of the
Mathematical Association of America
Spring 2004
Newsletter
Indiana State University
Terre Haute, IN
April 2-3, 2004
SECTION OFFICERS
Governor: Roger Nelson,
rbnelson (at) bsu.edu, (765) 285-8653
Chair: Michael Karls,
karls (at) math.bsu.edu, (765) 285-8656
Vice Chair: Amos Carpenter,
acarpent (at) butler.edu, (317) 940-9436
Secretary: David Housman,
dhousman (at) goshen.edu, (574) 535-7405
Treasurer: Mary Porter,
mporter (at) saintmarys.edu, (574) 284-4516
Newsletter Editor: John Lorch,
jdlorch (at) math.bsu.edu, (765) 285-2329
Public Information Officer: David Rader,
david.rader (at) rose-hulman.edu, (812) 877-8361
Student Activities Coordinator: Mohammad Azarian,
ma3 (at) evansville.edu, (812) 479-2945
MAA Sectional
Fall 2004: University of Evansville (Evansville, IN), November 5-6. (This is a Tri-Section Meeting with Kentucky and Illinois.)
Spring 2005: IPFW, (Fort Wayne, IN), April 1-2.
Fall 2005: Depauw University, (Greencastle, IN), TBA.
MAA National
Summer 2004: Mathfest, Providence, RI, August 12-14, 2004.
Winter 2005: MAA-AMS Joint Mathematics Meeting: Atlanta, GA, Janaury 5-8, 2005.
Other Meetings
21-st annual Rose Hulman Undergraduate Mathematics Conference: Rose Hulman Institute of Technology, March 19-20, 2004.
2004 Illinois Section Meeting of the MAA: Roosevelt University (Schaumberg campus), April 2-3, 2004.
2004 Michigan Section MAA Meeting: Oakland University, May 7-8, 2004.
STATEMENT FROM MICHAEL KARLS (CHAIR OF THE INDIANA SECTION)
Once again, it’s spring in Indiana, and you know what that means—tornado season. How often have you heard the National Weather Service Warnings and wondered about how to describe tornados mathematically? This spring, at our Indiana State University meeting, our keynote speaker will be Professor James Serrin, from the University of Minnesota. Friday night after dinner, he will show us what tornados look like and Saturday at the plenary talk, we will learn about how to mathematically model these swirling vortices. Our program is packed with a wide range of talks contributed by both faculty and students, addressing topics such as Cryptography, Numerical Ecology, Arabic Algebra, Lesson Planning, College Admission Decisions, Baseball, and Multivariable Calculus.
On Friday, we will host the 39^{th} annual Indiana College Mathematics Competition (ICMC). Again this spring, registration for the ICMC will be done on-line through the section's website. On Saturday, in addition to the talks, there will be a session on the contest solutions, and two workshops for students. Patricia Oakley from Goshen College is offering an Undergraduate Student Workshop on Fractals in Linear Algebra. Josh Holden from Rose-Hulman and Wesley Calvert from Notre Dame are organizing a Graduate Student Workshop that will address issues relevant to today’s graduate student.
The meeting has something for everyone! See you there.
Mike
Friday, April 2, 2004
3:00--3:50 ICMC Registration
3:00--4:30 Meeting Registration
3:00--6:00 MAA Book Sale
4:00--4:15 ICMC Instructions
4:15--6:15 ICMC
4:00--6:00 The FAST-SLO Algorithm for Lesson Planning Matt DeLong (Taylor University), Dale Winter (Bowling Green State University), and Carolyn Yackel (Mercer University).
In this workshop we will present and explore an algorithm for using a concept-map-like tool to produce student-learning objectives for instructional planning in college-level mathematics. First, we will present the FAST (Fact Action Scheme Transcript) tool for de-encapsulating the mathematics instructor's mathematical knowledge into its cognitive elements and their connections. We then will define a specific notion of student learning objectives (SLOs) and discuss advantages of grounding instruction in a set of such explicit learning objectives. We will then describe an algorithm for turning an instructor's FASTs into SLOs. Finally, we will discuss how to plan student-centered lessons based on the identified SLOs. The overarching goal will be to equip instructors to transform their knowledge of the content to be taught into objectives-based student-centered lesson plans. This will be a hands-on workshop in which participants will be encouraged and expected to produce their own examples of the tools presented.
4:00--4:25 Cover Pebbling Number of Graphs Zsuzsanna Szaniszlo (Valparaiso University).
