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 361-380 of 471 results.
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ID:
137
Year: 2005
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory
Title of Talk: Prime divisors of Mersenne numbers and Dirichlet series
Abstract: Mersenne numbers are the numbers 1, 3, 7, 15, ... 2^n - 1, ... It is a long-standing conjecture that this sequence contains infinitely many primes. We show how to get some asymptotic results on the 'average' prime divisor of Mersenne numbers using Dirichlet series. These series are useful for asymptotic counting, because there is a close link between their domain of convergence and the growth of their coefficients. Do not expect a big breakthrough, but a pretty result, few technicalities, and some exciting open questions.
Year: 2005
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory
Title of Talk: Prime divisors of Mersenne numbers and Dirichlet series
Abstract: Mersenne numbers are the numbers 1, 3, 7, 15, ... 2^n - 1, ... It is a long-standing conjecture that this sequence contains infinitely many primes. We show how to get some asymptotic results on the 'average' prime divisor of Mersenne numbers using Dirichlet series. These series are useful for asymptotic counting, because there is a close link between their domain of convergence and the growth of their coefficients. Do not expect a big breakthrough, but a pretty result, few technicalities, and some exciting open questions.
ID:
401
Year: 2014
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Probability
Title of Talk: Visual hypothesis testing - lineups and probability
Abstract: Police use lineups involving one suspect and several 'dummies' to get evidence that a witness can identify the suspect. In an abstract sense, we can form a hypothesis about 'suspect' data and test it in this way: literally have people looking at a lineup of plots with the task of identifying the data plot among the dummies. Repetition with several observers makes this approach surprisingly powerful. It also has potential when comparing the efficiency of different visual representations of the same data. Disclaimer: do not expect analysis of actual police lineups. But we will try out the method on the audience! This is joint work with Heike Hofmann, Di Cook, Phil Dixon, and Andreas Buja. I have investigated the underlying probability distributions. This meant evaluating some multiple integrals, and revising all the tricks from Calculus II.
Year: 2014
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Probability
Title of Talk: Visual hypothesis testing - lineups and probability
Abstract: Police use lineups involving one suspect and several 'dummies' to get evidence that a witness can identify the suspect. In an abstract sense, we can form a hypothesis about 'suspect' data and test it in this way: literally have people looking at a lineup of plots with the task of identifying the data plot among the dummies. Repetition with several observers makes this approach surprisingly powerful. It also has potential when comparing the efficiency of different visual representations of the same data. Disclaimer: do not expect analysis of actual police lineups. But we will try out the method on the audience! This is joint work with Heike Hofmann, Di Cook, Phil Dixon, and Andreas Buja. I have investigated the underlying probability distributions. This meant evaluating some multiple integrals, and revising all the tricks from Calculus II.
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:
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:
224
Year: 2008
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): geometry, teacher education, proof
Title of Talk: Proofs in elementary geometry - what IS the sum of angles in a triangle?
Abstract: One textbook for future teachers gives no less than four 'arguments' for this theorem. It is not claimed that they are proofs, and indeed they are not (all involve some circular reasoning). But the difference between such arguments and proofs is never made clear. We'll discover the flaws in the logic here, which are not obvious at all. Then we'll look at a number of examples from standard elementary geometry - some rock-solid one-line proofs, some examples where we all skip the proof and eyeball it, and finally an example which shows how 'eyeballing it' can lead to a 'proof' of 64=65.
Year: 2008
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): geometry, teacher education, proof
Title of Talk: Proofs in elementary geometry - what IS the sum of angles in a triangle?
Abstract: One textbook for future teachers gives no less than four 'arguments' for this theorem. It is not claimed that they are proofs, and indeed they are not (all involve some circular reasoning). But the difference between such arguments and proofs is never made clear. We'll discover the flaws in the logic here, which are not obvious at all. Then we'll look at a number of examples from standard elementary geometry - some rock-solid one-line proofs, some examples where we all skip the proof and eyeball it, and finally an example which shows how 'eyeballing it' can lead to a 'proof' of 64=65.
