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 201-220 of 471 results.
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ID:
402
Year: 2014
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Teaching techniques
Title of Talk: Using short "lecture challenge questions" in large lecture courses
Abstract: The talk describes my use of daily "lecture challenges" in large lecture courses such as Calculus or Mathematical Ideas. These "lecture challenges" are one-problem quizzes on material presented in the same lecture. Problems are typically easy problems that might be test questions. There is no partial credit. Students get one point for a wrong answer, two points for a correct answer. Absent students get no points, so students are motivated to attend. The problems are very fast to grade. Students may help and teach each other.
Year: 2014
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Teaching techniques
Title of Talk: Using short "lecture challenge questions" in large lecture courses
Abstract: The talk describes my use of daily "lecture challenges" in large lecture courses such as Calculus or Mathematical Ideas. These "lecture challenges" are one-problem quizzes on material presented in the same lecture. Problems are typically easy problems that might be test questions. There is no partial credit. Students get one point for a wrong answer, two points for a correct answer. Absent students get no points, so students are motivated to attend. The problems are very fast to grade. Students may help and teach each other.
ID:
149
Year: 2006
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: computing multivalued velocity and electric field of 1D Euler-Poisson equation
Abstract: We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The sys- tem of these equations arises in the semiclassical approximation of Schrodinger- Poisson equations and semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space | called field space, which incorpo- rates both velocity and electric fields into the configuration space. Multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. Numerical examples are presented to validate the proposed level set method.
Year: 2006
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: computing multivalued velocity and electric field of 1D Euler-Poisson equation
Abstract: We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The sys- tem of these equations arises in the semiclassical approximation of Schrodinger- Poisson equations and semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space | called field space, which incorpo- rates both velocity and electric fields into the configuration space. Multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. Numerical examples are presented to validate the proposed level set method.
ID:
150
Year: 2006
Name: Joseph Keller
Institution: Iowa State University
Subject area(s): functional analysis
Title of Talk: "Convergence depth": proof of the nonrotation and nontranslation of galaxies
Abstract: HC Arp (Max Planck Inst.) amassed evidence that most large redshift is intrinsic, not due to motion or expansion. WG Tifft (Univ. of Arizona) says that redshift periods, large and small, suggest abandoning the motion/expansion hypothesis altogether. "Convergence depth", a phenomenon studied by this author since 2002, means that the average velocity over successive shells of galaxies, converges in a mere 400 M lt yr, to the apparent velocity ("anisotropy") of the sources of the cosmic microwave background ("CMB"). The shape of the convergence depth curve, and the observed 400 M lt yr period of galaxy distribution, suggest that Hubble's parameter varies sinusoidally along the axis of the CMB anisotropy, with half-period 400 M lt yr. Taylor series extrapolation of the convergence depth curve to the origin, then shows that the velocity of the sun relative to distant galaxies is about equal to its velocity relative to nearby stars. Galaxies neither rotate nor translate. "Dark matter" need not exist. Oort's law is not due to motion. An absolute frame of reference (Maxwell/FitzGerald ether?) is supported. DC Miller (Case Univ.) found that apparent "ether drift" agrees, in its component parallel to Earth's axis, with the solar apex motion, i.e., motion in the extragalactic frame.
Year: 2006
Name: Joseph Keller
Institution: Iowa State University
Subject area(s): functional analysis
Title of Talk: "Convergence depth": proof of the nonrotation and nontranslation of galaxies
Abstract: HC Arp (Max Planck Inst.) amassed evidence that most large redshift is intrinsic, not due to motion or expansion. WG Tifft (Univ. of Arizona) says that redshift periods, large and small, suggest abandoning the motion/expansion hypothesis altogether. "Convergence depth", a phenomenon studied by this author since 2002, means that the average velocity over successive shells of galaxies, converges in a mere 400 M lt yr, to the apparent velocity ("anisotropy") of the sources of the cosmic microwave background ("CMB"). The shape of the convergence depth curve, and the observed 400 M lt yr period of galaxy distribution, suggest that Hubble's parameter varies sinusoidally along the axis of the CMB anisotropy, with half-period 400 M lt yr. Taylor series extrapolation of the convergence depth curve to the origin, then shows that the velocity of the sun relative to distant galaxies is about equal to its velocity relative to nearby stars. Galaxies neither rotate nor translate. "Dark matter" need not exist. Oort's law is not due to motion. An absolute frame of reference (Maxwell/FitzGerald ether?) is supported. DC Miller (Case Univ.) found that apparent "ether drift" agrees, in its component parallel to Earth's axis, with the solar apex motion, i.e., motion in the extragalactic frame.
