Proposals
Below are some proposals for talks from the past (and current). By clicking on the ID number, more details are shown. By default, these are sorted chronologically (recent first) and by then by last name. The data can be sorted by alternate means by using the links at the top right, each allowing ascending or descending orders.
Displaying 101-120 of 471 results.
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ID:
176
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Vignettes in Number Theory
Abstract: Properties and the history of several numbers that lend themselves naturally to undergraduate research projects will be discussed. Topics include Demlo numbers, polite numbers, sad numbers, decimal Columbian numbers, Smith numbers, and Niven numbers.
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Vignettes in Number Theory
Abstract: Properties and the history of several numbers that lend themselves naturally to undergraduate research projects will be discussed. Topics include Demlo numbers, polite numbers, sad numbers, decimal Columbian numbers, Smith numbers, and Niven numbers.
ID:
177
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
ID:
179
Year: 2007
Name: Russell Goodman
Institution: Central College
Subject area(s): Pedagogy; Elementary Mathematics
Title of Talk: Using Oral Exams to Help Prepare Future Elementary Mathematics Teachers
Abstract: The ability to effectively communicate mathematics is a priority for future elementary mathematics teachers. An oral examination, if used appropriately, is an excellent tool for assessing such skills. Moreover, an oral exam is a useful pedagogical tool for helping future elementary mathematics teachers improve their skills in communicating mathematical concepts. <br><br> The speaker has used oral exams in his department
Year: 2007
Name: Russell Goodman
Institution: Central College
Subject area(s): Pedagogy; Elementary Mathematics
Title of Talk: Using Oral Exams to Help Prepare Future Elementary Mathematics Teachers
Abstract: The ability to effectively communicate mathematics is a priority for future elementary mathematics teachers. An oral examination, if used appropriately, is an excellent tool for assessing such skills. Moreover, an oral exam is a useful pedagogical tool for helping future elementary mathematics teachers improve their skills in communicating mathematical concepts. <br><br> The speaker has used oral exams in his department
ID:
180
Year: 2007
Name: Wendy Weber
Institution: Central College
Subject area(s): teaching prospective teachers
Title of Talk: Mathematical Questions from the Classroom
Abstract: How can we bridge the gap between prospective teachers
Year: 2007
Name: Wendy Weber
Institution: Central College
Subject area(s): teaching prospective teachers
Title of Talk: Mathematical Questions from the Classroom
Abstract: How can we bridge the gap between prospective teachers
ID:
181
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
ID:
182
Year: 2007
Name: Jean Clipperton
Institution: Simpson College
Subject area(s): Graph Theory
Title of Talk: Strong Signals: L(d,2,1)-Labeling on Simple Graphs
Abstract: An L(d, 2, 1)-labeling is a simplified model for the channel assignment problem. It is a natural generalization of the widely studied L(2, 1) and L(3, 2, 1)-labeling. An L(d, 2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of positive integers such that if the distance between vertices x and y is 1, then |f (x)- f (y)| >= d; if the distance between x and y is 2, then |f (x)- f(y)| >= 2; and if the distance between x and y is 3, then |f (x)- f (y)| >= 1. The L(d, 2, 1)-labeling number k_d(G) of G is the smallest positive integer k_d such that G has an L(d, 2, 1)-labeling with k_d as the maximum label. This talk will present general results for k_d when labeling simple graphs, such as paths, bipartite graphs, and cycles.
Year: 2007
Name: Jean Clipperton
Institution: Simpson College
Subject area(s): Graph Theory
Title of Talk: Strong Signals: L(d,2,1)-Labeling on Simple Graphs
Abstract: An L(d, 2, 1)-labeling is a simplified model for the channel assignment problem. It is a natural generalization of the widely studied L(2, 1) and L(3, 2, 1)-labeling. An L(d, 2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of positive integers such that if the distance between vertices x and y is 1, then |f (x)- f (y)| >= d; if the distance between x and y is 2, then |f (x)- f(y)| >= 2; and if the distance between x and y is 3, then |f (x)- f (y)| >= 1. The L(d, 2, 1)-labeling number k_d(G) of G is the smallest positive integer k_d such that G has an L(d, 2, 1)-labeling with k_d as the maximum label. This talk will present general results for k_d when labeling simple graphs, such as paths, bipartite graphs, and cycles.
