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Iowa Section of the Mathematical Association of America |
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| 2:30-4:30 | Wendy Weber, Central College |
| 3:00-3:20 | An overview of Geometer's Sketchpad with applications to Calculus |
| Luz DeAlba, Drake University | |
| We present a quick overview of the basics of software packege Geometer's Sketchpad. Then move on to how one can use the software in the classroom. We showcase applications from several areas of mathematics including applications to Calculus. |
| 3:30-3:50 | Uniform distribution and invertible matrices |
| Christian Roettger, Iowa State University | |
| Uniform distribution is usually known as a property of sequences xn in the unit interval, like n alpha modulo 1, where alpha is irrational. We will present an example of uniform distribution in the unit square, explain the handy Weyl criterion used to prove uniform distribution, and conclude with an application to invertible 2x2 - matrices over the integers. |
| 4:00-4:20 | The distribution of digits in consecutive integers |
| Ronald Smith, Graceland College | |
| The distribution of digits problem asks for the frequency of each digit (0 … 9) in the list of integers from a to b. After considering the brute force algorithm, we give an efficient algorithm for solving this problem that is suitable for hand calculation. |
| 3:00-3:20 | The effect of philosophy on curriculum |
| a.m. fink | |
| I wrote a history of the Iowa State Mathematics Department and discovered that the curriculum offered was very dependent on outside influences and the philosophy of eductation of the those outside influences. |
| 3:30-3:50 | Avoiding Paradoxes in Joker Poker |
| Stephen Walk, St. Cloud State University | |
| If we add a Joker to an ordinary deck of cards, we'll find that the three-of-a-kind hands are more prevalent than the two-pair hands. (By convention, the Joker is always interpreted to make the hand's rank as high as possible.) Since the two-pair hands are rarer, by all rights they should outrank the threes-of-a-kind. But if the ranking is redone so that two-pair hands rank higher, then some of the Joker hands have to be interpreted as two-pair hands instead of threes-of-a-kind, and as a result the two-pair hands are again more prevalent than threes-of-a-kind. There is simply no consistent way to rank the poker hands in this Joker deck. It's enough to make Bret Maverick spin in his grave. \par What if we don't confine ourselves to the ordinary deck? Is it possible to find a deck that avoids paradoxes like the one above? Yes! Is it \emph{easy} to avoid paradoxes? Sure---if the deck is big enough. This talk will include the results of an investigation into this situation as well as a few details about the methodology. Only decks of size smaller than one million are considered; bigger decks become somewhat difficult to shuffle. |
| 4:00-4:20 | Making the Most of Blackboard/WebCT/Etc. in Mathematics |
| Mariah Birgen, Wartburg College | |
| With the proliferation of Course Management Systems on campuses across the country, I often ask myself several questions: How can this make my life easier? Won't it take more time and energy? And, probably the most important, how can I use this if it won't display mathematics? As a Liberal Arts college, Wartburg College is never going to ask me to teach a course solely online, but even we have purchased such a system to enhance student learning. I have been working with two (relatively unknown) systems for three years and will share some of the answers I have discovered to the previous questions, as well as others that have come up along the way. |
| 3:00-3:20 | Introduction to the statistical software Fathom |
| Al Hibbard, Central College | |
| This talk wiill give a brief introduction to how and why to use the Fathom software. If you are familiar with Geometer's Sketchpad, this produced by the same company and is similar in its ease of use |
| 3:30-3:50 | Using Letter-Writing to Enhance a Calculus Course |
| Russell Goodman, Central College | |
| In this talk, the presenter will describe the experience he is having with letter-writing in a first-semester calculus course. In particular, the presenter has his students write letters to family members, friends, or others in order to communicate what they are experiencing in their calculus class. The presenter will discuss his original goals for this activity, along with the procedural details he set forth. In addition, there will be examples of student letters along with a discussion of what the presenter might want to do differently the next time he runs this activity in the fall of 2004. |
