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 81-100 of 471 results.
ID: 154
Year: 2006
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Graph theory / mathematical biology
Title of Talk: Reconstructing genomes in the presence of hybridizations

Abstract: A homoplasy at a site in the DNA occurs when the value of a character (A, C, G, or T) changes more than once in the evolutionary history. Homoplasies create extra difficulties for reconstructing the evolutionary history of a collection of taxa. Recent interest has grown concerning evolutionary histories that are not described by trees but rather by more general networks that allow for hybridization events. A natural question is, in an idealized situation where homoplasies occur only at hybridization events, whether the characters at the leaves and the root of the network determine the characters at the internal vertices. Mathematically, one has a directed rooted acyclic graph in which the vertices correspond to taxa. At each vertex there is a set of genes. Under appropriate assumptions, the genes at all vertices are determined by the genes at the root and at the leaves.
ID: 155
Year: 2006
Name: Di Wu
Institution: Iowa State University
Subject area(s): Computational Biology and Applied Mathematics
Title of Talk: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data

Abstract: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data Di Wu and Zhijun Wu Program on Bioinformatics and Computational Biology Department of Mathematics Iowa State University Ames, Iowa 50011 Abstract. Given a set of distances for certain pairs of atoms in a protein, the coordinates of the atoms and hence the protein structure can then be determined through solving a so-called distance geometry problem. However, it has been proved to be a NP hard problem when only a set of partial distances given. Previously, we used a so-called geometric build-up approach to develop several algorithms for solving the distance geometry problem with a set of sparse distance data. In this method, the coordinates of the atoms in a protein are determined as one atom at a time, with the distances from four base atoms to the atom to be determined. However, the requirement for four base atoms for the unique determination of each atom is sufficient, but unnecessary and even redundant for rigid structural determination. Here we investigate a rigid geometric build-up algorithm, which requires three base atoms instead of four base atoms for the determination of each atom. It could generate rigid structures, even a unique structure for very sparse distance data of a protein eventually. Due to the reflection in the determination for some atoms, this algorithm may also produce multiple structures satisfying given distances. We present the results obtained by using the algorithm for the determination of the structures, which suggests the potential of applying the algorithm to the distance based protein structural modeling.
ID: 157
Year: 2006
Name: Irvin Hentzel
Institution: Iowa State University
Subject area(s): Voting Strategies
Title of Talk: Arrow's Hypotheses

Abstract: We prove three consequences of Arrow's Hypotheses. (1) If some of the ballots put x first and the rest put x last, then x has to be either first or last in the group ranking. (2) If the rankings of a with b match the rankings of c with d on each ballot, then the group ranking must also match the ranking of a with b and c with d. (3) The group ranking must match one of the ballots. This material was taken from "Three Brief Proofs of Arrow's Impossibility Theorem" by John Geanakoplos. The point of the talk is to show that the proofs are very elementary. The various strategies for voting are covered in many very elementary texts. Their discussion is directed towards with of the hypotheses the voting strategies violate. This talk shows how the hypotheses can be combined to directly obtain conclusions that do not seem as fundamentally fair as the original hypotheses.
ID: 158
Year: 2006
Name: Steve Bean
Institution: Cornell College
Subject area(s): math history
Title of Talk: Why does 0! = 1? The evolution of the gamma function

Abstract: The gamma function is typically introduced as an attempt to interpolate the factorial function, but what motivation does one have to do this? After giving a brief overview of the gamma function and its properties--from the modern point of view,--we will talk about the same function from a historical perspective. In particular, we will examine the reasons behind Euler's original formulation of this function.
ID: 159
Year: 2006
Name: WEN ZHOU
Institution: Iowa State University
Subject area(s):
Title of Talk: Chemotactic Collapse in Keller-Segel Equation

Abstract: Chemotaxis phenomenon is one of the most fundamental phenomenons in the biology field. In 1970s, Keller and Segel characterize this phenomenon with two coupled equations. Study on the blow up of the solutions of the this equation is one of the key part of the research on this equation. This short talk will briefly introduce some recent results of the study on this equation, including Nagai, Velazquez, Stevens, Levine, and Hortsman's work, etc.
ID: 160
Year: 2006
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Visualizing Linear Algebra with Geometer

