 |
Iowa Section of the Mathematical Association of America |
 |
| 3:00-5:00 |
| 3:30-3:50 | Patterns and Structure in M-ary Partitions |
| Theron Hitchman, University of Northern Iowa | |
| For a fixed natural number m, an m-ary partition of another number n is a way to write n as a sum of powers of m. For example 7= 3^0 + 3^1+3^1 is a 3-ary partition of 7. For each m, we can describe a sequence b_m(n) which counts the number of m-ary paritions of n, and this sequence has some some beautiful number theoretic properties. In joint work with James Sellers (Penn State) and Mac Roepke (UNI student), we describe and explain rich structure inside the m-ary partition sequences with a surprisingly straight-forward computation, and hint at other questions to come. |
| 4:00-4:20 | Unit-connected pseudo-arithmetic super sets in the Gaussian Integers |
| Peter Blanchard, University of Iowa | |
| A set is pseudo-arithmetic if it has a difference which divides all other differences. A set is a pseudo-arithmetic super set if every subset is a pseudo-arithmetic set. Every pseudo-arithmetic super set can be contracted to have a unit difference, so the classification of pseudo-arithmetics super sets in Z[i] starts with the units. We give a complete classification of the unit-connected pseudo-arithmetic super sets in Z[i], and discuss which are maximal, which are bounded, and which may be extended. |
| 4:30-4:50 | Exploring Group Theory with FGB |
| Ruth Berger, Luther College | |
| Finite Group Behavior (FGB) is a free windows-based program that gives beginning group theory students a chance to explore abstract group theory concepts in a very concrete setting. The heart of the software is an extensive collection of Cayley tables of groups: Cyclic groups, Dihedral groups, and groups whose structure is not immediately recognizable. Students can explore relations among the elements of a group, determine the order of each element, and even make subgroups generated by selected elements of the group. This easy to use program also includes features that allow for the investigation of isomorphisms of groups, and it gives a nice visualization of how Cosets are formed. I will share some of the worksheets that I wrote for my Abstract Algebra students to gain some hands-on experience with these otherwise abstract concepts. |
| 4:00-4:20 | Explicit Constructions of Functions whose Graphs are Dense in The Plane |
| * Luke Serafin, Coe College | |
| A set D is dense in the plane if and only if every open ball in the plane contains an element of D. We prove that there exists a function f from the real line R to itself whose graph is dense in the plane by explicitly constructing it using a partition of the rationals into countably many subsets dense in R. We then use this method of construction to prove that there are 2^(2^\aleph_0) functions whose graphs are dense in the plane, and that there exists a function f: R ->R such that f(U) = R for every non-empty open set U in R. |
| 4:30-4:50 | An Algorithm for the Detection of Transient Neural Oscillations |
| * John Berkowitz, Coe College | |
| The analysis of neural activity through measures of electrical potential affords researchers great opportunity to understand in detail the dynamic nature of certain brain processes. Electroencephalography (EEG) and Local Field Potential recording (LFP) are two of the most common methods for measuring this activity. Both are essentially recordings of the electrical potential over time in a highly localized segment of the brain, and produce data sets that can show surprising amounts of structure. Oscillations with very well defined frequencies are the most common examples of structure within these recordings, and a large portion of modern neuroscience research focuses on how different frequency bands of these oscillations relate to different modes of activity for the organism being studied. Such signals can easily be detected and quantified automatically with traditional signal processing tools such as the Fourier transform. However, there also exist very transient oscillations within such recordings that are of interest to researchers. These require more sophisticated techniques to detect, because of their dual localization in both the time and frequency domains. A combination of several classic signal processing tools, namely digital band-pass filters, the Hilbert transform, z-scoring, and numerical derivatives has yielded an efficient and accurate algorithm for the detection of such transient oscillations. This algorithm has been applied to LFP data for sleeping rats and used to detect the well-known phenomena of sleep spindles, which are a hallmark of late stage sleep in mammals. |
| 7:30-8:30 | Everyday Questions, Not-So-Everyday Mathematics |
| Rick Gillman, Valparaiso University | |
