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Iowa Section of the Mathematical Association of America |
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| 2:30-5:00 |
| 3:00-3:20 | Using Artificial Intelligence in the Teaching of Algebra and Precalculus |
| Monica Meissen, Clarke College | |
| Clarke College has been using software developed by Hawkes Learning to teach their Elementary Algebra, Intermediate Algebra and Precalculus courses with great success, especially during the current academic year. In addition to giving a demonstration of the software, Monica will describe how using Hawkes' products has helped with student placement and success in the classroom. |
| 3:30-3:50 | Class Research Projects in Elementary Statistics |
| Michael Smith, Morningside College | |
| This talk presents the results of a class data collection project completed in an elementary statistics class, as well as a philosophical discussion of what students can gain from collecting data in a statistics class. |
| 3:00-3:20 | Proofs in elementary geometry - what IS the sum of angles in a triangle? |
| Christian Roettger, Iowa State University | |
| One textbook for future teachers gives no less than four 'arguments' for this theorem. It is not claimed that they are proofs, and indeed they are not (all involve some circular reasoning). But the difference between such arguments and proofs is never made clear. We'll discover the flaws in the logic here, which are not obvious at all. Then we'll look at a number of examples from standard elementary geometry - some rock-solid one-line proofs, some examples where we all skip the proof and eyeball it, and finally an example which shows how 'eyeballing it' can lead to a 'proof' of 64=65. |
| 3:30-3:50 | A new formula for depth perception |
| K Stroyan, University of Iowa | |
| When you are moving, such as walking, and fix your gaze at an object ahead, but off to the side, say a tree, stationary objects behind the tree seem to move in the same direction as you, while objects in front seem to move in the opposite direction. This is a monocular cue to depth, as opposed to binocular disparity - the difference in the images in your two (separated) eyes. Working with a vision researcher, we have found a simple new formula for depth in terms of motion. Work is in progress in his laboratory to see how much of the geometric information contained in the formula is actually used by humans. The proof of the formula is a very simple application of trigonometry and infinitesimal calculus. We were led to discover it through experimental intuition and some interactive programs that we will demonstrate. |
| 4:00-4:10 |
| 4:10-4:30 | Geometer's Sketchpad and Undergraduate Research |
| Martha Waggoner, Simpson College | |
| We were able to purchase 12 student copies of Geometer's Sketchpad to be used by our pre-service teachers for their undergraduate research projects through a faculty development grant from the Simpson academic dean's office. In this talk, we will look at the variety of topics in geometry and computer aided design that our students worked on and how Geometer's Sketchpad helped the students in visualization, conjecture and proof. |
| 4:40-5:00 | Teaching an introduction to LaTeX course during May Term |
| Debra Czarneski, Simpson College | |
| During May Term of 2007, I taught a course that introduced students to typesetting in LaTeX. This talk will discuss the course goals, the material covered in the course, the course requirements, and student feedback. |
| 4:10-4:30 | Certain quasigroup homogeneous spaces |
| Bokhee Im, Chonnam National University, Rep. of Korea | |
| A quasigroup is defined as a set Q equipped with a multiplication, not necessarily associative, such that in the equation x y=z, knowledge of any two of the elements x, y, z of Q specifies the third uniquely. In particular, the solution for x in terms of y and z is written as z/y. The body of the multiplication table of a finite quasigroup is a Latin quare. Nonempty associative quasigroups are groups. In this talk, we consider the usual direct product G of the symmetric group of degree 3 and the cyclic group of order 2. By changing some intercalates of the body of the multiplication table of the group G, we get various quasigroup structures on the set G. We study homogeneous spaces derived from such a quasigroup and show how each action matrix acts on an orbit contained in the homogeneous space. Action matrices show the approximate symmetry. |
| 4:40-5:00 | The Ping and the Pong: Echolocating for fun and profit |
| Neil Martinsen-Burrell, Wartburg College | |
| Table tennis is the world's most popular sport. Little is known about the physical parameters of the game. In an effort to understand the basic flow of the game, we constructed an echolocation system that could find the location and time of the "ping" and the "pong" based on recordings from 4 microphones placed around the room. Such information can be used to approximately calculate the speeds at which the ball travels in a game of table tennis. |
| 5:00-7:20 |
| 7:30-7:50 | Connections Between Mathematics and Biology |