Abstract: I will present Sketchpad labs for visualizing the following concepts in linear algebra: Linear transformations and image, range, kernel, and projection. The determinant of a matrix and the orientation-preserving or-reversing property of the corresponding linear transformation. The determinant a matrix to the area of the image of a unit area under the corresponding linear transformation. Eigenvectors and eigenvalues
ID: 161
Year: 2006
Name: Jacob Manske
Institution: Iowa State University
Subject area(s): Philosophy of Mathematics
Title of Talk: Hey, Kids! Improve Your Theorems! Add Superfluous Hypotheses!

Abstract: In spite of the fact that we tell students not to assume what they are trying to prove, we all must do precisely that. The interesting theorems, then, turn out to be the ones whose tautologous nature is elusive. This will be a philosophical discussion; bellicose debate is encouraged.
ID: 162
Year: 2006
Name: Giovanna Llosent
Institution: University of Iowa
Subject area(s): Modular Representation Theory
Title of Talk: The stable endomorphism group of non-simple string modules over a very particular finite dimensional algebra.

Abstract: Let A be a finite dimensional algebra over an algebraic closed field k of characteristic 2 with a quiver representation and relations. Consider all non-simple string modules for this algebra which do not lie in the Auslander-Reiten component of the simple modules. Is there a non-simple string module M for which the group of stable endomorphisms is isomorphic to k? Under the hypothesis above we were able to prove that the underlying string S of the string module M has a substring S' and there is an endomorphism that does not factor through a projective A-module and lies in S'. The maximun lenght of the underlying string of a string module needed for completing the study of all stable endomorphism groups of non-simple string modules was 17. In particular, the cases needed for complete generalization are 54.
ID: 163
Year: 2006
Name: Justin From
Institution: Central College
Subject area(s):
Title of Talk: The Polynomial Root Squeezing Theorem

Abstract: Polynomials are one of the most widely used functions in mathematics, yet there are surprisingly many unanswered questions about their properties. This talk will present an innovative new idea referred to as the Polynomial Root Squeezing Theorem which shows that squeezing two of a polynomial
ID: 165
Year: 2006
Name: Luz De Alba
Institution: Drake University
Subject area(s): Linear Algebra, Matrix Theory, Graph Theory
Title of Talk: Comparison of P-matrix completions with Q-matrix completions.

Abstract: A P-matrix is a real square matrix, in which the determinant of every principal submatrix is positive. A Q-matrix is one in which the sum of the determinants of principal submatrices of the same size is positive. Clearly every P-matrix is a Q-matrix. A partial P-matrix is a matrix in which some entries are specified while others are not known, and every fully specified principal submatrix has positive determinant. The P-matrix completion problem asks the question: "Which partial P-matrices can be completed to a P-matrix?" In this talk we give the definition of partial Q-matrix, and compare the Q-matrix completion problem to the P-matrix completion problem. We also discuss some partial answers to the Q-completion problem.
ID: 166
Year: 2006
Name: Brian Birgen
Institution: Wartburg College
Subject area(s): Recreational Mathematics / Group Theory
Title of Talk: Subgroups of the Rubik's Group

Abstract: The set of possible arrangements of the Rubik's Cube forms a group with 4*10^19 elements. We will locate some well known groups which occur as subgroups of the Rubik's group and begin to understand the source of some of the complexities in understanding the Rubik's group.
ID: 167
Year: 2006
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): undergrad level analysis
Title of Talk: Mathematics by Experiment

Abstract: The use of computer packages has brought us to a point where the computer can be used for many tasks: discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, falsify conjectures, confirm analytically derived results, and perhaps most impressively for the purist, suggest approaches for formal proofs. This is the thrust of experimental mathematics. This talk will give some examples to discover or prove results concerning goemetry, integrals, binomial sums, and infinite series.
ID: 168
Year: 2006
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, analytic
Title of Talk: Primitive prime divisors of Mersenne numbers via Uniform Distribution