ID:
186
Year: 2007
Name: David Romano
Institution: Grinnell College
Subject area(s): Convex geometry
Title of Talk: Connected goalies for convex polygons
Abstract: Given a compact convex body K in the plane, call a connected 1-dimensional set G in the plane a goalie if it intersects all the straight lines that intersect K. This talk is concerned with the problem of finding the minimal length goalie for polygons. For any polygon P with n sides, we prove that any shortest goalie G for P has convex hull CH(G) a polygon with at most 2n sides. For triangles T, the minimal length goalie is the Steiner minimal tree for T. This is no longer true in the case of quadrilaterals, in which case a Steiner minimal tree need not be a minimal goalie.
Year: 2007
Name: David Romano
Institution: Grinnell College
Subject area(s): Convex geometry
Title of Talk: Connected goalies for convex polygons
Abstract: Given a compact convex body K in the plane, call a connected 1-dimensional set G in the plane a goalie if it intersects all the straight lines that intersect K. This talk is concerned with the problem of finding the minimal length goalie for polygons. For any polygon P with n sides, we prove that any shortest goalie G for P has convex hull CH(G) a polygon with at most 2n sides. For triangles T, the minimal length goalie is the Steiner minimal tree for T. This is no longer true in the case of quadrilaterals, in which case a Steiner minimal tree need not be a minimal goalie.
ID:
187
Year: 2007
Name: Thomas Britton
Institution: Coe College
Subject area(s):
Title of Talk: Dots and Lines
Abstract:
Year: 2007
Name: Thomas Britton
Institution: Coe College
Subject area(s):
Title of Talk: Dots and Lines
Abstract:
ID:
188
Year: 2007
Name: Neil Martinsen-Burrell
Institution: Wartburg College
Subject area(s): applied math, dynamical systems
Title of Talk: Assimilating Drifter Trajectories using Gradient Descent
Abstract: In geophysics, we frequently try to couple dynamical models of physical systems such as the atmosphere or ocean with direct observations of those systems. In the atmosphere, with fixed observing stations, there are advanced techniques for Numerical Weather Prediction. In the ocean, observations are often made by objects that drift with the flow. This presents difficulties for conventional data assimilation methods. I will discuss one possible way to assimilate drifter trajectories into a very simple dynamical model.
Year: 2007
Name: Neil Martinsen-Burrell
Institution: Wartburg College
Subject area(s): applied math, dynamical systems
Title of Talk: Assimilating Drifter Trajectories using Gradient Descent
Abstract: In geophysics, we frequently try to couple dynamical models of physical systems such as the atmosphere or ocean with direct observations of those systems. In the atmosphere, with fixed observing stations, there are advanced techniques for Numerical Weather Prediction. In the ocean, observations are often made by objects that drift with the flow. This presents difficulties for conventional data assimilation methods. I will discuss one possible way to assimilate drifter trajectories into a very simple dynamical model.
ID:
189
Year: 2007
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Dynamical Systems
Title of Talk: Pseudo-Random Walks
Abstract: In a recent Monthly article, O'Bryant, Reznick and Serbinowska [ORS] have given some fascinating new insights into the behavior of \[ S_{N}(\alpha) := \sum_{n=1}^N (-1)^{[n\alpha]} \] where [x] is the integer part of x. Since the fractional part of n*\alpha for n=1,2,3,\dots behaves 'random-ish', one can make various guesses and apply classical methods like exponential sums to explore these hypotheses. Remarkably, the guesses are often wrong and the classical methods don't seem to work very well. Instead, [ORS] use continued fractions to obtain sharp and explicit upper and lower bounds for |S_{\alpha}(N)| in terms of \log N, and as a by-product get a way of evaluating S_{\alpha}(N) for large N with amazing efficiency.\\ We will explain that last part of their work. Then we will show how to use exponential sums with a twist that gives a lower bound for |S_{\alpha}(N)| - less explicit, but more general than what the methods from [ORS] give you. And if we omit tedious computations (which we will, and which are only long, not hard), the approach is as clear-cut and beautiful as that using exponential sums to the case of the fractional part of n*\alpha. Lit.: K.~O'Bryant, B.~Reznick, M.~Serbinowska: {\em Almost alternating sums}, Monthly vol.~113/8, pp. 673-688. Prerequisites: only complex exponentials e^{it}.