| The world is full of un-explored mathematical problems. This talk presents the stories of three problems that the presenter found in his everyday world and investigated with undergraduate research partners. One is solved completely, one quickly reaches deep and un-explored mathematical territory, and the third, while not solved, opens many paths for further exploration. |
| 8:30-9:30 |
| 8:00-11:00 |
| 8:30-8:50 | Ideas and Examples for Calculus |
| Irvin Hentzel, Iowa State University | |
| We give some non traditional problems from various sources that help with the understanding of the ideas of calculus. We show how the concept of continuity can be used to get a better grasp of a situation and to correct bad judgement. The goal is not to show nice calculations, but to show ways of thinking. |
| 9:00-9:20 | Projects in Calculus Class |
| K Stroyan, University of Iowa | |
| My favorite calculus question is: Why did we eradicate polio by vaccination, but not measles? I use this as a training project for student projects in calculus. I'll talk about my experience with "modeling" projects in calculus. |
| 9:30-9:50 | Reals Revisited: NO SUP FOR YOU! |
| ** Samuel Ferguson, University of Iowa | |
| Traditionally, first courses in analysis have started with certain axioms and then, in the course of deducing the consequences of these axioms, they prove the major theorems of calculus. The chief among these axioms is the "sup/least upper bound axiom," which seems obscure to most beginners. Where did such a thing come from, and how do we know that such a number system, satisfying such axioms, actually exists? Are the "reals" real? If teachers and students leave such questions unasked, they risk getting the impression that mathematics is just what happens when a somebody writes down a set of axioms and uses them to go on, in the words of Steven G. Krantz, "a magical mystery tour." Fortunately, in 1872 Dedekind and Cantor, independently and with different approaches, which have come to be known as the "Dedekind cut" approach to the "sup" and the "Cauchy sequence" approach to "completeness," constructed such real number systems, but their approaches are considered too complicated to present in their entirety at the beginning of most courses in analysis. In this talk, assisted by the intuition of Cauchy, Weierstrass, Courant, and others, we will give another (new?) construction of the reals, which has the advantages of both of the other constructions discussed and the complications of neither. Time permitting, the number "e" will be defined with this approach, or the Intermediate Value Theorem will be proved. |
| 8:30-8:50 | Recurrences, power series, and ODE |
| Christian Roettger, Iowa State University | |
| A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects. |
| 9:00-9:20 | Random walks in a sparse ``cookie" environment |
| ** Reza Rastegar, Iowa State University | |
| ``Cookie random walks" is a popular model of self-interacting random walks. Several variations of this model have been studied during the last decade. In this talk we will focus on the random walk on the integer lattice, where the ``cookies" perturbing the random walk are placed in a regular random sub-lattice of Z. We will present the model, briefly discuss an associated branching process, and then state criteria for transience and recurrence for this random walk. |
| 9:30-9:50 | A New Look at IQ |
| A. M. Fink, Iowa State University | |
| We will discuss the Isoperimetric Quotient for low order polygons. If time permits, we can illustrate its connection with some linear algebra and markov chains. There are some intriguing geometric open problems. |
| 8:30-8:50 | The Iowa Mathematical Modeling Challenge: Modeling in an Experimental Learning Setting |
| ** Darin Mohr, University of Iowa | |
| We discuss the recent success of the third annual Iowa Mathematical Modeling Challenge (IMMC). The IMMC is a twenty-four hour contest similar to COMAP's Mathematical Contest in Modeling, but with an added emphasis on student assessment and mathematical communication. We also discuss the future of the IMMC at the University of Iowa. |
| 9:00-9:20 | Starting a Math Colloquium: Experiences from Loras College |
| Matthew Rissler, Loras College | |
| Also presenting: Angela Kohlhass (Loras College). In this talk, the speakers will describe their experiences initiating and maintaining the Loras College half of the Bi-State Mathematics Colloquium. The BSMC is a partnership between the math departments of UW-Platteville and Loras College and is in its second year. The Loras talks provide a venue for Loras math students and faculty to hear from mathematicians in the region surrounding Loras College on a biweekly basis. Topics that will be addressed in this talk include finding speakers, getting students to attend, establishing regional buy-in, and the issues that we have yet to resolve. |