Cover pebbling is a variation of the pebbling game on graphs. A pebbling move consists of lifting two pebbles from a vertex and moving one of them along an edge to another vertex. Given a graph, the cover pebbling number of a graph is the smallest number of pebbles so that regardless of the distribution of the pebbles a pebble can be moved to every vertex of the graph simultaneously using pebbling moves. We find the cover pebbling number of certain graphs, including those of trees. We present several open problems.
4:30--4:55 Analyzing Transposition Ciphers with Permutations Robert Talbert (Franklin College).
One of the oldest methods of encoding a message is the transposition cipher, which enciphers messages by permuting the positions of the plaintext characters. Their structure makes them ideally suited for analysis using permutations and permutation groups. In this talk, we analyze the ``rail-fence'' cipher and columnar transposition ciphers, arriving at an explicit formula for the permutations which implement these ciphers. Knowing the permutation will then let us explore the security (or lack thereof) of transposition ciphers. We specifically take a look at the effects of iterating a transposition cipher on a plaintext.
5:00--5:25 Have You Seen These Theorems? Three Geometric Gems That Used to be Part of Multivariable Calculus Robert Foote (Wabash College)
I'm always on the lookout for neat geometric things I can do when I teach multivariable calculus. I found these delightful results in old calculus books. Why aren't they in current books?
5:30--6:00 Creating Interactive Web Pages Peter Turbek (Purdue University Calumet)
For the past year the author has been developing the CAS Math project. It's goal is the construction of a freeware package that facilitates the easy construction of interactive web pages for mathematics and the sciences. CAS Math pages are written in standard HTML or XML and use JavaScript as a programming language. With it, graphs can be constructed and manipulated by students ön the fly", and questions and scenarios can be dynamically generated in response to student input. The talk will highlight the capabilities of the package and describe its construction.
6:30--7:30 Banquet
7:30--7:45 Awards
7:45--8:45 What do Tornadoes Look Like? James Serrin (University of Minnesota)
Saturday, April 3, 2004
7:30--8:15 Chairs & Liaison Breakfast
8:00--9:00 Registration
8:00--3:00 MAA Book Sale
9:00--9:05 Welcome ISU Representative
9:05--9:25 The Hawkins Random Sieve John Lorch (Ball State University)
A simple probabilistic variation of Eratosthenes' sieve is used to create sequences of `Hawkins primes.' As a model for the `real' primes, we see that the Hawkins primes are both reasonable and useful.
NOTE: The next three lists describe parallel sessions.
Session 1
9:30--9:55 An Exploration of the Focus-Directrix Definition of the Conics Elizabeth Brown (Indiana State University)
We will explore the effects of varying eccentricity on the conic sections using focus-directrix graph paper. This is an easy, low-tech way to explore conic sections with undergraduates and high school students.
10:00--10:15 Recirculation Models and Biotech Applications Mark Bailey, Mark Hilgert, and Herb Bailey (Rose-Hulman Institute of Technology).
Product separation by homogenization is an important operation in biotechnology applications. In this talk we consider two recirculation models of this operation and compare the results with repeated batch homogenization.
The continuous recirculation model leads to a sequence of differential equations. The partial batch model leads to a partial difference equation. We discuss both analytical and spread sheet solutions of these equations.
10:20--10:35 Zeros of the Partial Sums of e^{z} Amos Carpenter (Butler University)
Let s_{n}(z) : = å_{j = 0}^{n}[(z^{j})/ j!], n ³ 1, be the familiar partial sum of the exponential function e^{z}, and let z_{k,n} be the k-th zero (counted in the sense of increasing argument) of s_{n}(z). In this talk we give a formal power series expansion for z_{k,n} which we use to obtain asymptotic approximations for z_{k,n} as n ® ¥.
10:40-10:55 Trisecting an Angle Stephen Chamblee (Indiana State University)
An original method for trisceting an angle using a compass, a straight edge, and an infinite number of steps.
11:00--11:25 What the Shortstop Sees Elton Graves (Rose-Hulman Institute of Technology)
In this paper the author will use the concepts of related rate, tangent line, implicit differentiation, unit vectors, and dot products to answer the following question. A runner on first base tries to steal second base. Assume the catcher throws the ball to second base at an average speed of 70 mph and the speed of the runner is 30 feet per second. How fast is the distance between the runner and the ball changing when the base runner is 10 feet from second base and the ball is 30 feet from second base. The problem will be generalized to find the rate of change of distance between any two moving bodies whose paths intersect.
11:30--11:55 An Application of Linear Algebra in Numerical Ecology John Boardman (Franklin College)
Since the data in most ecological studies is autocorrelated, ecologists must look beyond classical statistics to analyze these complex data sets. This talk will describe how linear algebra is used extensively in the analysis of multidimensional data and will discuss the method of Principal Component Analysis (PCA).