| 4:00-4:45 | Panel discussion: Life as a faculty member at a four-year college or a community college |
| Kathryn Davis, Kirkwood Community College; Cal Van Niewall, Coe College; Murphy Waggoner, Simpson College |
| 4:45-5:30 | What should be in the curriculum for a mathematics major? |
| 4:45-5:30 | What career advice can be given to potential and registered mathematics majors? |
| 5:30-7:30 |
| 7:30-7:50 | The Edge of the Universe--Hyperbolic Wallpaper |
| Frank Farris, Santa Clara University and Editor of Mathematics Magazine | |
| The universe couldn't have an edge, because if it did, you could go there, put your hand through and find more of the universe on the other side, right? This reasoning breaks down if you and your measuring devices shrink as you approach the edge, making it infinitely far away. We show a mathematical model of such a universe, called the Poincare Upper Halfplane, and study some of its features. The classical topic of circle inversion plays a prominent role. Physics suggests that this turns out to be a cold and lonely place, but we make beautiful wallpaper for the inhabitants. |
| 8:30--- |
| 8:45-9:05 | Forbidden Symmetry: Relaxing the Crystallographic Restriction |
| Frank Farris, Santa Clara University and Editor of Mathematics Magazine | |
| If you look at enough swatches of wallpaper, you will see centers of 2-fold, 3-fold, 4-fold, and 6-fold rotation. Why not 5-fold centers? They cannot occur, according to the Crystallographic Restriction, a fundamental result about wallpaper patterns, which are defined to be invariant under two linearly independent translations. Even so, we offer convincing pictures that appear to show wallpapers with 5-fold symmetry. The talk is intended to be accessible to students who know something about level curves in the plane and linear algebra. |
| 9:45-10:15 |
| 10:00-1:00 | Ruth Berger, Luther College |
| 10:15-10:35 | The mathematics of navigation in aviation |
| Irvin Hentzel, Iowa State University | |
| We explain the how and why of Compass errors and how to work around them. We discuss the NDB (non-directional beacon) and the geometry behind its use for navigation. We mention the Precision approach. And we present some contradictions from explaining lift by using Bernoulli's theorem. |
| 10:45-11:05 | Fun & Games with Permutation groups |
| Ruth Berger, Luther College | |
| This talk will give an introduction to the "Oval track puzzle" software that is available through the MAA in the book "Oval Track and other permutation puzzles, and just enough group theory to solve them" by J. Kiltinen. This fun program has several numbered disks on a circular track. The object of the game is to try and get the shuffled disks back into the original order, using only rotations and certain flips. For a track with n disks the moves that are allowed can be viewed as elements of the permutation group . I will give a short overview on how the concepts of inverses, commutators and conjugates come up naturally in solving the puzzles. Kiltinen's book is published in the MAA's Classroom Resources Materials series, and it is indeed a great tool to make Group Theory more interesting to students. Audience members who have used the puzzles are welcome to share their experiences. |
| 10:15-10:35 | Experiences of Tauqir Bibi in Teaching Calculus Courses |
| Tauqir Bibi, Iowa State University | |
| I have taught calculus courses for many years. Most of the students in these courses are engineering majors. Many of these students appreciate seeing applications to their majors. I will present examples of some problems and projects that introduce students to applications of Calculus in their majors. |
| 10:45-11:05 | Some Research-based Results on Technology and Visualization in Multivariable Calculus |
| Jonathan White, Coe College | |
| This talk will summarize some results of a multi-year study on the effects of technology use in multivariable calculus classes. The research focused especially on some differences in visualization skills between students who used computer algebra systems and others who did not. |
| 10:15-10:35 | Six degrees of graph theory: Kevin Bacon, Paul Erdos, William McKinley and me |
| Ryan Martin, Iowa State University | |
| Popularized by the Kevin Bacon game, the Small World problem is a question of measuring distance between members of a given set, upon which is a binary symmetric relationship. In the game, the set is the set of actors and two actors are linked if they appeared in the same movie. The distance between two actors is the fewest number of links to get from one to the other. In this talk, we discuss the game and a random graph model that gives an answer to a Small World-type question. |