ID:
151
Year: 2006
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s): calculus, differential equations, analysis, dynamical systems
Title of Talk: Global Dynamics and Chaos
Abstract: Global Dynamics and Chaos Wolfgang Kliemann Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A. February 27, 2006 Abstract We discuss dynamical systems given by a time set - in our case the real line R, a state space M - a compact subset of Rd or a compact metric space, a continuous map : R M ��! M with two properties (0; x) = x for all x 2 M (t + s; x) = (t; (s; x)) for all x 2 M, all t; s 2 R. Typical examples are solutions of (time-homogeneous) di
Year: 2006
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s): calculus, differential equations, analysis, dynamical systems
Title of Talk: Global Dynamics and Chaos
Abstract: Global Dynamics and Chaos Wolfgang Kliemann Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A. February 27, 2006 Abstract We discuss dynamical systems given by a time set - in our case the real line R, a state space M - a compact subset of Rd or a compact metric space, a continuous map : R M ��! M with two properties (0; x) = x for all x 2 M (t + s; x) = (t; (s; x)) for all x 2 M, all t; s 2 R. Typical examples are solutions of (time-homogeneous) di
ID:
407
Year: 2014
Name: Kenneth Driessel
Institution: Iowa State University
Subject area(s): economics, ordinary differential equations
Title of Talk: Business cycles and predator-prey ordinary differential equations
Abstract: Richard M. Goodwin (1913-1996) was an American mathematician and economist. During most of his career he taught at the University of Cambridge. Goodwin studied economic growth and the business cycle. In 1967 he published a paper with title "A Growth Cycle". In this paper he described an economic model consisting of two nonlinear first order ordinary differential equations that exhibits cyclic behavior. This system is similar to the well-known system of predator-prey equations of Lotka and Volterra. Goodwin seems to have had mixed opinions about his system. He writes (in 1967): "Presented here is a starkly schematized and hence quite unrealistic model of cycles in growth rates." He also writes (in 1972): "[These assumptions] were chosen because they represent, in my opinion, the most essential dynamic aspects of capitalism; furthermore, they are factually based, to the order of accuracy implicit in such a model." In this talk, I shall present my version of Goodwin's growth cycle system.
Year: 2014
Name: Kenneth Driessel
Institution: Iowa State University
Subject area(s): economics, ordinary differential equations
Title of Talk: Business cycles and predator-prey ordinary differential equations
Abstract: Richard M. Goodwin (1913-1996) was an American mathematician and economist. During most of his career he taught at the University of Cambridge. Goodwin studied economic growth and the business cycle. In 1967 he published a paper with title "A Growth Cycle". In this paper he described an economic model consisting of two nonlinear first order ordinary differential equations that exhibits cyclic behavior. This system is similar to the well-known system of predator-prey equations of Lotka and Volterra. Goodwin seems to have had mixed opinions about his system. He writes (in 1967): "Presented here is a starkly schematized and hence quite unrealistic model of cycles in growth rates." He also writes (in 1972): "[These assumptions] were chosen because they represent, in my opinion, the most essential dynamic aspects of capitalism; furthermore, they are factually based, to the order of accuracy implicit in such a model." In this talk, I shall present my version of Goodwin's growth cycle system.
ID:
152
Year: 2006
Name: Kunlun Liu
Institution: Iowa State University
Subject area(s): PDE
Title of Talk: Existence of strong solution for a class of nonlinear parabolic systems
Abstract: This paper deals with the local and global existence of the strong solution for a class of nonlinear parabolic PDEs in the domain [0,T]
Year: 2006
Name: Kunlun Liu
Institution: Iowa State University
Subject area(s): PDE
Title of Talk: Existence of strong solution for a class of nonlinear parabolic systems
Abstract: This paper deals with the local and global existence of the strong solution for a class of nonlinear parabolic PDEs in the domain [0,T]
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.
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.
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.
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:
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.
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:
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.
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:
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.
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:
426
Year: 2015
Name: Kristopher Lee
Institution: Iowa State University
Subject area(s):
Title of Talk: MATH 106X: A New Course at Iowa State
Abstract: Last year, the College of Liberal Arts and Sciences at Iowa State approved the creation of an inquiry-based mathematics course for the liberal arts. The course has begun this semester, and I will discuss my experience as the faithful guide to the intrepid explorers who so bravely signed up for this journey to discover mathematics.
Year: 2015
Name: Kristopher Lee
Institution: Iowa State University
Subject area(s):
Title of Talk: MATH 106X: A New Course at Iowa State
Abstract: Last year, the College of Liberal Arts and Sciences at Iowa State approved the creation of an inquiry-based mathematics course for the liberal arts. The course has begun this semester, and I will discuss my experience as the faithful guide to the intrepid explorers who so bravely signed up for this journey to discover mathematics.
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.
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:
434
Year: 2015
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Rashomon sculptures - reconstructing 3D shapes from inexact measurements
Abstract: The art installation 'Rashomon' was displayed on the Iowa State University campus during summer 2015. It consists of 15 identical, abstract sculptures. Artist Chuck Ginnever posed the challenge whether it is possible to display the sculptures so that no two of them are in the same position (modulo translation/rotation). We investigated the related question of reconstructing such a sculpture from (ordinary tape-measure) inexact measurements. Mathematics involved are the Cayley-Menger determinant, and the gradient method / Steepest Descent. We'll explain the mathematics with some simple examples and then show the results of our reconstruction. We will only assume elementary linear algebra (matrix - vector multiplication, determinants).