Session 2
9:30--9:55 If You Walk n Steps in a Hyperbolic Graph, How Many Paths Can You Take? Chris Wu (Penn State University, Beaver Campus)
Imagine that you are standing at an intersection in a city where the street system is like a square grid. You choose a street at random and begin walking away. At each intersection you reach, you choose either to continue straight ahead or to turn left or right. There is only one rule: you must not return to any intersection which you have visited. In other words, your path should be self-avoiding. One of the fundamental questions is: if you walk n blocks, how many possible paths could you have followed?
What we have described above is the self-avoiding walk on the square lattice. In this talk we will first give an intuitive definition on hyperbolic graphs and then introduce self-avoiding walks on these graphs. It only requires the first year calculus to understand this talk. This is a joint work with J. Barry, an undergraduate student at Penn State.
10:00--10:30 Arabic Algebra and its Latin Translations Jeffrey Oaks (University of Indianapolis)
Al-jabr (restoration) and al-muq¯abala (confrontation) are the names of two steps in the solutions of equations in medieval Arabic algebra. Combined into a phrase, al-jabr wa'l-muq¯abala was the name given to the art of algebra. Our word ``algebra" in fact derives from al-jabr.
A careful look into the uses of these terms forms the backdrop to a discussion of the role of algebra within Islamic society, and its transmission to the Latin west in the 12th century.
10:35--10:55 The Butler Game Rebecca Wahl (Butler University)
An analysis of an acyclic digraph and its application to a two-person combinatorial game.
11:00--11:25 What Happens to the Fundamental Theorem of Arithmetic when `Product' is Replaced by 'Sum"? William Weakley (IPFW)
The Fundamental Theorem of Arithmetic assures us that each integer $n > 1$ has an essentially unique expression as a product of prime numbers. If we consider sums instead of products, some restrictions will be needed if we wish to have uniqueness of expression. We consider different types of restrictions and their corresponding analogue of prime numbers.
11:30--11:55 A Mathematical Programming Approach to College Admissions Decisions Concetta DePaolo (Indiana State University)
Session 3
9:30--10:30 ICMC Solutions
10:35--10:55 The Range Nucleolus for Cooperative Games Andrew Histand (Goshen College)
The nucleolus is a well known allocation method for cooperative games. This presentation proposes a variation of the nucleolus, the range nucleolus. While the nucleolus lexicographically minimizes the excess vector, the range nucleolus lexicographically minimizes the range vector, which is the vector of all of the differences between two excesses, arranged from highest to lowest. The range nucleolus is proven to be individually rational and to have the dummy axiom. Also shown are several interesting properties of the extremal excesses and the players involved with them.
11:00--11:55 Graduate Student Workshop-Part 1 Wesley Calvert (Notre Dame University) and Joshua Holden (Rose-Hulman Institute of Technology)
11:00--11:55 Undergraduate Student Workshop: Fractals in Linear Algebra-Part 1 Patricia Oakley (Goshen College)
Fractals can be constructed by affine transformations and affine transformations can be understood via the language of linear algebra. In this workshop, we will look at constructing such fractals and explore the linear algebra concepts used in creating the fractals and understanding their properties.
12:00--1:00 Lunch
1:00--1:55 Graduate Student Workshop-Part 2
1:00--1:55 Undergraduate Student Workshop: Fractals in Linear Algebra-Part 2
1:00--1:55 Business Meeting
2:00--3:00 The Swirling Vortex: A Mathematical Model for Tornadoes James Serrin (University of Minnesota)
SPRING 2004 MEETING INFORMATION
Campus Map
Look here for an ISU map. (Holmstedt Hall, at the center of campus and labeled 23 on the map below, is the main meeting site.)
Directions to Indiana State University
(Traveling east on Interstate 70) Take Exit 7 (U.S. 41) and turn north. Travel 2.5 miles to Wabash Avenue. Turn right (east) on Wabash Avenue. Travel to Fifth Street (stoplight). Turn left and travel three blocks to Spruce Street. Turn right and park in Visitors' Pay Lot A.
(Traveling west on Interstate 70) Take Exit 11 (S.R. 46) and turn north. Travel 2.5 miles to S.R. 40 (Wabash Avenue). Turn left (west) on Wabash Avenue. Travel to Fifth Street (stoplight). Turn right and travel three blocks to Spruce Street. Turn right and park in Visitors' Pay Lot A.
(Traveling south on U.S. 41) Turn left (east) on Ohio Street and travel to Fifth Street (stoplight). Turn left. Travel four blocks to Spruce Street. Turn right and park in Visitors' Pay Lot A.