| 9:30-9:50 | A Survey of Technology Use and District Spending in North Iowa Schools |
| Scott Searcy, Waldorf College | |
| Also presenting: Dr. Jeffrey Biessman. Conventional wisdom holds that technology use in public schools is commonplace and therefore college freshman have wide exposure to and experience with technology. Anecdotal suggest this may not be true. This survey was designed to reveal the extent of technology use in North Iowa school districts. The survey indicates that larger schools are less likely to budget money for technology on a per pupil basis than smaller districts. |
| 9:50-10:10 |
| 10:10-10:30 | Linear Algebra: When am I ever going to use this? |
| Martha Ellen Waggoner, Simpson College | |
| I tell my students that linear algebra is the most useful mathematical subject they will take, and of course, they expect me to support that claim. In this talk I will discuss applications that I use in both Linear Algebra and Mathematical Modeling that require matrix operations. I will focus on the difference between a forward problem and an inverse problem. The subject areas will include games, historical geography, and ray-based tomography. |
| 10:40-11:00 | Introduction to Mathematical Research through Graph Theory |
| Debra Czarneski, Simpson College | |
| In the fall semester of 2009, I taught an Introduction to Mathematical Research through Graph Theory course for incoming first-year students. Students learned how to ask questions, how to form conjectures, and how to present their findings orally and in writing. This talk will discuss the course format, topics covered, and course outcomes. |
| 10:10-10:30 | Retrolife Generation of the Twelve Pentominoes |
| Charles Ashbacher, #none | |
| The "Game of Life" invented by J. H. Conway has fascinated people for decades and was the impetus for the field of artificial life. Retrolife is determining if a specific pattern can be created from another with one iteration of the rules of life. This presentation will answer the question whether each of the twelve pentominoes can be generated via an iteration of the rules and poses new questions. |
| 10:40-11:00 | Multi-Resolution Cellular Automata for Real Computation |
| ** Brian Patterson, Iowa State University | |
| We will first briefly review cellular automata and why representing and computing with real numbers with a computer is problematic. Then we will discuss a new approach that uses the concept of fissioning cells to approximate real-valued regions. I will close with a brief explanation of my simulator. |
| 10:10-10:30 | An Introduction to Logo |
| Daniel Willis, Loras College | |
| An introduction to Logo (Turtle Geometry) using MSWLogo, a freeware version of Logo for 32-bit Windows. The talk will introduce basic commands, loops, procedures, and the use of variables, with applications to regular polygons, stars, tessellations, rotations, translations, reflections, and symmetry. The speaker has used Logo with teachers (and pre-service teachers) of elementary school, middle school, and high school mathematics. |
| 10:40-11:00 | SageTeX: Computing inside LaTeX documents |
| Jason Grout, Drake University | |
| I will talk about SageTeX, a system for embedding computer mathematical calculations or graphs inside TeX documents. The user simply puts a few simple commands in the TeX document and a computation is performed automatically and the output or graph appears in the PDF file. The system uses the powerful free open-source Sage computer algebra system (http://www.sagemath.org), but can also embed results and graphs from Mathematica, Maple, and a variety of other software. The author has used this in writing quizzes, tests, solution guides, papers, etc. Others have used SageTeX to generate interactive books and online worksheets. |
| 11:10-12:00 |
| 1:30-1:50 | Representation Theory |
| Jitka Stehnova, Mt. Mercy College | |
| In this talk, we first give an introduction to the representation theory of p-adic groups. We will then focus on the subset of unitary groups, specifically U(1,1) and U(2) and show a process of parametrization of irreducible admissible supercuspidal representations. |
| 2:00-2:20 | Monotonicity of mixed Ramsey numbers |
| ** Jihyeok Choi, Iowa State University | |
| For two graphs, G, and H, an edge-coloring of a complete graph is (G;H)-good if there is no monochromatic subgraph isomorphic to G and no rainbow subgraph isomorphic to H in this coloring. The set of number of colors used by some (G;H)-colorings of Kn is called a mixed-Ramsey spectrum. In this talk, we will discuss whether the spectrum is an interval. This is joint work with Maria Axenovich. |
| 2:30-2:50 | Minimum rank, maximum nullity and zero forcing number for selected graph families |
| ** Travis Peters, Iowa State University | |