ID:
478
Year: 2017
Name: Diego Rojas
Institution: Iowa State University
Subject area(s): Computability Theory, Analysis
Title of Talk: Differentiation of Functions on the Cantor Space and Connections to Real-Valued Functions
Abstract: The notion of online functions of the Cantor space $2^{\mathbb{N}}$, and more generally, of continuous and of computable functions on $2^{\mathbb{N}}$, have been studied recently in connection with algorithmic randomness. In this talk, we present a notion of the derivative of functions on $2^{\mathbb{N}}$, and we establish some connections between functions and their derivatives on $2^{\mathbb{N}}$ and on $\mathbb{R}$, where we can represent real-valued functions as functions acting on the dyadic representation of real numbers. This is joint work with Douglas Cenzer.
Year: 2017
Name: Diego Rojas
Institution: Iowa State University
Subject area(s): Computability Theory, Analysis
Title of Talk: Differentiation of Functions on the Cantor Space and Connections to Real-Valued Functions
Abstract: The notion of online functions of the Cantor space $2^{\mathbb{N}}$, and more generally, of continuous and of computable functions on $2^{\mathbb{N}}$, have been studied recently in connection with algorithmic randomness. In this talk, we present a notion of the derivative of functions on $2^{\mathbb{N}}$, and we establish some connections between functions and their derivatives on $2^{\mathbb{N}}$ and on $\mathbb{R}$, where we can represent real-valued functions as functions acting on the dyadic representation of real numbers. This is joint work with Douglas Cenzer.
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:
460
Year: 2016
Name: Mark Ronnenberg
Institution: University of Northern Iowa
Subject area(s): topology
Title of Talk: Reidemeister Moves and Equivalence of Butterfly Diagrams for Links
Abstract: By a theorem of Reidemeister, two links are equivalent if and only if they have regular projections which can be related by a finite sequence of special changes called Reidemeister moves. It is an open problem to find a complete set of "butterfly moves" to turn a butterfly diagram for a given link into a butterfly diagram for an equivalent link. In this talk, we will translate the Reidemeister moves into butterfly moves and present some examples.
Year: 2016
Name: Mark Ronnenberg
Institution: University of Northern Iowa
Subject area(s): topology
Title of Talk: Reidemeister Moves and Equivalence of Butterfly Diagrams for Links
Abstract: By a theorem of Reidemeister, two links are equivalent if and only if they have regular projections which can be related by a finite sequence of special changes called Reidemeister moves. It is an open problem to find a complete set of "butterfly moves" to turn a butterfly diagram for a given link into a butterfly diagram for an equivalent link. In this talk, we will translate the Reidemeister moves into butterfly moves and present some examples.
ID:
217
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
ID:
474
Year: 2017
Name: Aqeeb Sabree
Institution: University of Iowa
Subject area(s): Advanced Calculus would be helpful
Title of Talk: Research Topics from Reproducing Kernel Hilbert Spaces
Abstract: Reproducing Kernel Hilbert Spaces (RKHS) have applications to statistics, machine learning, differential equations, and more. The goal of this presentation is to introduce the concept of a RKHS, and discuss it’s applications to many research areas. The amazing thing about this research area is that there are many research questions/topics for dissertations or undergraduate research experiences. I will give a brief history of RKHSs, highlighting where it has appeared and how it has been applied. Then I will present the theoretical foundation(s) of the subject; from here I will go into its applications. Below, you will find highlights of the theory that I will present, and some highlights of its application. You can discuss the existence of RKHSs in different ways: one, you can prove that the evaluation functional is bounded; or, two, you can prove that (given a Hilbert space) the Hilbert space has a reproducing kernel function. A nice property of the reproducing kernel is that it is unique. Thus, every RKHS has exactly one reproducing kernel; furthermore, every reproducing kernel is the reproducing kernel for a unique RKHS (Moore--Aronszajn). The process of recreating the RKHS from the kernel function is termed the it reconstruction problem, and is an interesting research area. The usefulness of the theory of RKHSs can be seen in the fact that the finite energy Fourier, Hankel, sine, and cosine transformed band-limited signals are specific realizations of the abstract reproducing kernel Hilbert space (RKHS). Sampling Theory: Sampling theory deals with the reconstruction of functions (or signals) from their values (or samples) on an appropriate set of points. When given a reproducing kernel Hilbert space, H; one asks: What are some (suitable) sets of points which reproduce (or interpolate) the full values of functions from H? And when given points in a set S, one asks: What are the RKHSs for which S is a complete set of sample points? Meaning the values of functions from H are reproduced by interpolation from S.
