Spring 2012 Program

Abstracts are listed at the end of the page. (link)

Friday, April 20

4:00-5:30 Common Core Standards - Meyer Hall 215
Prof. Sonja Goerdt (St. Cloud State University)
Open to **ALL**
6:30-8:00 Registration - Buenger Education Center (just north of Meyer Hall)
$10; Students, first time attendees and speakers free;
$5 for MAA-NCS Section NExT members.
6:30-9:30 Book Sales - Meyer Hall 211
Evening Session - Buenger Education Center (just north of Meyer Hall), Professor Rob Krueger, Presiding
7:15-7:20 Welcome, Dr. Lonn Maly, Vice President of Academic Affairs, Concordia Univeristy
7:20-7:35 Prof. Paul Zorn, St. Olaf College
What's Happening at MAA Central
7:40-7:55 Prof. Joy Lind, University of Sioux Falls
The STEM Real World Applications of Mathematics Project
8:00-9:00 Invited Lecture

Professor Richard McGehee, University of Minnesota
A Dynamical Systems Approach to Paleoclimate Models
9:00-10:30 Reception - Buenger Education Center

Saturday, April 21

7:00-8:30 Executive Board Meeting, President's Conference Room
8:00-11:00 Registration - Buenger Education Center
Book Sales - Meyer Hall 211
Morning Session A - Buenger Education Center, Professor Sarah Jahn, Presiding
9:05-9:25 Prof. Bruce Peckham, University of Minnesota-Duluth
Student Projects on Newton's Method
9:30-9:50 Brett Bozyk (graduate student), University of Minnesota-Duluth
A Special Family of Maps of the Plane
Morning Session B - Meyer Hall 215, Professor Helen Wong, Presiding
9:05-9:25 Prof. Roger B. Kirchner (retired), Carleton College
A Dual Number Expression RPN Calculator for Automatic Differentiation
9:30-9:50 Prof. Walter Sizer, Minnesota State University-Moorhead
How I discovered that (9/4)(27/8) = (27/8)(9/4)
9:50-10:10 Break - Buenger Education Center Lobby
Morning Session A, Continued - Buenger Education Center, Professor Sarah Jahn, Presiding
10:10-10:30 Prof. Ruijun Zhao, Minnesota State University-Mankato
We Can End Malaria!
10:35-10:50 Brian Barthel (graduate student), Minnesota State University-Mankato
On Active and Passive Propagation Models
Morning Session B, Continued - Meyer Hall 215, Professor Helen Wong, Presiding
10:10-10:30 Mr. John Hanenburg
Estimating the Standard Deviation
10:35-10:50 Prof. Aaron Wangberg, Winona State University
Using WeBWorK to Understand Calculus Students' Use of Function Composition
11:00-12:00 Invited Lecture - Buenger Education Center, Professor Sarah Jahn, Presiding

Prof. Jill Dietz, St. Olaf College
Research with Students Under the Big Tent
12:00-1:00 Luncheon Dining Hall
1:00-1:30 Business Meeting Buenger Education Center, Prof. Michael Hvidsten, Presiding
Afternoon Session A - Buenger Education Center, Prof. Michael Hvidsten, Presiding
1:30-1:50 Prof. James A. Walsh, Oberlin College
The Jormungand Global Climate State from a Dynamical Systems Perspective
1:55-2:15 Prof. Pangyen Weng, Metropolitan State College
Teach Essential Mathematics, When Less is More
2:20-2:40 Prof. William Schwalm, University of North Dakota
When do Differential Equations Share Solutions?
2:45-3:00 Dr. Barry Cipra
Mathematics of Planet Earth 2013
Afternoon Session B - Meyer Hall 215, Professor James Brooks, Presiding
1:30-1:50 Prof. Kaisa Taipale, St. Olaf College
A Puzzle Rule for Quantum Cohomology
1:55-2:15 Prof. Aaron Wangberg, Winona State University
Identifying Groups by Viewing the Fourth (Fifth, and Sixth!) Dimensions
2:20-2:40 Prof. Kathryn Lenz, University of Minnesota-Duluth
Voting Methods Propaganda Versus Mathematically Informed Discourse in the Public Sphere
2:45-3:00 Prof. Namyong Lee, Minnesota State University-Mankata
Do Dogs & Cockroaches Know Calculus?



