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Iowa Section of the Mathematical Association of America |
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| 3:00-5:00 |
| 3:30-3:50 | A tour of the new Iowa section web site |
| # Al Hibbard, Central College | |
| I will give an overview of the content and structure of the new section web site including special emphasis on the tools portion and some of the pages related to the history of the section. I will also explain the process I took in coming to its current structure. |
| 4:00-4:20 | Math Summer Camp for Professors |
| # Mariah Birgen, Wartburg College | |
| This summer I spent three weeks at the Park City Mathematics Institute as an Undergraduate Faculty Participant. The focus was on the interaction between Geometry and Analysis, but in reality, this turned out to be General Relativity. As Undergraduate Faculty they brought us up to speed academically on this cool topic, but they also depended on us to be the glue to get the other participants communicating with each other. This talk will address how the mathematics institute works and why you should find a way to attend this fabulous experience. |
| 4:30-4:50 | Student vs. Instructor Expectations: Can we bridge the gap? |
| # Joy Becker, Wartburg College | |
| Students and instructors often come into a course with expectations that don�t necessarily agree. These different sets of expectations can impact the learning environment in a negative way for students, as well as instructors. One way to bridge the gap between these multiple sets of expectations is to openly communicate with students about the variety of expectations, including giving students opportunities to voice their own expectations. Narrowing the gap between student and instructor expectations can lead to increased student engagement and a more positive learning environment. |
| 3:30-3:50 | IBL, Calculus, and Pens |
| # Amanda Matson, Clarke University | |
| After attending the IBL Workshop this summer, I got inspired to incorporate parts of an IBL atmosphere in my general education differential calculus course. Here I will convey the things that worked and some of the things that didn't work as well as they could have. |
| 4:00-4:20 | Critical Locations in Infrastructure |
| # Debra Czarneski, Simpson College | |
| Critical locations in infrastructure are roads that if damaged would cause a large disruption in the ability of vehicles to navigate a city. This talk will introduce a model that determines the critical locations of Indianola, Iowa. This research was completed by three undergraduate students as part of the Bryan Summer Research Program at Simpson College. This talk will also discuss several extensions of the research that students at your institution could explore. |
| 4:30-4:50 | Graph Forcing Games |
| # ** Nathan Warnberg, Iowa State University | |
| Let G be a graph with some vertex set initially colored blue and the rest of the vertices colored white. The goal of the game is to color the entire graph blue, based on some a set of rules. Depending on which set of rules are used the minimum number of initial blue vertices needed to force the entire graph blue has implications for the minimum rank of the graph's corresponding matrix family. We will demonstrate some of these games and show the connections with the minimum rank problem. |
| 5:00-7:00 |
| 7:00-8:00 | Fibonacci's Flower Garden |
| # Jennifer Quinn, Mathematical Association of America | |
| It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden. |
| 8:00-9:00 |
| 8:30-9:30 | Survivor X |
| # Wartburg Students, Wartburg College | |
| Based on CBS�s widely-seen show Survivor, the math capstone class project Survivor X will incorporate mini math challenges in search of a final victor. Participants will be split into teams competing together for immunity. Eventually the teams will be merged and the game will turn to an individual competition. But watch out for those voted out, they will decide who is to be given the title of sole mathematical survivor. |
| 8:00-11:00 |
| 8:30-9:30 | Mathematics to DIE for: The Battle Between Counting and Matching |
| # Jennifer Quinn, Mathematical Association of America | |
| Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide. |
| 9:40-10:00 | TeX in the Classroom |
| # Paul Muhly, University of Iowa | |
| In this talk I will advocate for and share my experiences when requiring students to write their homework in LaTeX. The experiences I have had when requiring students to TeX their homework have been surprisingly positive. I will explain what I have done and offer suggestions, especially suggestions about how to get students started using TeX. |
| 10:10-10:30 | Calculus Bloopers I Have Made |
| # Irvin R. Hentzel, Iowa State University | |
| There are "simplifying assumptions" used in First Year Calculus which have become so ingrained in my teaching that I never give them a second thought. I examine the following statements as they are often presented in Calculus Books and show inconsistencies which are often overlooked. (1) Work = Integral F ds (2) For a force to move an object in a certain direction, there must be a component of the force in that direction. (3) Acceleration normal to the direction of motion changes the direction, but leaves the speed unchanged. (4) The Bernoulli Principle: the greater the velocity, the lower the pressure. (5) Neglecting air resistance in earth's gravity, all things fall at the same rate. (6) The Proof of Rolle's Theorem. |
| 10:40-11:00 | Remedial Mathematics at Iowa State University |
| # Chris Schultz, Iowa State University (with Wolfgang Kliemann) | |