| 10:45-11:05 | Building supertrees using distances |
| Stephen Willson, Iowa State University | |
| Suppose that a family of rooted phylogenetic trees Ti with different sets Xi of leaves is given. A supertree for the family would be a single rooted tree T whose leaf set is the union of all the Xi, such that the branching information in T corresponds to the branching information in all the trees Ti. This talk proposes a polynomial-time method BUILD-WITH-DISTANCES that makes essential use of distance information provided on the trees Ti to construct a rooted tree T. When a supertree containing also the distance information exists, then the method produces a supertree T. This supertree often shows increased resolution over the trees found by methods that utilize only the topology of the input trees. |
| 11:15-11:30 |
| 11:30-12:15 | Joel Haack, University of Northern Iowa, Chair of the Iowa Section of the MAA |
| 12:15-1:45 |
| 1:45-2:05 | "Fill 'er Up!" -- Packing a VW Beetle with Ping-Pong Balls |
| * Perry Keely, Coe College | |
| Ever wonder how people guess how many jelly beans are in a jar, or say, ping pong balls in a car? Using calculus, of course! (OK, well most of the time it's sheer luck!) Coe College's Calculus III course required students to do a project to display a real world application of calculus. After hearing a radio commercial about a contest to guess as close as possible the number of ping pong balls in a car to win a prize (the car!), our group realized that we could apply calculus to the situation. Our group designed a project to guess how many ping pong balls would fit into a new Volkswagen Beetle. Much to our luck, the Volkswagen website provided the actual number of ping pong balls that would fit into a Beetle, giving us a clue how accurate our estimation really is. Modeling the Beetle after a frustum of an ellipsoid, we used simple integration to estimate the volumes of both the interior space of the car and a ping pong ball, and figured out how many balls would fit. Who ever thought calculus could help you win a prize?! |
| 2:15-2:35 | Perfect Codes on Odd Dimension Sierpinski Graphs |
| * Stephanie Kleven, Central College | |
| Sierpinski graphs are built by an iterative construction from a complete graph on d vertices. These graphs have essentially one perfect one-error-correcting code defined on their vertices. We investigate assigning strings over 0,…, d -1 to vertices so that the resulting code on strings has several desirable properties. Our "SF" labeling is defined when d is odd and it becomes the Towers of Hanoi Labeling when d = 3. The SF labeling preserves the Gray code property observed in the Towers of Hanoi labeling, it has an explicit codeword characterization which is based on powers of two, and it has a finite state machine for error detection and error correction. |
| 2:45-3:05 | Chaos in Action: Discovering a Basin of Attraction |
| * Andrea Brennen, Grinnell College | |
| This project is an analysis of the dynamics of a particular subset of 3-D discrete nilpotent maps represented by the general system of equations: x=y; y=x^2-y^2. The analysis focuses on defining the Basin of Attraction and locating invariant manifolds for maps of this type using Liapunov Equations, Functional Equations, and computer imaging/modeling. |
| 3:15-3:35 | Apollonius' Problem: A study of Solutions and Their Connections |
| ** David Gisch, University of Northern Iowa | |
| In Tangencies, Apollonius of Perga shows how to construct a circle that is tangent to three given circles. More generally, Apollonius' problem asks to construct the circle which is tangent to any three objects, which may be any combination of points, lines, and circles. The case when all three objects are circles is the most complicated case since up to eight solution circles are possible depending on the arrangement of the given circles. Within the last two centuries solutions have been given by J. D. Gergonne in 1816, Frederick Soddy in 1936, and most recently David Eppstein in 2001. We illustrate the solutions using the geometry software Cinderella™, survey some connections among the three solutions, and provide a framework for further study. |
| 3:45-4:30 | Panel discussion: What do four-year colleges and community colleges look for in a job applicant? |
| Adriana Attleson, NIACC; Jim Freeman, Cornell College; Mark Mills, Central College |
* denotes an undergraduate speaker and ** indicates a graduate student speaker
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