 |
Iowa Section of the Mathematical Association of America |
 |
| 9:15-2:30 |
| 3:00-5:00 |
| 3:30-3:50 | Using short "lecture challenge questions" in large lecture courses |
| # Stephen Willson, Iowa State University | |
| The talk describes my use of daily "lecture challenges" in large lecture courses such as Calculus or Mathematical Ideas. These "lecture challenges" are one-problem quizzes on material presented in the same lecture. Problems are typically easy problems that might be test questions. There is no partial credit. Students get one point for a wrong answer, two points for a correct answer. Absent students get no points, so students are motivated to attend. The problems are very fast to grade. Students may help and teach each other. |
| 4:00-4:20 | Planning a Course in Sports Analytics |
| # Russ Goodman, Central College | |
| Sports analytics is becoming a popular topic of interest for many, but there are few mathematics courses that tap into this student interest. This presentation will offer the speaker's preliminary work in organizing a spring 2015 one-credit honors seminar in Sports Analytics. Comments, questions, critiques, and perspectives will be sought from the audience, as the planning for the course is ongoing. |
| 4:30-4:50 | Patterns and Perspective: Math in Art and Music |
| # Angela Kohlhaas, Loras College | |
| During January term at Loras College, we offer various courses which fulfill our mathematical modeling general education requirement as well as our experiential learning J-term requirement. I designed a course in this category which investigates mathematical reasoning underlying perspective art and musical compositions. I will discuss the class structure, activities, and assignments I plan to use when teaching it this January. |
| 3:30-3:50 | What did J.S. Bach know about fractals? |
| # ** Jennifer Good, University of Iowa | |
| The mathematical term 'fractal', coined in the late 20th century, is used to describe detailed mathematical objects with certain repeating patterns. Bach's 3rd cello suite, composed 250 years earlier, contains evidence of a fractal embedded in one of its movements. Come learn about fractals as we see (and hear) how one appears in this famous piece of music! |
| 4:00-4:20 | Business cycles and predator-prey ordinary differential equations |
| # Kenneth Driessel, Iowa State University | |
| Richard M. Goodwin (1913-1996) was an American mathematician and economist. During most of his career he taught at the University of Cambridge. Goodwin studied economic growth and the business cycle. In 1967 he published a paper with title "A Growth Cycle". In this paper he described an economic model consisting of two nonlinear first order ordinary differential equations that exhibits cyclic behavior. This system is similar to the well-known system of predator-prey equations of Lotka and Volterra. Goodwin seems to have had mixed opinions about his system. He writes (in 1967): "Presented here is a starkly schematized and hence quite unrealistic model of cycles in growth rates." He also writes (in 1972): "[These assumptions] were chosen because they represent, in my opinion, the most essential dynamic aspects of capitalism; furthermore, they are factually based, to the order of accuracy implicit in such a model." In this talk, I shall present my version of Goodwin's growth cycle system. |
| 4:30-4:50 | Conic Sections in Grid City |
| # Ruth Berger, Luther College | |
| I will present some word problems that can be used at the high school level, or with pre-service teachers, to make students think about the definition of distance and the definitions of the figures known as conic sections in Euclidean Geometry. These real-world problems about distance measurement on a city grid introduce students to Taxicab geometry, an easily accessible topic that can lead to thought provoking questions at many different levels. |
| 3:30-3:50 | Mutual Dimension |
| # ** Adam Case, Iowa State University | |
| The mutual (shared) information between two random variables is a well-understood concept in Shannon information theory, but how do we think about mutual information between other kinds of objects such as strings or real numbers? In this talk, we discuss various notions of mutual information from the perspective of algorithmic information theory. First we explore the algorithmic information content of a binary string. We then discuss the notion of the dimension (density of algorithmic information) of a real number. Finally, we explain our recent solution to an open problem: the correct formulation of the mutual information between two real numbers. This is joint work with Jack Lutz. The talk will be accessible to math undergraduates. |