| Success in a developmental math course is not truly measured until the student success rate in the downstream class is measured. Iowa State University�s Department of Mathematics has started such a study and would like to share our preliminary data for discussion. Concern is often also expressed that students who start in developmental math classes will never graduate and we have gathered 2 years� worth of data addressing this concern. The format of our developmental course, Math 10, will be shared as well as the data described above. |
| 9:40-10:00 | 291 decillion ways to tile with Tetirs |
| # Steve Butler, Iowa State University | |
| We look at the problem of finding the number of ways to tile a board using tetronimoes (i.e., Tetris pieces). In particular, we show how to transform tiling problems into problems of counting walks. Using this approach we were able to get the exact number of ways to tile the 10x20 board. |
| 10:10-10:30 | Taxicab Geometry |
| # Ruth Berger, Luther College | |
| Making a small change in how distance is measured has a huge effect on the geometry of the plane. Circles now look like squares, Pi is an integer, and many other familiar objects have very unfamiliar shapes. Tilting a segment changes its size! Working in this geometry reinforces important skills that every math major needs to have: carefully read definitions and not make any assumptions based on intuition or previous experience. In this talk I will present some of the findings that my geometry students are expected to come up with. |
| 10:40-11:00 | Beautiful Strings |
| # Ronald Smith, Graceland University | |
| Let S and T be strings. S is more beautiful than T if (i) S is longer than T, or (ii) if S and T have the same length, then S > T lexicographically. S derives T, if T is a subsequence (not necessarily a substring) of S. T is unique if each character in T appears exactly once. The "Beautiful Strings Problem" is to find the most beautiful unique string that can be derived from a given string S. This problem appeared on the web and in at least one programming contest last year, with no correct solution known to this author. We give an efficient solution, showing the usefulness of a mathematical approach. |
| 11:10-12:10 |
| 12:15-1:40 |
| 1:40-2:00 | Declining Marginal Utility Is Not Ordinal - an inconsistency in microeconomics. |
| # Kenneth Driessel, Iowa State University | |
| Economists like to confine their attention to ordinal properties of utility functions. But, the often-quoted principle of declining marginal utility is not ordinal. This situation seems incongruous/inconsistent. I shall carefully define mathematically the following phrases: "utility function", "declining marginal utility" and "ordinal property" in the setting of microeconomics. I shall then show that declining marginal utility is not ordinal. |
| 2:10-2:30 | Are Drug Tests As a Precondition for Welfare Receipt Cost-Effective? |
| # Charles Ashbacher, Independent | |
| Recently some states have implemented a program where an applicant for welfare must take and pass a drug test in order to receive benefits. Using the current law regarding how testing can be performed and some fact-based assumptions, a model for how cost-effective this program is can be developed. This model has been used as an exercise in a management science class as it can be applied to both public and corporate policies. |
| 2:40-3:00 | Some Gauss Sums found in Category Theory |
| # ** Ryan Johnson, Iowa State University | |
| I will present a 21st century problem that requires some 18th century mathematics. Fusion categories lie in the intersection of group theory, knot theory, and quantum physics. If one is given a fusion category, a sequence of complex numbers can be computed which are called the Frobenius-Schur indicator. In this talk I will consider a particular subclass of fusion categories whose data is defined using a finite abelian group and a bilinear form on that group. Computing the indicator of these categories requires the use of quadratic Gauss sums. The aim of my research is to show the uniqueness of the indicator on this particular subclass of fusion categories. |
| 1:40-2:00 | Geometric distribution of primes in Z[sqrt(2)] |
| # Christian Roettger, Iowa State University | |
| It all starts with the question: what can we say about integers a, b such that a^2 - 2b^2 is a prime? We will show some ways to make this question more precise - in particular, we study the distribution of the corresponding points (a,b) in the plane. The fundamental tool is the ring Z[sqrt(2)], and from there we make connections to analytic number theory (L-functions, Hecke characters) which arise very naturally - this is the context where Hecke invented 'Hecke characters', and they are much easier to understand here than when you read about them in MathWorld. |
| 2:10-2:30 | Matrix sign patterns that require eventual exponential nonnegativity |
| # ** Craig Erickson, Iowa State University | |
| The matrix exponential function can be used to solve systems of linear differential equations. For certain applications, it is of interest whether or not the matrix exponential function of a given matrix becomes and remains entry-wise nonnegative after some time. Such matrices are called eventually exponentially nonnegative. Often the exact numerical entries in the matrix are not known (for example due to uncertainty in experimental measurements), but the qualitative information is usually known. In this talk we discuss what structure on the signs of the entries of a matrix guarantee the matrix is eventually exponentially nonnegative. |
| 2:40-3:00 | The Upper and Lower Limits of a Function and Semicontinuous Functions |
| # Dave Renfro, ACT, Inc. | |
| A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts. |
| 1:40-3:00 |
# denotes a talk indicated as suitable for undergraduates, * denotes an undergraduate speaker, and ** indicates a graduate student speaker.
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