Year: 2017
Name: Aqeeb Sabree
Institution: University of Iowa
Subject area(s): Advanced Calculus would be helpful
Title of Talk: Research Topics from Reproducing Kernel Hilbert Spaces
Abstract: Reproducing Kernel Hilbert Spaces (RKHS) have applications to statistics, machine learning, differential equations, and more. The goal of this presentation is to introduce the concept of a RKHS, and discuss it’s applications to many research areas. The amazing thing about this research area is that there are many research questions/topics for dissertations or undergraduate research experiences. I will give a brief history of RKHSs, highlighting where it has appeared and how it has been applied. Then I will present the theoretical foundation(s) of the subject; from here I will go into its applications. Below, you will find highlights of the theory that I will present, and some highlights of its application. You can discuss the existence of RKHSs in different ways: one, you can prove that the evaluation functional is bounded; or, two, you can prove that (given a Hilbert space) the Hilbert space has a reproducing kernel function. A nice property of the reproducing kernel is that it is unique. Thus, every RKHS has exactly one reproducing kernel; furthermore, every reproducing kernel is the reproducing kernel for a unique RKHS (Moore--Aronszajn). The process of recreating the RKHS from the kernel function is termed the it reconstruction problem, and is an interesting research area. The usefulness of the theory of RKHSs can be seen in the fact that the finite energy Fourier, Hankel, sine, and cosine transformed band-limited signals are specific realizations of the abstract reproducing kernel Hilbert space (RKHS). Sampling Theory: Sampling theory deals with the reconstruction of functions (or signals) from their values (or samples) on an appropriate set of points. When given a reproducing kernel Hilbert space, H; one asks: What are some (suitable) sets of points which reproduce (or interpolate) the full values of functions from H? And when given points in a set S, one asks: What are the RKHSs for which S is a complete set of sample points? Meaning the values of functions from H are reproduced by interpolation from S.
ID:
342
Year: 2012
Name: Bill Schellhorn
Institution: Simpson College
Subject area(s): math modeling, undergraduate research
Title of Talk: The Feasibility of Electric Vehicles: Driving Interest in Mathematical Modeling
Abstract: The study of electric vehicles can be used to promote interest in mathematical modeling in a variety of courses and student projects. In this presentation, I will discuss how the feasibility of electric vehicles can be investigated using fundamental topics in algebra, calculus, and statistics. I will also give examples of how technology can be incorporated into the investigation.
Year: 2012
Name: Bill Schellhorn
Institution: Simpson College
Subject area(s): math modeling, undergraduate research
Title of Talk: The Feasibility of Electric Vehicles: Driving Interest in Mathematical Modeling
Abstract: The study of electric vehicles can be used to promote interest in mathematical modeling in a variety of courses and student projects. In this presentation, I will discuss how the feasibility of electric vehicles can be investigated using fundamental topics in algebra, calculus, and statistics. I will also give examples of how technology can be incorporated into the investigation.
ID:
493
Year: 2017
Name: Sarah Schoel
Institution: Loras College
Subject area(s):
Title of Talk: Fractal Sequence Analysis and Creation of Art and Music
Abstract: For my seminar project, I have been analyzing fractal sequences and using them to create images and to modify musical compositions. A fractal sequence has a pattern that repeats at all scales. One well-known sequence is the Thue-Morse Sequence. This sequence is created by translating the positive integers into base(2) and then adding the digits for each number and taking mod(2) of the result. This forms a pattern of zeroes and ones that continues infinitely. If consecutive numbers are put into groups of two, a unique characteristic about this sequence is revealed. When the first number of every set is kept and the second removed, the remaining numbers create the original pattern. I have shown that translating the integers into base(n) and summing digits mod(n) elicits a similar pattern. I will show how these sequences can then be translated into art and music and analyze the results.