| 4:00-4:20 | Khovanov Homology: An undergraduate research project |
| # Robert Todd, University of Nebraska at Omaha | |
| Khovanov homology is a sophisticated construction in knot theory, a branch of mathematics which is foreign and mysterious to many undergraduates. However, with only some linear algebra, some computer skills, and a little maturity as prerequisites, Khovanov homology can be used as a context to introduce many important mathematical ideas. I will discuss an on-going undergraduate research project whose goal is to compute the Khovanov homology of some families of knots. Such computations have only been performed for a handful of examples, thus our results will be of interest to researchers in the field. There will be many pictures and examples. |
| 4:30-4:50 | Separation of NP-Completeness Notions |
| # ** Debasis Mandal, Iowa State University | |
| Informally speaking, reductions translate instances of one problem to instances of another problem; a problem A is polynomial-time reducible to a problem B if A can be solved in polynomial-time by making queries to problem B. By varying the manner in which the queries are allowed to make, we obtain a wide spectrum of reductions. At one end of the spectrum is Cook/Turing reduction where multiple queries are allowed and the i-th query made depends on answers to previous queries. On the other end is the most restrictive reduction, Karp-Levin/many-one reduction, where each positive instance of problem A is mapped to a positive instance of problem B, and so are the negative instances. This raises the following question: For complexity class NP, is there a Turing complete language that is not many-one complete? The first result that achieves such separation, under a reasonable hypothesis, is due to Lutz and Mayordomo. We show this separation for NP, under a believable worst-case hardness hypothesis. This is a joint work with A. Pavan and Rajeswari Venugopalan. |
| 3:30-3:50 | Toward an integrative model of suction feeding using the immersed boundary method |
| # Tyler Skorczewski, Cornell College | |
| Suction feeding is among the most common forms of aquatic prey capture. During a suction feeding strike a fish rapidly opens its mouth creating a fluid flow that draws in the prey. This is an example of indirect prey capture; the fish does not directly manipulate the prey, but rather the fluid flow around the prey. Previous studies of suction feeding have either studied jaw mechanics or the flow field in isolation, or have only considered rigid jaw motions (think of a fish mouth as a collection of metal plates). In this talk I will describe work in progress to develop a new methodology to study fish suction feeding that relaxes some of these conditions. In particular we will allow for more realistic flexible jaws and examine how the kinematics of the jaw motion affects the resultant flow field and subsequent prey capture. |
| 4:00-4:20 | Arrowgrams: Tips and Pointers |
| # Kenneth Price, University of Wisconsin Oshkosh | |
| An arrowgram is a type of puzzle based on the transitive relation, directed graphs, and groups. To solve the puzzle a group element is assigned to each arrow of a directed graph. This is called a grading and the group element assigned to an arrow is called its grade. Grades for some arrows are given. The rest of the arrows are assigned grades using a rule which is based on transitivity. Arrowgrams also contain secret messages. The words are formed by pairs of letters which stand for the arrows. The puzzle is solved when every arrow is graded and the secret message is revealed. We answer some mathematical questions related to constructing and solving arrowgrams. How many arrows have to be given grades? Which arrows can be used? Can the same set of arrows be used for different groups? |
| 4:30-4:50 | Cops and Robbers on Oriented Graphs |
| # Chris Spicer, Morningside College | |
| Cops and Robbers is a turn-based game traditionally played on graphs. In this talk, we extend this game to oriented graphs. Although a complete characterization of 1-cop-win graphs is known, there is not yet a corresponding characterization for oriented graphs. Necessary conditions are described for an oriented graph to be 1-cop-win, and several results are provided toward finding sufficient conditions. |
| 5:00-7:00 |
| 7:00-8:00 | The Fractal Geometry of the Mandelbrot Set |
| # Robert Devaney, Boston University | |
| In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the "Devaney" sequence. There might even be a joke or two in the talk. |
| 8:00-9:00 |
| 7:00-8:00 |
| 8:00-11:00 |
| 8:30-9:30 | An Excursion into the Strange World of Singular Geometry |
| # Ruth Charney, Brandeis University | |