Dr. Sonja Goerdt, Common Core Standards

The development of the Common Core State Standards was coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers. The goal of the Common Core State Standards is to better prepare students for college and career readiness at a level that is competitive internationally. In this session, we will discuss the development of the Common Core mathematics standards, initiatives to align college-entrance exams to these standards, specifics of the mathematical content in the standards, and the implications for higher education.

Invited Addresses

Jill Dietz, Research with Students under the Big Tent

Undergraduate research in mathematics seems to be for the 1%, with the brightest students from elite institutions having all the advantages when it comes to being admitted to just 64 NSF REU sites around the country. What about the 99%? In this talk I lay out a plan for developing research skills throughout the mathematics curriculum – much as our colleagues in the sciences do by developing lab skills from day 1 – so that the vast majority of mathematics majors have had some sort of research-like experience by the time they graduate. Some examples and lessons learned from one of the biggest, big tent programs will be given.

Richard McGehee, A Dynamical Systems Approach to Paleoclimate Models

Simple mathematical models have been used to explore the Earth’s past climates. We will present some of these models and discuss them from a dynamical systems perspective.

Contributed Student Talks

Brian Barthel, On Active and Passive Propagation Models

With recent advancements in social networks, the interest in better understanding the social influence on the adoption of an idea has again been brought to the forefront. In this study, we look at the spread of ideas in different network models, such as large- and small-world networks, and local networks such as paths, stars and their variations. The main interest of our study is to find the minimum number of early adopters to influence the entire network through active and passive propagation models, with applications to real-world situations in management and the spread of violence.

Brett Bozyk, A Special Family of Maps of the Plane

Nonlinear maps of the plane can have very complicated dynamics. We present some results for the family xn + c + β/zd, which we call “non-analytic singular perturbations of complex analytic maps.” Numerical escape experiments yield fascinating pictures. These can be compared to well-known (filled) Julia sets for polynomials and for analytic singular perturbations. When c = 0 and n = d, the maps simplify enough to allow analytical results.

Contributed Talks

Barry Cipra, Mathematics of Planet Earth 2013

The MAA is a participant in Mathematics of Planet Earth 2013, a yearlong effort to highlight the role of mathematics in addressing problems of global importance. I will describe some of MPE2013's plans, including a special issue of The College Mathematics Journal, which has a deadline for submissions later in the current year (see http://www.maa.org/pubs/mpe2013.html for more).

John Hanenburg, Estimating the Standard Deviation

I used to have to determine the statistical accuracy of time studies in manufacturing which required determining the standard deviation, s2=∑((Xi-X)/(n-1)), of the mean using a hand calculator. This was very time consuming when you had a relatively large set of numbers. I determined several interesting ways to approximate the standard deviation, also, several approximating formulas for the approximating formulas. Finally, I came up a method that took almost no math and worked surprisingly well. I will discuss several of these methods.

Roger Kirchner, A Dual Number Expression RPN Calculator for Automatic Differentiation

Dual numbers have the form a + b e, where a, b are real and e2=0, and can be implemented as pairs ⟨a,b⟩ with ⟨u,u’⟩⟨v, v’⟩=⟨u v, u v’+ u’ v⟩. Then f(x + h e) = f(x) + h f’(x)e for any rational function f. Define F(X +He)=F(X)+HF(X)e for functions F of one or more variables built into a dual number calculator. The chain rule implies f(x + e)=f(x)+f’(x)e for any function f computable with the calculator, and f’(x) is computed automatically as a by-product of evaluating f(x + e). A dual number RPN calculator for automatic differentiation, modeled on the old HP-45, is available at http://demonstrations.wolfram.com/AutomaticDifferentiation/

Namyong Lee, Do Dogs & Cockroaches Know Calculus?

This talk is intended as a sequel of Dr. Timothy Pennings' popular paper "Do Dogs Know Calculus?". We review the Pennings problem quickly and will move to multi-variable calculus problem solved by cockroaches. We also try to answer "But... How can they...?". This talk is geared towards undergraduate students.

Kathryn Lenz, Voting methods propaganda versus mathematically informed discourse in the public sphere

Mathematicians have a role to play in helping civic leaders and the public distinguish propaganda from truth concerning alternative voting methods and their potential impacts on political elections in the US. This presentation will describe several voting algorithms, including instant run-off voting (IRV), the Borda count and score voting, distortions of their mathematical properties propagating in the public arena and the opportunity this gives mathematicians to engage in civic dialogue. Examples will be given of city election results, propaganda found on websites, misrepresentations in newspaper opinion pieces and discussions with Duluthians.