(Traveling north on U.S. 41) Turn right (east) on Wabash Avenue and travel to Fifth Street (stoplight). Turn left. Travel three blocks to Spruce Street. Turn right and park in Visitors' Pay Lot A.
Parking on Campus
For both days of the meeting (April 2-3), participants can park in Lot A North of the University Library for free. To find Lot A, see the driving directions given above or the campus map given below.
Meeting Registration
The MAA meeting will be held in Holmstedt Hall and registration will be held on April 2nd. Registration will begin at 3PM. The regular meeting registration fee is $10.00. Cash and personal checks made out to Ïndiana Section, MAA" will be accepted. There is no registration fee for students or speakers. All participants, including students and speakers, are expected to sign-in at the registration table. Please note that Indiana State University is a smoke free environment.
Meeting and Meal Reservations
We would appreciate all persons planning to attend the meeting to let us know in advance. Your name tag will be prepared, and you will spend less time in the registration line.
Lunch (Saturday, April 3) will be served at Sycamore Towers (54 on the ISU Map) and will cost $7.00 per person. The lunch will be a buffet.
Dinner (Friday, April 2) will be served at Hulman Center (54 on the ISU Map) and you should enter on the west side 8th Street entrance. Dinner will be a buffet and the cost is $18.00. The dinner menu includes Sumac Chicken - (chicken breast topped with sumac, lemon, garlic, and onions); Spinach Pies; Rice with Green Bean Sauce; Cucumber Salad; Chocolate Bars, Backlava, Lemon Bars; Coffee, Tea, lemonade.
Advanced reservation for the banquet and/or lunch is required and must be made no later than March 26. Payment should be made at the meeting registration table. To place your meeting and lunch reservation, send an e-mail message to masam (at) isugw.indstate.edu. Please include
your name as you would like it to appear on your name tag;
the name of your school or company;
whether you are a student, faculty, or other;
whether you are a member of the MAA; and
whether you will be coming to lunch.
E-mail reservations will be acknowledged by e-mail. If you prefer voice to print, call Arvana Edwards at 812-237-2130.
Accommodations
Blocked rooms (with discounts) have been negotiated with the following hotels:
Holiday Inn (I-70 and US 41)
3300 U.S. Highway 41 S.
Terre Haute, IN 47802
(812) 232-6081
$74.00 plus tax until March 19, 2004. Mention INMAA conference at ISU.
Drury Inn (I-70 and US 41)
3040 U.S. Highway 41 S.
Terre Haute, IN 47802
(812) 238-1206
$79.99 plus tax until March 19, 2004. Mention IMAA Conference at
ISU.
Additional hotels may be found at http://www.terrehaute.com/lodging.asp.
Information for Student Presenters
The Indiana Section of the MAA awards free memberships to all students (including graduate students) who present papers at an Indiana Section meeting. The recipients of these memberships are allowed to select any one journal. In case the prize winner is already a member, an MAA-published book can be substituted for the membership
2004 ICMC
All colleges and universities throughout the state are invited to register three-member teams of undergraduate students to compete in the Indiana Mathematics Competition (ICMC). This year's contest will mark the 39th anniversary of the competition. It will take place at Butler University in conjunction with the Indiana Section Spring Meeting.
The competition will be held Friday afternoon, April 2, starting with on-site registration from 3:00-3:50pm. A briefing session on the competition will begin at 4:00pm and the test will be administered from 4:15-6:15pm immediately following the briefing. The math competition is held on Friday afternoon so that students have the opportunity to fully participate in the MAA meeting held during Friday evening and all day Saturday. The test will be graded overnight and the winning teams announced at the business meeting on Saturday afternoon.
The ICMC is designed as a team competition, with members of the team working together on the test and turning in a single team solution for each problem attempted. No books, calculators, computers, slide rules, rulers, compasses, or other such aides will be allowed in the testing rooms. The contest questions are designed in such a way that a calculator provides no significant advantage to any team.
Each school may enter as many teams as desired; those teams must register in advance. There is a $5.00 registration fee per team. Team members wishing to attend the dinner and luncheon must also make reservations. (See ACCOMMODATIONS and MEAL RESERVATIONS above.)
It is strongly recommended that teams pre-register for ICMC, so that the host institution can reserve enough rooms for the contest. Teams that pre-register will be guaranteed admission to the contest, while those teams that register on-site will be granted admission provided that space is available.
Teams may pre-register online by visiting the INMAA website http://www.maa.org/indiana.
Local Organizer
For general information regarding the meeting contact Robert Jaycay (jajcay (at) laurel.indstate.edu 812-237-2138).