Abstract: Given a sequence a of integers, a primitive divisor of a(n) is an integer which divides a(n) but no earlier term of the sequence. Last year, we presented a result about a weighted average of primitive prime divisors of the well-known Mersenne numbers M(n) = 2^n-1. This year, we have an entirely different, simple proof of the same result, using cyclotomic polynomials and uniform distribution. We are indebted to Carl Pomerance for helpful insights. We will also mention possible applications to other sequences like the Fibonacci numbers.
ID: 169
Year: 2006
Name: Rick Spellerberg
Institution: Simpson College
Subject area(s): Biology / Mathematics
Title of Talk: Sperm Competition Games

Abstract: Sperm Competition occurs when ejaculates of multiple males compete to fertilize the eggs of one female. In this talk we will discuss the work of G.A. Parker in his paper; Sperm Competition: sneaks and extra-pair copulations. In this paper, Parker examines ejaculation strategies for cases when an opportunist male "steals" a mating with the female of a paired male.
ID: 170
Year: 2006
Name: Alexander Kleiner
Institution: Drake University
Subject area(s): analysis, history of mathematics
Title of Talk: The Toeplitz-Silverman Theorem Part II

Abstract: In the first two decades of the twentieth century summability developed from collection of special results used in other parts of analysis into a full-blown field. One of the main points of this transition was a collection of general results that gave conditions for a method to sum every convergent sequence. Part I of this presentation, which was given last spring, laid out the work that led to the general theory. Papers by Toeplitz, Silverman, Kojima, Schur and others established the theory. This note will look at the development of these conditions and, as time permits, the reoccurrence of these results in the early day of the "Polish" school of functional analysis
ID: 171
Year: 2006
Name: Reginald Laursen
Institution: Luther College
Subject area(s): Real Analysis
Title of Talk: Classroom Capsule: Teaching Challenge-Response Arguments

Abstract: The forward-backward method is a fundamental proof technique for helping students understand how to construct proofs. I will describe my latest variation in the application of this technique for addressing challenge-response arguments in a Real Analysis class. Using this variation my lower ability students have had greater success.
ID: 172
Year: 2006
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Linear Algebra, Voting Theory
Title of Talk: Decomposing Voters

Abstract: Recent developments in the mathematics of Social Choice by Don Saari, among others, have added an element of geometry and linear algebra to a field that has been dominated by combinatorics. This talk will introduce the linear algebra behind a three-candidate election, including how symmetries underlie traditional voting paradoxes.
ID: 173
Year: 2006
Name: M. Anne Dow
Institution: Maharishi University of Management
Subject area(s): Developmental math course materials
Title of Talk: Some Hands-on Workshops for Elementary and Intermediate Algebra Courses

Abstract: I found all the topics of my Elementary and Intermediate Algebra courses in the greenhouses we recently built on campus to provide organic vegetables for our campus dining hall. In my talk I will present two workshops on linear functions, one about the amount of broccoli seed needed to produce N thousand pounds of broccoli per week, and one about heat loss to the greenhouse during winter. Both require students to think carefully about what the slope means.
ID: 174
Year: 2006
Name: Ryan Martin
Institution: Iowa State University
Subject area(s): Graph Theory
Title of Talk: Vertex identifying codes in graphs: definitions, theorems and open problems

Abstract: In 1998, Karpovsky, Chakrabarty and Levitin introduced a new graph invariant called the vertex identification code. If C is a subset of the vertices, then C is a vertex-identifying code if each set N[v]\cap C is distinct and nonempty, where N[v] denotes the closed neighborhood of vertex v. We will discuss a number of results on the size of the smallest code in a graph, particularly on the Erdos-Renyi random graph and we will present open problems.
ID: 175
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Episodes in The Early History of The Lucasian Chair

Abstract: In 1663, Henry Lucas, the long-time secretary to the Chancellor of the University of Cambridge, made a bequest, subsequently granted by Charles II, to endow a chair in mathematics. A number of conditions were attached to the Chair. Among the more prominent Lucasian professors were Newton, Babbage, Stokes, Dirac, and Hawking. We focus attention on the early Lucasians. Many of whom were very diligent in carrying out their Lucasian responsibilities but as history has shown such was not always the case. In the process, we uncover several untold stories and some interesting mathematics