Joy Lind, The STEM Real World Applications of Mathematics Project

Traditional curricula seldom offer students concrete examples of real world applications of mathematics. As a result, students often finish their undergraduate mathematics career asking themselves the question, “What else can I do with a mathematics degree besides teach?” To address this, we launched the STEM Real World Applications of Mathematics Project funded by an NSF-CCLI grant. Topics included in this talk will include applications of graph theory to telecommunication networks (National LambdaRail) and information about the Careers in Mathematics Speaker Series launched this spring at the University of Sioux Falls.

Bruce Peckham, Student Projects on Newton’s Method

Newton's method for finding complex roots of polynomials leads to some great fractal pictures, fairly easily generated by students. If chosen carefully a family can have a ''natural'' parameter plane to investigate. Moreover, families can be chosen so that a real family of one-dimensional maps lives inside the full family, like ''x2+c'' lives inside ''z2+c.'' The one-dimensional family admits more complete analysis, while the complex plane pictures suggest conjectures. We present snippets from three such student projects.

William Schwalm, When do differential equations share solutions?

Consider the DEs (1-4xy)q + 2p3 – 4x p2 + 4yp – 2 = 0, and xyq + x p2 – 2y p + 1 = 0, where p = y', q = y''. Each is a polynomial set to zero. Do the general solutions intersect? In other words, do these DEs have any common solutions? I don’t want to solve them to find out. In general, given two DEs in the polynomial ring Q[x, y, p, q], when do the solutions intersect? Although the answer may be obvious and well known, we did not know it. We came across problems like this in solving Einstein’s equations when a quantity y would need to satisfy two conditions. Some of the ideas seemed interesting.

Walter Sizer, How I discovered that (9/4)(27/8) = (27/8)(9/4)

If you are already aware of this relationship, now might be a good time for a cup of coffee.

Kaisa Taipale, A puzzle rule for quantum cohomology

Joint work with undergraduates Warren Shull and Erik Wyatt has produced a quantum puzzle rule -- a way of computing quantum cohomology of Grassmannians using puzzles. I'll introduce puzzles and how they compute cohomology of Grassmannians (or Littlewood-Richardson coefficients, if you prefer!) then present our rule. If time remains, I'll present some interesting avenues for future research.

James A. Walsh, The Jormungand global climate state from a dynamical systems perspective

The Jormungand global climate state, introduced in recent work of Abbot, Voigt and Koll, serves as an alternative to the Snowball Earth model of extensive glacial episodes in the Proterozoic Era. The Jormungand model will be presented from a dynamical systems perspective. The focus will be placed on the attractive nature of an equilibrium solution for which glaciers exist in the tropics but do not extend all the way to the equator.

Aaron Wangberg, Identifying groups by viewing the fourth (fifth, and sixth!) dimensions

Can you see the fourth dimension? In our universe, the interactions of particles seem to be governed by symmetry groups. Finding these small subgroups within a large group, a difficult algebraic task, can be done easily via sight. There’s just one problem: The large symmetry group exists in 6 dimensions! In this talk, I’ll show how simple linear algebra techniques can help us explore subgroups in four, five, and six dimensions. This talk is geared towards undergraduate students.

Aaron Wangberg, Using WeBWorK to understand calculus students’ use of function composition

The concept of function composition appears repeatedly throughout first semester calculus. By implementing modifications to the open-source and MAA-supported online homework system WeBWorK, we’ve captured both quantitative and qualitative data showing how students attempt to solve calculus problems. We’ll share some of these modifications to the WeBWorK system as well as some of the preliminary results of our study.

Pangyen Weng, Teaching essential mathematics, when less is more.

Learning objectives of a lower division math course should focus not on improving students' math literacy, but on mastery of essential concepts and skills. The author uses data from two of his own case studies: A 4-year study of an online math learning program he created in New Jersey, and a set of following-up data from his developmental math classes at Metropolitan State University

Ruijun Zhao, We Can End Malaria!

In this talk, I will review what mathematicians did for control of malaria, a mosquito-borne parasitic disease caused by malaria parasite. I will show the basic disease facts of malaria, and the current goal and challenge in disease control, prevention, and eradication. At last, I will demonstrate two mathematical models of malaria, one addressing the optimal usage of insecticide-treated nets (ITNs) and one addressing the disease transmission under the possible employment of partially effective vaccine.

Paul Zorn, What's Happening at MAA Central

In this talk, I will share some news from the national headquarters of the MAA. I intend to field a question or two, too.

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