| Carl Cowen, Indiana University--Purdue University Indianapolis | |
| Dr. Rita Colwell, a research microbiologist and former Director of the National Science Foundation, regards the mathematical sciences as the backbone for US Scientific and Engineering research. Many scholars see the next few decades as a time of intensive progress in the biological sciences. Dr. Colwell sees mathematics as being an integral part of the progress in biology, not a traditional view, but a forward looking one. In this talk, Carl Cowen will outline some of the research areas in the emerging collaborations between mathematical and biological scientists. In addition, Cowen, who began his study of the mathematics of neuroscience in 2002-03 at the Mathematical Biosciences Institute at Ohio State University, and who worked in 2003-04 as a junior post-doc in the lab of Prof. Christie Sahley in the Purdue University Biology Department, will illustrate the connection between mathematics and neuroscience with a discussion of the Pulfrich phenomenon, an experiment that helps illuminate how the brain processes visual images. There are few mathematical or biological prerequisites for this discussion. |
| 8:30- |
| 8:00-11:25 |
| 8:30-8:50 | Rearranging the Alternating Harmonic Series |
| Carl Cowen, Indiana University--Purdue University Indianapolis | |
| The commutative property of addition is so familiar to all of us as school children that it comes as a shock to those studying college level mathematics that NOT all 'natural extensions' of the law are true! One of the first instances that we see the failure of an extended commutative law of addition is in infinite series. Often in the introduction to infinite series in calculus, one sees Riemann's Theorem: A conditionally convergent series can be rearranged to sum to any number. Unfortunately, the usual proof of this theorem does not indicate what the sum of a given rearrangement is. In this talk, we will examine the best known conditionally convergent series, the alternating harmonic series, and show how to find the sum of any rearrangement in which the positive terms and the negative terms are each in their usual order. |
| 9:30-9:40 |
| 9:40-10:00 | Activities to Nspire College Algebra and Calculus |
| Patsy Fagan, Drake University | |
| This hands-on workshop will present activities for a College Algebra and Calculus class. This is for the novice user of the TI-Nspire CAS handheld. |
| 9:45-10:05 | Matrix functions |
| Palle Jorgensen, University of Iowa | |
| When I was little my father, for reasons unbeknownst to me, told me about low-pass and high-pass filters. He was a telephone engineer and worked on filters in signal processing. The 'high' and 'low' part of the story refers to frequency bands. Not that this meant much to me at the time. Rather, I was fascinated by the pictures of filter designs in the EE journals stacked up on the floor. And it was only many years later I came across this stuff in mathematics: quadrature mirror filters and all that; yet the visual impression still lingered. The talk will cover some of this math, especially wavelets: Subband filters define operators in Hilbert space which satisfy all kinds of abstract relations, and they are terribly useful. They are used in math and in signal processing. Matrix functions from math are called poly-phase matrices by engineers, and they are scattering matrices in other circles, and quantum gates in physics. In fact a lot of the things we do in math are known and used in other fields, but under different names, and known in different ways. |
| 10:15-10:35 | Bloch Band Based Level Set Method for the Schrodinger Equation |
| ** Zhongming WANG, Iowa State University | |
| We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method. |
| 10:45-11:05 | variable selection in high dimensional regression |
| ** Fengrong Wei, University of Iowa | |
| My research work studies statistical regression models for data sets with a small sample but huge number of variables. For example, we may wish to study the same 5000 genes in only 200 individuals with the goal of predicting whether they will develop a certain rare cancer. A classical linear regression for the cancer outcome in terms of the 5000 genes does not work with only 200 data points because the associated linear equations are not full rank. We might choose 200 of the genes and do a regression, but there are over 10^363 such choices. My work uses "penalty functions" add to the linear equations which will make the problem solvable. Theoretically, we can show that the result have the "oracle" property which means it will give us the baseline true model with probability going to 1. |
| 9:45-10:05 | Math for Elementary Teachers |
| Dan Willis, Loras College | |
| The speaker will survey some of the available research on the mathematics content needs of elementary school teachers and future teachers. He will also discuss the impact this research has had on the development of a two-course 8-credit sequence "Math for Elementary Teachers I/II" at Loras College. This new two-course sequence is a program requirement for all Elementary Education majors at Loras College. |