| In high school we learn about the geometry of the plane. Later, we encounter the geometry of smooth manifolds. In this talk, we take a peek at the mind-bending geometry of singular spaces and their applications. |
| 9:40-10:00 | Student Presentations in Calculus II |
| # Debra Czarneski, Simpson College | |
| In Calculus II, I have student groups teach the integral application sections to the rest of the class. The groups of three students prepare and deliver the lecture, assign homework, and provide feedback on the homework assigned. In this talk, I will discuss the details of the assignment and student responses to the assignment. |
| 10:10-10:30 | Toys, Puzzles, and Games: the Importance of Play in the Classroom |
| # Jacob Heidenreich, Loras College | |
| Much research has been done over the past few decades concerning using games in education. One fruitful line of investigation has been on the importance of play in the learning experience. In this talk, I will discuss college-level educational goals and how they can be served by creating a playful learning environment in the classroom. I will also discuss and demonstrate the toys, puzzles, and games I developed for use in the classroom. |
| 10:40-11:00 | Adding Context to Calculus |
| # Matt Rissler, Loras College | |
| This semester in Calculus I, my students have been doing weekly assignments to help provide them with context for the mathematics they are learning in the rest of the course. These assignments have investigated connections to historical and present day developments in mathematics, as well as to the utility of calculus for problem-solving in students' current lives and future careers. I will discuss what assignments I have done/will do and how students have responded to them. |
| 9:40-10:00 | Generalized Augmented Happy Numbers |
| # Susan Crook, Loras College | |
| What makes a number a happy number? Is it sitting on the beach with no cares in the world or is there more to it than that? In this talk, we'll mathematically define happy numbers and discuss some properties. We'll explore some of their properties and look at variations on the idea of happy numbers to see if we can extend any of these properties. This work was done collaboratively with other undergraduate math faculty at a Research Experience for Undergraduate Faculty this summer at the American Institute for Mathematics, so there will also be a short plug for REUs and the REUF. |
| 10:10-10:30 | How can i be more than Imaginary for Future HIgh School Mathematics Teachers |
| # Olena Ostapyuk, University of Northern Iowa (with Catherine M. Miller) | |
| High school teachers introduce i as a solution to the equation x^2=-1 without understanding the geometry of complex numbers. This results in students not understanding the role of complex numbers in other contexts. The purpose of this talk is to share an introduction to complex numbers used in a mathematics course for future secondary mathematics teachers to demystify i and provide a rationale for its use in both pure and applied mathematics. |
| 10:40-11:00 | Visual hypothesis testing - lineups and probability |
| # Christian Roettger, Iowa State University | |
| Police use lineups involving one suspect and several 'dummies' to get evidence that a witness can identify the suspect. In an abstract sense, we can form a hypothesis about 'suspect' data and test it in this way: literally have people looking at a lineup of plots with the task of identifying the data plot among the dummies. Repetition with several observers makes this approach surprisingly powerful. It also has potential when comparing the efficiency of different visual representations of the same data. Disclaimer: do not expect analysis of actual police lineups. But we will try out the method on the audience! This is joint work with Heike Hofmann, Di Cook, Phil Dixon, and Andreas Buja. I have investigated the underlying probability distributions. This meant evaluating some multiple integrals, and revising all the tricks from Calculus II. |
| 9:40-10:00 | Fractals: A Basic Introduction |
| # Victor Vega, College of Coastal Georgia | |
| We present a basic introduction to fractals by looking and understand the concept of Hausdorff dimension and Topological dimension by looking at simple examples of classic fractals and geometric constructs. We also define the Julia set and Mandelbrot set as an iterative function on the complex plane and present some examples together with some historical remarks. |
| 10:10-10:30 | Amplification and damping of an oscillating streamflow signal in a river network |
| # ** Morgan Fonley, University of Iowa | |