Year: 2007
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Dynamical Systems
Title of Talk: Pseudo-Random Walks
Abstract: In a recent Monthly article, O'Bryant, Reznick and Serbinowska [ORS] have given some fascinating new insights into the behavior of \[ S_{N}(\alpha) := \sum_{n=1}^N (-1)^{[n\alpha]} \] where [x] is the integer part of x. Since the fractional part of n*\alpha for n=1,2,3,\dots behaves 'random-ish', one can make various guesses and apply classical methods like exponential sums to explore these hypotheses. Remarkably, the guesses are often wrong and the classical methods don't seem to work very well. Instead, [ORS] use continued fractions to obtain sharp and explicit upper and lower bounds for |S_{\alpha}(N)| in terms of \log N, and as a by-product get a way of evaluating S_{\alpha}(N) for large N with amazing efficiency.\\ We will explain that last part of their work. Then we will show how to use exponential sums with a twist that gives a lower bound for |S_{\alpha}(N)| - less explicit, but more general than what the methods from [ORS] give you. And if we omit tedious computations (which we will, and which are only long, not hard), the approach is as clear-cut and beautiful as that using exponential sums to the case of the fractional part of n*\alpha. Lit.: K.~O'Bryant, B.~Reznick, M.~Serbinowska: {\em Almost alternating sums}, Monthly vol.~113/8, pp. 673-688. Prerequisites: only complex exponentials e^{it}.
ID:
190
Year: 2007
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): sequences, number theory, dynamics, fractals
Title of Talk: The Mean-Median Map
Abstract: Starting with a non-empty finite set S_n={x_1,\ldots,x_n} contained in R, generate the unique number x_{n+1} which satisfies the mean-median equation (x_1 + \cdots + x_n + x_{n+1}/(n+1) = median(S_n) . As usual, we define the median of the set S_n = {x_1,\ldots,x_n}, where x_1<= ... <= x_n, as median (S_n) = \left\{ x_{(n+1)/2}, n odd , \frac{x_{n/2} + x_{n/2+1}}{2}, n even . By applying the mean-median equation repeatedly to a set one generates an infinite sequence {x_k}_{k=1}^\infty. The dynamics of this map are surprising! Most maps tend to have either relatively simple dynamics or chaotic dynamics. While the mean-median map seems to be asymptotically constant, it seems very hard to predict. This talk will showcase the work done to date. This is joint work with Mario Martelli (Claremont McKenna College).
Year: 2007
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): sequences, number theory, dynamics, fractals
Title of Talk: The Mean-Median Map
Abstract: Starting with a non-empty finite set S_n={x_1,\ldots,x_n} contained in R, generate the unique number x_{n+1} which satisfies the mean-median equation (x_1 + \cdots + x_n + x_{n+1}/(n+1) = median(S_n) . As usual, we define the median of the set S_n = {x_1,\ldots,x_n}, where x_1<= ... <= x_n, as median (S_n) = \left\{ x_{(n+1)/2}, n odd , \frac{x_{n/2} + x_{n/2+1}}{2}, n even . By applying the mean-median equation repeatedly to a set one generates an infinite sequence {x_k}_{k=1}^\infty. The dynamics of this map are surprising! Most maps tend to have either relatively simple dynamics or chaotic dynamics. While the mean-median map seems to be asymptotically constant, it seems very hard to predict. This talk will showcase the work done to date. This is joint work with Mario Martelli (Claremont McKenna College).