| 10:15-10:35 | REU 2007 at University of Iowa--A Personal Experience |
| Yi Li, University of Iowa | |
| This talk is about the summer '07 REU work I supervised. I want to tell you about work of three wonderful visiting undergraduate students and the paper they recently submitted: "Chaotic Dynamics, Fractals and Billiards." I also want to tell you about my experience as a first time REU mentor. |
| 10:45-11:05 | The Mathematical Contest in Modeling: An Advisor's Perspective |
| ** Benjamin Galluzzo, University of Iowa | |
| This past February, The University of Iowa participated in The Mathematical Contest in Modeling (MCM) for the first time. This talk will focus on the organizational challenges we encountered while preparing for MCM as well as ideas that we hope to implement for future contests. |
| 9:45-10:05 | Euler and Music: a look at the Tentamen of 1739 |
| Joel Haack, University of Northern Iowa | |
| Musicians regard Euler as the leading contributor to theoretical acoustics. Why? This presentation will explore Euler's long interest in music theory. |
| 10:15-10:35 | Computer Investigations of Problems in Pickover's "The Mathematics of Oz" |
| Charles Ashbacher, #none | |
| Clifford Pickover, who has been described as the "human idea machine" stated many mathematics problems in his book "The Mathematics of Oz", published by Cambridge University Press. Those problems can largely be placed in the category of recreational mathematics. In this presentation, the results of computer investigations of some of those problems will be explained. The programs were all written in Java using the BigInteger class. |
| 10:35-10:55 | Activities to Nspire College Algebra and Calculus |
| Patsy Fagan, Drake University | |
| This hands-on workshop will present activities for a College Algebra and Calculus class. This is for the novice user of the TI-Nspire CAS handheld. This is a repeat of the earlier session. |
| 11:25-12:10 |
| 12:10-1:30 |
| 1:35-1:55 | A model of cardiac action potential incorporating caveolae-associated ion currents |
| ** Ian Besse, University of Iowa | |
| The contraction of a cardiac cell is initiated by a transient depolarization of the cell membrane called an action potential. Action potentials result from the rapid movement of ions across the membrane through pores called ion channels. Recent electrophysiological data regarding caveolae, small invaginations of the cell membrane, reveal that caveolae are reservoirs of 'recruitable' ion channels. As such, caveolar ion channels constitute a substantial and previously unrecognized source of ion currents that can significantly influence action potential morphology. While many mathematical models of cardiac action potential exist, none take into account these caveolae-associated ion currents. In this talk, a three-compartment ODE model of cardiac action potential incorporating a caveolar component will be introduced. I will demonstrate that this model yields results that are consistent with experimental data and that this model promises to offer insight into the composition of the caveolar membrane at the molecular level and into the biophysical mechanisms underlying some cardiac arrhythmias. |
| 2:05-2:25 | Digitalization in the signal processing |
| ** Le Gui, University of Iowa | |
| In real life when we store and transmit analog audio or video signals, we first obtain a digital representation of the signal. This process is called Digitalization or Analog-to-Digital (A/D) conversion and consists of two steps: sampling and quantization. In the "sampling" step we restrict time to a discrete sample of the continuous times. In the "quantization" step we discretize the real values of the time-discrete sample of the first step. We will discuss different quantization methods based on binary expansion or Beta-expansion and compare their "accuracy." "Accuracy" means that we can re-construct a good approximation of the original signal from its digitalization. Or "can you hear me now?" |
| 1:35-1:55 | Running a Math Circle |
| Elgin Johnston, Iowa State University | |
| For the last ten years I have been running a Math Circle for local middle and high school students. I will talk a little about the organization of the circle, how the circle is conducted, and about the mathematics we investigate. |
| 2:05-2:25 | Leading a Book Discussion in a Liberal Arts Mathematics Class |
| Russell Goodman, Central College | |
| One of the purposes of Central College's liberal arts mathematics class, Contemporary Mathematics, is to explore the use of mathematics to better understand the world. The presenter is currently teaching the course and is leading a class book discussion of "The Curious Incident of the Dog in the Night-Time" about a fictional young boy, Chris, with autism who has a love for mathematics. Through Chris' narration of the book, the presenter hopes his students will experience a unique perspective on mathematics that will enhance their appreciation of the discipline, but also open their eyes a bit more to the world around them.
