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Iowa Section of the Mathematical Association of America |
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| 3:00-5:00 |
| 3:30-3:50 | Catalan Numbers and Hankel Transformations |
| Christopher French, Grinnell College | |
| We explore recurrence relations obtained from taking the Hankel transform of various linear combinations of Catalan numbers. |
| 4:00-4:20 | Baumslag-Solitar Groups and Their Representations |
| Russell Goodman, Central College | |
| The presenter will provide the audience with background on the Baumslag-Solitar groups and will share results from his search for simple representations of such groups. There will also be a discussion of the deformations of his simple representations and how this leads to determining the dimension of the representation variety and representation scheme at those simple representations. |
| 4:30-4:50 | Beginning a history of the Iowa Section of the MAA |
| Joel Haack, University of Northern Iowa | |
| An interactive session focused on sources for the history of the Iowa Section of the MAA as part of its Centennial celebration in 2015. |
| 7:00-8:00 | The Truth of Proofs |
| David Bressoud, #non-IA section | |
| Mathematicians often delude themselves into thinking that we create proofs in order to establish truth. In fact, that which is "proven" is often not true, and mathematical results are often known with certainty to be true long before a proof is found. I will use some illustrations from the history of mathematics to make this point and to show that proof is more about making connections than establishing truth. |
| 8:00-8:30 |
| 8:00-11:00 |
| 8:30-9:30 | Issues of the Transition to College Mathematics |
| David Bressoud, #non-IA section | |
| Over the past quarter century, 2- and 4-year college enrollment in first semester calculus has remained constant while high school enrollment in calculus has grown tenfold, from 60,000 to 600,000, and continues to grow at 6% per year. We have passed the cross-over point where each year more students study first semester calculus in US high schools than in all 2- and 4-year colleges and universities in the United States. In theory, this should be an engine for directing more students toward careers in science, engineering, and mathematics. In fact, it is having the opposite effect. This talk will present what is known about the effects of this growth and what needs to happen in response within our high schools and universities. |
| 9:40-10:00 | Calculus at Luther College |
| Ruth Berger, Luther College | |
| Calculus at Luther College: Over the past two decades Calculus instruction at Luther has slowly moved from Reform Calculus back towards a more traditional approach. Several aspects of Reform Calculus, especially the use of technology, have been retained as essential components to teaching Calculus in the modern age. The main reason we moved back to a more traditional way of teaching Calculus was that we found we needed a more intellectually challenging course with sound theoretical foundations for our math majors. |
| 10:00-10:20 | A First Calculus Course Using Numerical Tools and Modeling |
| Brian Birgen, Wartburg College | |
| Our Calculus redesign consists of students learning the concepts of differentiation and integration by focusing on mathematical modeling and numerical solutions to differential equations. Topics covered include Euler's method, the Newtonian model for air resistance, the buoyancy of hot air ballooning, predator-prey models, Malaria and more. |
| 10:20-10:40 | Group Activities In Calculus |
| Irvin Hentzel, Iowa State University | |
| I have been devoting one day a week to group work in calculus. I show the type of activities that I have used. I have some data on the interest shown, and how these group scores compare with the traditional tests scores. |
| 10:50-11:10 | Free Online Homework with Webwork |
| Jason Grout, Drake University | |
| Webwork (http://webwork.maa.org) is a mature popular open-source system for online homework. Sponsored by the NSF and MAA, the system includes tens of thousands of class-tested problems for a large number of undergraduate math courses. Webwork has not only enhanced the quantity and quality of interaction around homework in my class, but it has also dramatically cut costs for students by enabling them to use inexpensive editions of textbooks. I will discuss how Webwork fits into the larger landscape of free open-source educational tools, how I use it in my class, and how you can set it up for your courses. |
| 11:10-11:30 | Developments in Calculus Instruction |