ID:
191
Year: 2007
Name: Mark Mills
Institution: Central College
Subject area(s):
Title of Talk: What I did on my sabbatical: Experiencing the "real world"
Abstract: In an effort to gain some "real world" experience with mathematics and statistics during my sabbatical this year, I have been working at a local windows manufacturer doing a number of things that involve mathematical and statistical thinking. This talk will describe some of the things I have been doing, as well as some of the things I have learned through the experience. I will also discuss how I went about setting-up this experience, how I think my employer perceives my experiences, and how I expect this to be something that lasts beyond this year.
Year: 2007
Name: Mark Mills
Institution: Central College
Subject area(s):
Title of Talk: What I did on my sabbatical: Experiencing the "real world"
Abstract: In an effort to gain some "real world" experience with mathematics and statistics during my sabbatical this year, I have been working at a local windows manufacturer doing a number of things that involve mathematical and statistical thinking. This talk will describe some of the things I have been doing, as well as some of the things I have learned through the experience. I will also discuss how I went about setting-up this experience, how I think my employer perceives my experiences, and how I expect this to be something that lasts beyond this year.
ID:
192
Year: 2007
Name: Chris Kurth
Institution: Iowa State University
Subject area(s): Number Theory
Title of Talk: Farey Symbols and subgroups of $SL_2(Z)$
Abstract: The structure of subgroups of SL_2(Z) (2x2 integer coefficient matrices with determinant 1) is important in the study of modular forms. Associated to these subgroups is an object called a Farey Symbol which contains the structure of the group in a very compact form. For instance, from the Farey Symbol one can easily calculate an independent set of generators for the group, a coset decomposition, and determine if the group is congruence. In this talk, I will discuss finite index subgroups of SL_2(Z)$ and the computation and use of Farey Symbols for these subgroups.
Year: 2007
Name: Chris Kurth
Institution: Iowa State University
Subject area(s): Number Theory
Title of Talk: Farey Symbols and subgroups of $SL_2(Z)$
Abstract: The structure of subgroups of SL_2(Z) (2x2 integer coefficient matrices with determinant 1) is important in the study of modular forms. Associated to these subgroups is an object called a Farey Symbol which contains the structure of the group in a very compact form. For instance, from the Farey Symbol one can easily calculate an independent set of generators for the group, a coset decomposition, and determine if the group is congruence. In this talk, I will discuss finite index subgroups of SL_2(Z)$ and the computation and use of Farey Symbols for these subgroups.
ID:
193
Year: 2007
Name: Evan Jones
Institution: Coe College
Subject area(s): Combinatorial games theory
Title of Talk:
Abstract: I conducted research in the summer of 2006 dealing with the game of Hex, the two player combinatorial game developed independently by Piet Hein and John Nash. I wanted to know if modifying the game board by removing available playing spaces would effect the outcome of the game. I analyzed a 3x3 size board, then a 5x5 board, and some preliminary work on a 7x7 board.
Year: 2007
Name: Evan Jones
Institution: Coe College
Subject area(s): Combinatorial games theory
Title of Talk:
Abstract: I conducted research in the summer of 2006 dealing with the game of Hex, the two player combinatorial game developed independently by Piet Hein and John Nash. I wanted to know if modifying the game board by removing available playing spaces would effect the outcome of the game. I analyzed a 3x3 size board, then a 5x5 board, and some preliminary work on a 7x7 board.
ID:
194
Year: 2007
Name: Ronald Smith
Institution: Graceland University
Subject area(s):
Title of Talk: Optimal arrangement of digits
Abstract: Problem: Arrange a sequence of mn positive digits into m n-digit numbers whose product is minimized or maximized. We show how to recognize optimal arrangements of digits, and give an efficient algorithm for finding solutions.
Year: 2007
Name: Ronald Smith
Institution: Graceland University
Subject area(s):
Title of Talk: Optimal arrangement of digits
Abstract: Problem: Arrange a sequence of mn positive digits into m n-digit numbers whose product is minimized or maximized. We show how to recognize optimal arrangements of digits, and give an efficient algorithm for finding solutions.