In his talk, the presenter will provide a brief overview of the book and then describe how he is leading this class book discussion. He will also present up-to-the-minute results of his efforts. |
| 2:35-2:45 |
| 2:45-3:05 | Orthogonal Polynomials on the Cantor Set |
| * Greg Ongie, Coe College | |
| The middle-thirds Cantor set is an uncountable set of Lebesgue measure zero. The Cantor measure is defined such that it assigns the Cantor set measure one, and has the Cantor set as its support. An orthogonal polynomial sequence (OPS) is traditionally defined by means of Riemann integration, but more generally an OPS can be defined by means of integration with respect to a measure. First we construct the Cantor measure and show it satisfies the properties of a measure. Then, we verify the existence of an associated OPS by examining the positivity of its moment matrix. Finally, using the Gram-Schmidt method we construct the OPS, and derive various properties of the polynomials based on results for classical orthogonal polynomials. |
| 3:15-3:35 | Alternating evolution (AE) schemes for hyperbolic conservation laws |
| ** Haseena Ahmed, Iowa State University | |
| An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes. |
| 2:45-3:05 | Calculus: The 800 lb Gorilla in the Curriculum---Ideas from Wartburg |
| Mariah Birgen, Wartburg College | |
| Even though there has been over 30 years of trying to keep the 800 lb gorilla (calculus) from dominating the room (collegiate level mathematics curriculum), the gorilla is still with us. Whether it is arguing about what and how calculus material is taught; what to do with over-prepared (high school calculus) and under-prepared students; and how to keep calculus from dominating the mathematics major in the zero sum game of available courses in most schools in Iowa, we all must deal with the gorilla. In this presentation, we will discuss two different answers to these questions currently being tried at Wartburg and Cornell and hopefully get a lively discussion going on what everyone is doing to control the gorilla. Wartburg is teaching a calculus sequence consisting of an applied calculus followed by a foundations of calculus course. |
| 3:15-3:35 | Calculus: The 800 lb Gorilla in the Curriculum---Ideas from Cornell |
| James Freeman, Cornell College | |
| Even though there has been over 30 years of trying to keep the 800 lb gorilla (calculus) from dominating the room (collegiate level mathematics curriculum), the gorilla is still with us. Whether it is arguing about what and how calculus material is taught; what to do with over-prepared (high school calculus) and under-prepared students; and how to keep calculus from dominating the mathematics major in the zero sum game of available courses in most schools in Iowa, we all must deal with the gorilla. In this presentation, we will discuss two different answers to these questions currently being tried at Wartburg and Cornell and hopefully get a lively discussion going on what everyone is doing to control the gorilla. Cornell is following the lead of Grinnell and replaced our 4 sequence calculus offering with a two course sequence which covers several variable calculus in the second course. |
| 3:45-4:15 |
* denotes an undergraduate speaker and ** indicates a graduate student speaker
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