| Panel Discussants, #none | |
| All Special Session Speakers, along with representatives from several other institutions in the Section, will discuss and entertain questions about current and impending developments. |
| 1:00-1:50 |
| 2:00-2:20 | Mathematics and Writing – A One Week Course |
| Debra Czarneski, Simpson College | |
| Each fall at Simpson College, Student Support Services helps a group of new students transition to college through the week-long CampusConnect program. The students in the program must be from low-income families, be first-generation college students, and/or have a disability. A one-week course is offered as part of the program. This fall I team-taught a Mathematics and Writing course with the Director of Writing Across the Curriculum. This talk will discuss the topics covered, the assignments given, and student responses to the class. |
| 2:30-2:50 | Math Modeling Course Confidential |
| Tony DeLaubenfels, Cornell College | |
| Mathematical modeling has in recent years become the course of choice to provide a foundation in applied math to math majors. Common traits of this course include "real world" problems and a "projects" orientation. There are many decisions to be made when designing such a course--topics, text, software, labs, team or individual projects, source of projects, and more. I review the decisions I made in teaching the math modeling course at Cornell College in May 2011 and report some conclusions. |
| 3:00-3:20 | Discovery learning in linear algebra using dynamical geometry software. |
| Martha Ellen Waggoner, Simpson College | |
| I have developed several Geometers Sketchpad sketches that students can use to help them understand transformations, eigenvalues, eigenvectors and a geometrical interpretation of the determinant. These dynamic sketches are used in discovery learning exercises in a computer classroom. In this talk I will demonstrate a couple of sketches and explain how they are used in the classroom. |
| 3:30-3:50 | Squigonometry: Developing non-euclidean trigonometry with elementary calculus |
| Bill Wood, University of Northern Iowa | |
| Differential equations offers one approach to defining the classical trigonometric functions sine and cosine that parameterize the unit circle. We adapt this approach to develop analogous functions that parameterize the unit "squircle" defined by $x^4+y^4=1$. As we develop our new theory of "squigonometry" using only elementary calculus, we will catch glimpses of some very interesting and deep ideas in elliptic integrals, non-euclidean geometry, number theory, and complex analysis. |
| 4:00-4:20 | The ALEKS Placement Assessment at Iowa State University |
| Elgin Johnston, Iowa State University | |
| We are in the process of introducing a new Mathematics placement tool at Iowa State University. This presentation will give some information about the ALEKS system, our background with it, and discuss some preliminary results from our analysis of the effectiveness of the tool. |
| 2:00-2:20 | A Simple Puzzle in Arithmetic Logic For Mathematical Exercise |
| Charles Ashbacher, #none | |
| The KenKen is a simple math puzzle that was created by Tetsuya Miyamoto and is based on the operations of simple arithmetic on an n x n grid. The question of note is, how many puzzles are there up through the 9 x 9 grid? |
| 2:30-2:50 | Harmonic Maps and Discrete Groups |
| Theron Hitchman, University of Northern Iowa | |
| We explain a framework for how a new theorem about harmonic maps can be used to advance the rigidity theory of some discrete groups of matrices. |
| 3:00-3:20 | Zero forcing number, maximum nullity, and path cover number of complete edge subdivision graphs |
| ** 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. The path cover number is the fewest number of vertex disjoint induced paths that cover all the vertices of the graph. We study the effect of edge subdivisions of a graph on the zero forcing number, maximum nullity, and path cover number. |
| 3:30-3:50 | Just Plane Numbers |
| Ronald Smith, Graceland University | |
| The vocabulary of a typical introduction to complex numbers challenges the beginner with a bewildering array of words with strong connotations of "imaginary," "complex," and "non-real." By combining a geometric approach to complex arithmetic found in Roger Penrose's book "The Road to Reality" with the interactive geometry package, Geogebra, we show that it is possible and even insightful to characterize these as just plane numbers. |
* denotes an undergraduate speaker and ** indicates a graduate student speaker
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