| The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This talk discusses the graph families ciclos and estrellas. In particular, these families provide the examples showing that the maximum nullity of a graph and its dual may differ, and similarly for zero forcing number. |
| 1:30-1:50 | Discrete Observations or Continuous Ramblings: Some Thoughts on Historical Projects in Discrete Mathematics |
| Robert Keller, Loras College | |
| I will share some of my recent experiences on the use of historical projects in a discrete mathematics course. I used the projects to reinforce broad key topics from discrete in a provocative way. These topics included recursive vs. exact formulas, counting and patterns, and proof techniques such as induction. I will share some details on how I integrated the projects into the class and some (limited) responses from students. |
| 2:00-2:20 | A System to Place Incoming Students in Computer Science, Mathematics and Statistics |
| Henry Walker, Grinnell College | |
| Joint work with Andrew Hirakawa and Russel Steinbach. Colleges utilize various methods of placing students, but many methods are time intensive, have limited scope, or lack precision. The placement system described here resolves many of these issues using a PHP based inference engine with extensively-researched rules. The system's placements compare favorably with those created manually by faculty, and students perform well in the system-recommended courses. Scripts store placements in a MySQL database and later generate individual LaTeX-based letter for each student. The scripts from this project run efficiently, follow established software-engineering principles, and are easily modifiable. The project automates every step of the process from loading student data into the database to generating individual letters for students. |
| 2:30-2:50 | Continuous Problems Are Easier Than Discrete Ones |
| Kenneth Driessel, Iowa State University | |
| I claim: Continuous problems are (usually) easier than analogous discrete problems. Consequently, when teaching, we should emphasize the relation between continuous and discrete problems whenever possible. I shall use a historical example to support my claim. In particular, I shall review J.W.S. Rayleigh's treatment of beaded and continuous strings, which appears in his book "Theory of Sound" (Macmillan, 1894). |
| 1:30-1:50 | Expected Utility Maximization in an Optimal stopping Environment |
| ** Ranojoy Basu, Iowa State University | |
| In this paper we study an investment problem where an investor has the option to invest in a risk free asset (such as a bank account ) and a risky asset. His wealth can be transferred between the two assets and there are no transaction costs. The proportion of wealth in the risky asset is a priori chosen deterministic function of wealth. The objective is to …nd an optimal quitting time which maximizes the expected discounted utility from terminal wealth. First, we consider a situation when the wealth process is not subject to bankruptcy and obtain an optimal quitting time. Second, we consider the more realistic scenario when an investor’s wealth is subject to default. We develop necessary mathematical techniques to obtain an optimal selling time in both the circumstances. In both cases, it turned out that the optimal selling time is of threshold type. Numerical methods can easily be implemented to compute the optimal threshold. |
| 2:00-2:20 | Stock Loan Subject to Bankruptcy |
| ** Subhra Bhattacharya, Iowa State University | |
| In this paper, risk of bankruptcy has been introduced in the valuation of a financial derivative called stock loan. Bankruptcy has been modelled in both structural and reduced form approach. In structural form model, stock loan with finite maturity is considered following the Black-Cox specification of bankruptcy. It has been shown that the valuation of such an asset can be obtained explicitly in terms of the distribution of the first hitting time of Brownian motion and the pricing of the barrier options. In reduced form model, the default intensity has been introduced as in hazard rate models. A closed form solution of the initial value function is obtained, which implicitly defines the optimal exercise boundary. Moreover, this value function reflects an interrelationship between the optimal loan amount and the relevant variables (e.g. loan interest rate, stock price volatility etc). This interrelationship can be used to explain interesting issues such as: how does stock price volatility (or the reputation of the stock) or the loan interest rate affects the optimal loan amount? |
* denotes an undergraduate speaker and ** indicates a graduate student speaker
Back up to the top. MAA disclaimer If you have additions, corrections, or comments on anything on this page, please pass this information to the webmaster.