| When river flow is observed under dry conditions (such as late summer), a daily fluctuation can be seen. Without the addition of precipitation, the source of these fluctuations is understood to be evapotranspiration of water from the riparian zone of trees near the river network. The flow at any point in the river network exhibits a time delay between the time of maximal evaporation (around midday) and the minimal streamflow. Several hypotheses suggest reasons for this time delay including different methods by which water moves through the soil. An alternative hypothesis is that the time delay instead comes from constructive and destructive interference that occurs when the oscillating flows of river links undergo different phase shifts and combine their signals. In this way, the flow at a downstream river link can be amplified or damped. I present an analytic solution to the transport equation, a linear ordinary differential equation that can be used to determine the flow at any point in a river network when all hillslopes are assumed to have uniform parameters. I use this solution to demonstrate the extent of amplification or damping that can occur when different parameter values are varied. |
| 10:40-11:00 | Missing Avalanche Sizes in the 1 dimensional sandpile model |
| # Mike Johnson, Luther College (with Grant Barnes, Cadence Sawyer (collaborators)) | |
| The one-dimensional sandpile model has many interesting connections with number theory. When looking at the size of sandpile avalanches, powers of 2 seem to be mysteriously absent. Using a trough model, we classify avalanches into two categories. The size of each type can be described as either a sum of consecutive integers or a product of two integers with controlled sum. Since powers of two cannot be written as a sum of two or more consecutive positive integers, this explains why powers of two are not common avalanche sizes. We then estimate the minimal sandpile length required to find an avalanche of a given size. |
| 9:40-10:00 | A "Weird" Limit Representation of Pi |
| # Mu-Ling Chang, University of Wisconsin-Platteville | |
| It is well known that $e=\lim_{n \rightarrow \infty}{\left( 1+\frac{1}{n} \right) }^n$ by mathematicians. Does the irrational number pi have such an unexpected limit representation like e, which can be proved by using only undergraduate mathematical skills? In this talk we will use geometry, trigonometry, mathematical induction, and the concept of limits to prove the existence of such a limit. |
| 10:10-10:30 | History of the Iowa Section of the MAA |
| # * Riley Burkart, Central College | |
| The history of the Iowa Section stretches back to 1915, even predating the foundation of the Mathematical Association of America by a month. In this talk, the speaker will present his research on the history of the Iowa Section from its origin to the present, examining the trends and changes in the organization. |
| 10:40-11:00 | Mathemagic: A Centennial Tribute to Martin Gardner |
| # Benjamin V.C. Collins, University of Wisconsin-Platteville (with Quinn Collins (Platteville Middle School)) | |
| Marting Gardner (1914-2010) was a mathematician and writer who inspired generations of mathematicians through his ``Mathematical Games'' column in Scientific American and other written work. He was also an accomplished magician, and many of his tricks have interesting mathematical underpinnings. In this talk, ``Quinntinnius Maximus'' (otherwise known as Quinn Collins, an eighth grader at Platteville Middle School) will present several of these feats of Mathemagic. If you are lucky, his assistant ``Sabino'' (otherwise known as Ben Collins, a professor of mathematics at the University of Wisconsin-Platteville) will explain some of the mathematics underlying them. |
| 11:10-12:10 |
| 12:15-1:00 |
| 1:10-3:00 |
| 1:10-1:30 | Inquiry Based Learning |
| # Jason Smith, Graceland University | |
| A discussion about the Inquiry Based Learning(IBL) Workshop I attended this summer as well as my experience using the IBL methods in Probability and Stochastic Processes. I will discuss some early successes and early failures in class. I will mention some of the research in support of IBL. |
| 1:40-2:00 | Constructing the Naturals -- An Inquiry-Based Approach |
| Jonathan White, Coe College | |
| The construction of the natural numbers via the Peano Axioms is a strangely neglected backwater of the undergraduate curriculum. It deserves more attention. Meanwhile, although inquiry-based learning has gained some traction, it usually is considered a binary decision, where a course either is or is not taught using an IBL approach. I propose a standalone unit, giving our number systems the foundation they deserve, and offering a "trial size" taste of IBL. |
| 1:10-1:30 | Teaching Managers to Think Of All Factors When Making Decisions |