Year: 2015
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Rashomon sculptures - reconstructing 3D shapes from inexact measurements
Abstract: The art installation 'Rashomon' was displayed on the Iowa State University campus during summer 2015. It consists of 15 identical, abstract sculptures. Artist Chuck Ginnever posed the challenge whether it is possible to display the sculptures so that no two of them are in the same position (modulo translation/rotation). We investigated the related question of reconstructing such a sculpture from (ordinary tape-measure) inexact measurements. Mathematics involved are the Cayley-Menger determinant, and the gradient method / Steepest Descent. We'll explain the mathematics with some simple examples and then show the results of our reconstruction. We will only assume elementary linear algebra (matrix - vector multiplication, determinants).
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:
445
Year: 2016
Name: Heather Bolles
Institution: Iowa State University
Subject area(s): calculus I (engineering)
Title of Talk: Team-Based Learning in a Large Calculus Class
Abstract: Research shows that students are more successful in STEM when they are actively engaged during class. We have adapted Team-Based Learning following Michaelsen's model for use in our large (150 students) calculus classes. Currently in our second implementation of TBL Calculus I, we will share our process, some materials, and preliminary results.
Year: 2016
Name: Heather Bolles
Institution: Iowa State University
Subject area(s): calculus I (engineering)
Title of Talk: Team-Based Learning in a Large Calculus Class
Abstract: Research shows that students are more successful in STEM when they are actively engaged during class. We have adapted Team-Based Learning following Michaelsen's model for use in our large (150 students) calculus classes. Currently in our second implementation of TBL Calculus I, we will share our process, some materials, and preliminary results.
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:
454
Year: 2016
Name: John Hsieh
Institution: Iowa State University
Subject area(s): IBL
Title of Talk: IBL for an Undergraduate Bioinformatics Survey Course
Abstract: The Moore Method was originally developed by R.L. Moore to teach advanced mathematics in the college setting. There have been many adaptations of the Moore Method, under the broad term Modified Moore Method (M3), which are now classified as a variant of inquiry based learning (IBL). Despite the growing popularity of M3, it is rarely applied beyond mathematics. At Iowa State University, we designed and taught an “Introduction to Bioinformatics” survey course using M3 for the first time during Fall semester 2015. The class size was small (n=12), and students all had a background in the natural sciences, most in the biological sciences. Students had little to no formal training in computational sciences. During the 16-week course, students learned to: 1) work on a remote Linux server, 2) read and write Python code, 3) tackle classic bioinformatics problems, and 4) solve current bioinformatics problems with available tools. As with all M3 courses, learning objectives were met through carefully designed questions given to students prior to each class session. Class sessions were completely led by students (i.e., reversed classroom) presenting solution to the assigned questions. The application of M3 to our course has led to several desirable student outcomes: 1) engagement and ownership of the course material, 2) development of a strong sense of community, and 3) uniform learning outcomes. One of the difficulties we experienced with applying M3 was the creation of the course material. It was tough to create questions that were challenging enough without overwhelming the students.
Year: 2016
Name: John Hsieh
Institution: Iowa State University
Subject area(s): IBL
Title of Talk: IBL for an Undergraduate Bioinformatics Survey Course
Abstract: The Moore Method was originally developed by R.L. Moore to teach advanced mathematics in the college setting. There have been many adaptations of the Moore Method, under the broad term Modified Moore Method (M3), which are now classified as a variant of inquiry based learning (IBL). Despite the growing popularity of M3, it is rarely applied beyond mathematics. At Iowa State University, we designed and taught an “Introduction to Bioinformatics” survey course using M3 for the first time during Fall semester 2015. The class size was small (n=12), and students all had a background in the natural sciences, most in the biological sciences. Students had little to no formal training in computational sciences. During the 16-week course, students learned to: 1) work on a remote Linux server, 2) read and write Python code, 3) tackle classic bioinformatics problems, and 4) solve current bioinformatics problems with available tools. As with all M3 courses, learning objectives were met through carefully designed questions given to students prior to each class session. Class sessions were completely led by students (i.e., reversed classroom) presenting solution to the assigned questions. The application of M3 to our course has led to several desirable student outcomes: 1) engagement and ownership of the course material, 2) development of a strong sense of community, and 3) uniform learning outcomes. One of the difficulties we experienced with applying M3 was the creation of the course material. It was tough to create questions that were challenging enough without overwhelming the students.
ID:
458
Year: 2016
Name: Steve Butler
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to the Mathematics of Juggling
Abstract: Juggling and mathematics have been done for thousands of years, but the mathematics of juggling is a relatively new field that dates back a few decades and looks at using the tools of mathematics to analyze, connect, and count various juggling patterns. We will introduce some of the very basic results related to the mathematics of juggling with a particular emphasis at looking at the various methods used to describe juggling patterns.
Year: 2016
Name: Steve Butler
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to the Mathematics of Juggling
Abstract: Juggling and mathematics have been done for thousands of years, but the mathematics of juggling is a relatively new field that dates back a few decades and looks at using the tools of mathematics to analyze, connect, and count various juggling patterns. We will introduce some of the very basic results related to the mathematics of juggling with a particular emphasis at looking at the various methods used to describe juggling patterns.