NEWS FROM AROUND THE MAA
Professional Enhancement Program
The MAA's Professional Enhancement Program (PREP) will offer a wide variety of workshops during summer 2004. PREP workshops offer you the chance to spend a few days exploring topics of mutual interest with colleagues from other institutions, with experienced leaders to guide the group towards a deeper understanding and broader perspective. Most of the cost of attending a PREP workshop is covered by the program, so what are you waiting for? Visit the PREP web site, http://www.maa.org/prep to see this year's schedule and to obtain registration materials.
Preparing Mathematicians to Educate Teachers
A growing set of national reports calls for better preparation of the nation's mathematics teachers by mathematics faculty. To help meet this need, the MAA is organizing a multifaceted program, Preparing Mathematicians to Educate Teachers (PMET). The PMET program will have three major components:
Faculty Training: Workshops of varying duration throughout the year and minicourses at professional meetings;
Information and Resources: Articles in professional journals, panels at meetings, multimedia web sites and hard-copy material to support faculty instruction for teachers;
Mini-grants and Regional Networks: To nurture and support grassroots innovation in teacher education on individual campuses. The initial regional networks will be in California, New York, North Carolina, Nebraska, and Ohio.
Faculty who are interested in attending a
PMET workshop should visit the PMET web site for more information.
http://www.maa.org/pmet
SECTION NEWS
Ball State University
The Department of Mathematical Sciences at Ball State University has introduced a new journal for undergraduate research in the mathematical sciences: the Ball State Undergraduate Mathematics Exchange. An online version of the first issue of this publication can be found at www.bsu.edu/math/exchange.
The Exchange is a forum for student activities, which are not necessarily original research but go beyond standard classroom material. Among other information, every issue contains senior thesis abstracts, extra curricular projects, as well as seminar and colloquium papers.
The target audience of the journal consists of majors in any of the mathematical sciences. Contributions are accepted from all undergraduates who have worked on a mathematical topic beyond the classroom. Appropriate papers from other departments and other institutions are welcome. Please visit the above website for more information.
Indiana University Northwest
The Department of Mathematics and Actuarial Science is pleased to welcome Dr. Gayla S. Domke as a visiting associate professor in the Spring 2004. Dr. Domke is a graph theorist and is on leave from Georgia State University.
Indiana University South Bend
The Indiana University South Bend Masters Program in Applied Mathematics and Computer Science anticipates having its first graduate this semester. There are over 40 students admitted to the program, 22 of which are currently taking courses.
The Master of Science in Applied Mathematics and Computer Science at IUSB started in fall 2001. It is a joint degree program between the Department of Mathematical Sciences and Department of Computer and Information Sciences. This 36-credit hour degree program meets the needs of professionals who have undergraduate degrees in mathematics, computer science or engineering; those who are in transition from other disciplines; and those who wish to seek advanced degrees to enter academia.
Also:
Morteza Shafii-Mousavi, the new INMAA Liaison for IUSB, had a well-earned sabbatical leave during fall 2003.
Yu Song is the new department chair at IUSB, starting fall 2003.
University of Southern Indiana
Dr. Adrian Gentle from Los Alamos National Laboratory came to the University of Southern Indiana as an Assistant Professor of Mathematics in the fall of 2004. Dr. Gentle’s research at Los Alamos focused on the numerical solution of the Einstein equations. He is currently developing computer codes to investigate the stability of his recent reformulation of the Einstein equations to actively enforce the constraints within the evolution algorithm. He plans to present this work at the Seventeenth Meeting of the International Society on General Relativity and Gravitation, to be held Dublin, Ireland, in July 2004.
Dr. Gene Freudenburg, Associate Professor of Mathematics, spent the month of June 2003 visiting a research colleague at the University of Bourgogne in Dijon, France. He also gave talks in Seville, Spain and Basel, Switzerland. In September, Dr. Freudenburg spent a week in Lukecin, Poland conducting a workshop for graduate students in mathematics. Daniel Daigle of the University of Ottawa assisted with this workshop. The theme of the workshop was Group Actions in Algebraic Geometry, which is the subject of much of Professor Freudenburg's research.
Dr. Ruben Schwieger, Associate Professor of Mathematics at the University of Southern Indiana, is working on a funded project to design and produce a prototype of a solar powered shallow well water pump for use in underdeveloped parts of the world where there is no fossil fuel or machinery and machinery maintenance available. An engineering student, Rodney Taylor, is working with Dr. Schwieger and using this task as his senior project. The hope is to field test the prototype in rural East Africa where people have plenty of sunshine but difficulty getting water to the surface.
Wabash College
Peter Thompson was tenured.