ID:
195
Year: 2007
Name: Tim Schwickerath
Institution: Wartburg College
Subject area(s):
Title of Talk: Historical Roots of Math and Physics in Germany
Abstract: In May 2006, a class of thirteen students and Dr. Brian Birgen from Wartburg College toured Germany and examined math and physics from a historical perspective. The class toured various musuems and universities all around Germany. The class also explored the German culture through home stays and other experiences. Two students from the class will share and discuss highlights of their experiences.
Year: 2007
Name: Tim Schwickerath
Institution: Wartburg College
Subject area(s):
Title of Talk: Historical Roots of Math and Physics in Germany
Abstract: In May 2006, a class of thirteen students and Dr. Brian Birgen from Wartburg College toured Germany and examined math and physics from a historical perspective. The class toured various musuems and universities all around Germany. The class also explored the German culture through home stays and other experiences. Two students from the class will share and discuss highlights of their experiences.
ID:
196
Year: 2007
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Undergraduate Mathematics Teaching
Title of Talk: Why Do Students Have Textbooks?
Abstract: Textbooks should be readable and students should read them! In fact, students should be expected to read the textbook before they come to class!! Reading questions test student
Year: 2007
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Undergraduate Mathematics Teaching
Title of Talk: Why Do Students Have Textbooks?
Abstract: Textbooks should be readable and students should read them! In fact, students should be expected to read the textbook before they come to class!! Reading questions test student
ID:
197
Year: 2007
Name: Tim Schwickerath
Institution: Wartburg College
Subject area(s):
Title of Talk: Historical Roots of Math and Physics in Germany
Abstract: In May 2006, a class of thirteen students and Dr. Brian Birgen from Wartburg College toured Germany and examined math and physics from a historical perspective. The class toured various musuems and universities all around Germany. The class also explored the German culture through home stays and other experiences. Two students from the class will share highlights of their experiences.
Year: 2007
Name: Tim Schwickerath
Institution: Wartburg College
Subject area(s):
Title of Talk: Historical Roots of Math and Physics in Germany
Abstract: In May 2006, a class of thirteen students and Dr. Brian Birgen from Wartburg College toured Germany and examined math and physics from a historical perspective. The class toured various musuems and universities all around Germany. The class also explored the German culture through home stays and other experiences. Two students from the class will share highlights of their experiences.
ID:
198
Year: 2007
Name: Al Hibbard
Institution: Central College
Subject area(s):
Title of Talk: Overview of the version of Mathematica currently in development
Abstract: This talk will look at some of the new features that are being developed for the version of Mathematica currently in development. An overview will be given as well as some illustrations of how to exploit some of the new features.
Year: 2007
Name: Al Hibbard
Institution: Central College
Subject area(s):
Title of Talk: Overview of the version of Mathematica currently in development
Abstract: This talk will look at some of the new features that are being developed for the version of Mathematica currently in development. An overview will be given as well as some illustrations of how to exploit some of the new features.
ID:
199
Year: 2007
Name: Mark Mills
Institution: Central College
Subject area(s):
Title of Talk: An algorithm for creating "equal" regions
Abstract: This talk will discuss an algorithm that is still in development. The goal of the algorithm is to take a large area that has been broken up into counties and use some quantifiable information for each county (e.g., population) to create a given number of geographically compact regions having relatively equal quantities. The speaker will discuss the evolution of the algorithm from first being a greedy algorithm to now being what you might call an "altruistic" algorithm.
Year: 2007
Name: Mark Mills
Institution: Central College
Subject area(s):
Title of Talk: An algorithm for creating "equal" regions
Abstract: This talk will discuss an algorithm that is still in development. The goal of the algorithm is to take a large area that has been broken up into counties and use some quantifiable information for each county (e.g., population) to create a given number of geographically compact regions having relatively equal quantities. The speaker will discuss the evolution of the algorithm from first being a greedy algorithm to now being what you might call an "altruistic" algorithm.