The most frequent cause of loss of blood supply to brain tissue is atherosclerosis, which is a disease of the large- and medium-sized arteries. Atherosclerosis preferentially occurs in the arteries with bends or branches. It involves complex interactions between the artery wall and blood flow. Both clinical observations and experimental results show that hemodynamics plays a significant role in the physical processes that lead to atherosclerosis. Therefore a detailed hemodynamic evaluation of disturbed flow in atherosclerotic arteries may give additional insight to understanding the progression of atherosclerosis and may have useful clinical value, such as early detection of a highly stenosed artery segment, prediction of future disease progression, and treatment planning. I will present a computer simulation of the blood flow in curved atherosclerotic arteries. Through the numerical solutions obtained under physiological conditions, we will observe the flow patterns in curved atherosclerotic arteries and we will see how these patterns are affected by flow parameters and the artery geometry. Biyue Liu received her Ph. D. in Applied Mathematics from the University of Maryland in 1993. She taught at the University of Wyoming from 1993 to 1996 and at the University of Rhode Island from 1996 to 2000. She is currently working at Monmouth University, New Jersey. She has published work in numerical analysis, mathematical modeling, and computational fluid dynamics. Recently, she has been working on the simulation of blood flows in arteries. _________________ The 12 NOON Session Presider: Karen D. Ivy, NJCU Mathematics Department, kivy@njcu.edu 12:00 pm. Dawn A. Lott, Delaware State University, dlott@desu.edu Mathematical Model for the Rupture of Cerebral Saccular Aneurysms through Three-dimensional Stress Distribution in the Aneurysm Wall A mathematical model for the rupture of cerebral saccular aneurysms is developed through the analysis of three-dimensional stress distribution in the aneurysm wall. We assume in this paper, that a saccular aneurysm resembles a thin spherical shell (a spherical membrane), and then develop a strain energy function valid for finite strain to analyze 3-dimensional stress distribution in the aneurysm wall. We find that rupture occurs when the ratio of the wall thickness to the radius of the aneurysm is 6.1 X 10-3. We also conclude from our analysis that rupture can occur when the ratio of thickness to radius of the parent aneurysm equals the ratio of thickness to radius of the daughter aneurysm. These findings may be useful to the neurosurgeon to help predict the rupture potential in patients presenting with unruptured aneurysms. Dawn Alisha Lott, a former MAA-NAM David Blackwell Lecturer, is an Associate Professor of Applied Mathematics at Delaware State University in Dover, Delaware. She has published work in biomechanics, neurosurgery, biomedical engineering, and computational physics. Her major research interest is the numerical study of solutions of partial differential equations that model physical phenomena in nonlinear solid and fluid mechanics, biomechanics and physiology, in particular, research in the mathematical predictions for aneurysm treatment. _________________ Presentation of Prentice E. Whitlock Award: Yi Ding, NJCU Mathematics Department Closing Remarks: Richard Riggs, Chair of the NJCU Mathematics Department