| # Charles Ashbacher, Upper Iowa University | |
| Abstract: Major management decisions are often made without the proper analysis of all the details and consequences of the actions. The current wave known as 'reshoring' is where companies that transferred production facilities to other countries are now returning that production to the United States. This is a consequence of rising costs of labor and materials in other countries coupled with additional factors such as lax IP laws. Proper training of managers includes cost projections that incorporate all factors and two major projects in a management science class at Upper Iowa University where these aspects are included will be presented. |
| 1:40-2:00 | complex roots of polynomials and why it pays to talk mathematics |
| # a m fink, none | |
| For quadratic polynomials, a negative discriminant is a criteria for non real roots. Is there one for nth degree polynomials? Sure,and I found it because I talked to someone who pointed the way. |
| 1:10-1:30 | An Elementary Solution to a Problem of Ramanujan's Interest |
| # * Brian Diaz, Cornell College | |
| In the early 1900's, Srinivasa Ramanujan discovered an intriguing, yet exotic, integral that he believed could have a 'simple', beautiful closed form. However, he never gave a simple solution to this integral. It wouldn't be until the mid-1950's when Russian mathematician V. I. Levin revisited Ramanujan's integral. He used non-elementary calculus techniques to prove that the integral, indeed, had a closed form for a single parameter; however, that parameter was only defined for positive integers. The integral would not be fully explored for the sake of itself until half a century later. Recently, V. Adamchik found that exact same integral that Ramanujan had encountered nearly a century ago. He showed a closed form using methods of Euler sums and related non-elementary techniques. This presentation will show a closed form of the integral does exist, but use only methods of elementary calculus. In addition, these techniques can be used to extend the result to double parameters! |
| 1:40-2:00 | Exact Analytical Solutions of a Chemical Oscillator |
| # ** Titus Klinge, Iowa State University | |
| A chemical reaction network (CRN) is a mathematical model used extensively in chemistry with deep connections to ordinary differential equations (ODEs). CRNs have been used to model naturally occurring reactions that are periodic such as the Brusselator and the Oreganator. However, the nonlinearity of the underlying ODEs is often complex and a large amount of research has been devoted to approximating the solutions to these ODEs. Recently, Luca Cardelli defined a CRN that has similar desirable periodic behavior. In this talk we present a general analysis of this CRN including exact analytical solutions to the underlying ODEs. This is joint work with James I. Lathrop. This talk will be accessible to both undergraduate and graduate students. |
| 1:10-1:30 | Calculus Curiosities |
| # Dave Renfro, #business/industry/government | |
| Over the years I have collected a lot of little-known mathematical curiosities and minutia from various books and journal articles. This talk is intended to be a "show and tell" for some of this material, mostly restricted to things that could be of use in first year calculus courses, or at least to things likely to be of interest to teachers of such courses. |
| 1:40-2:00 | Interplay between function theory and Hilbert space |
| Jonas Meyer, Loras College | |
| Some classic results in Hilbert space theory are best described through the lens of functions of a complex variable, and vice versa. This survey talk will focus on some examples of that interplay, including how invariant subspaces of some operators on Hilbert space can be described using complex functions, and how Hilbert space theory can be used to prove results on interpolation with analytic functions. |
| 2:10-3:00 | Building Towards Student Ownership |
| # Theron Hitchman, University of Northern Iowa | |
| Why should a student choose to continue his or her study of mathematics beyond high school? How can we enrich our mathematics classes to make them more interesting and engaging? How can we introduce students to the culture of mathematics, and bring them into the community? I will argue that one way to address these questions is to trust in the students and return to them the ownership of the mathematics, both the content and the process. We might even have some time to discuss how we can pull that off without looking too foolish. |
# denotes a talk indicated as suitable for undergraduates, * denotes an undergraduate speaker, and ** indicates a graduate student speaker.
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