Year: 2017
Name: Sarah Schoel
Institution: Loras College
Subject area(s):
Title of Talk: Fractal Sequence Analysis and Creation of Art and Music
Abstract: For my seminar project, I have been analyzing fractal sequences and using them to create images and to modify musical compositions. A fractal sequence has a pattern that repeats at all scales. One well-known sequence is the Thue-Morse Sequence. This sequence is created by translating the positive integers into base(2) and then adding the digits for each number and taking mod(2) of the result. This forms a pattern of zeroes and ones that continues infinitely. If consecutive numbers are put into groups of two, a unique characteristic about this sequence is revealed. When the first number of every set is kept and the second removed, the remaining numbers create the original pattern. I have shown that translating the integers into base(n) and summing digits mod(n) elicits a similar pattern. I will show how these sequences can then be translated into art and music and analyze the results.
ID:
492
Year: 2017
Name: Alex Schulte
Institution: Iowa State University
Subject area(s):
Title of Talk: Anti-Van der Waerden number of 3-term arithmetic progression
Abstract: A set is rainbow if each element of the set is a di erent color. The anti-van der Waerden number of the integers from 1 to n, denoted by aw([n]; k), is the least positive integer r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. The exact value of the anti-van der Waerden number of the integers where k = 3 is given by aw([n]; 3) = dlog3 ne+2. The anti-van der Waerden number can also be de ned on graphs, where aw(G; k) is the least number of colors such that every coloring contains a rainbow k-term arithmetic progression. Bounds on the anti-van der Wareden number of graphs have been established and exact values are known for certain families of graphs. Keywords: Rainbow, r
Year: 2017
Name: Alex Schulte
Institution: Iowa State University
Subject area(s):
Title of Talk: Anti-Van der Waerden number of 3-term arithmetic progression
Abstract: A set is rainbow if each element of the set is a di erent color. The anti-van der Waerden number of the integers from 1 to n, denoted by aw([n]; k), is the least positive integer r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. The exact value of the anti-van der Waerden number of the integers where k = 3 is given by aw([n]; 3) = dlog3 ne+2. The anti-van der Waerden number can also be de ned on graphs, where aw(G; k) is the least number of colors such that every coloring contains a rainbow k-term arithmetic progression. Bounds on the anti-van der Wareden number of graphs have been established and exact values are known for certain families of graphs. Keywords: Rainbow, r
ID:
365
Year: 2013
Name: Chris Schultz
Institution: Iowa State University
Subject area(s): Developmental Math
Title of Talk: Remedial Mathematics at Iowa State University
Abstract: Success in a developmental math course is not truly measured until the student success rate in the downstream class is measured. Iowa State University’s Department of Mathematics has started such a study and would like to share our preliminary data for discussion. Concern is often also expressed that students who start in developmental math classes will never graduate and we have gathered 2 years’ worth of data addressing this concern. The format of our developmental course, Math 10, will be shared as well as the data described above.
Year: 2013
Name: Chris Schultz
Institution: Iowa State University
Subject area(s): Developmental Math
Title of Talk: Remedial Mathematics at Iowa State University
Abstract: Success in a developmental math course is not truly measured until the student success rate in the downstream class is measured. Iowa State University’s Department of Mathematics has started such a study and would like to share our preliminary data for discussion. Concern is often also expressed that students who start in developmental math classes will never graduate and we have gathered 2 years’ worth of data addressing this concern. The format of our developmental course, Math 10, will be shared as well as the data described above.
ID:
549
Year: 2019
Name: Carol Schumacher
Institution: Kenyon College
Subject area(s):
Title of Talk: All Tangled Up
Abstract: Toys have inspired a lot of interesting mathematics. The SpirographTM helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve “rolls” along another curve. Another children’s toy, the TangleTM, inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a “tangle curve,” which is made up of quarter circles. The resulting roulettes we named “tangloids.” In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties. As a bonus, I will discuss the nature of generalization, which is very important in mathematics.
Year: 2019
Name: Carol Schumacher
Institution: Kenyon College
Subject area(s):
Title of Talk: All Tangled Up
Abstract: Toys have inspired a lot of interesting mathematics. The SpirographTM helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve “rolls” along another curve. Another children’s toy, the TangleTM, inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a “tangle curve,” which is made up of quarter circles. The resulting roulettes we named “tangloids.” In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties. As a bonus, I will discuss the nature of generalization, which is very important in mathematics.
ID:
550
Year: 2019
Name: Carol Schumacher
Institution: Kenyon College
Subject area(s):
Title of Talk: Fast Forward, Slow Motion
Abstract: A graphical link between fast and slow time scales: The world is shaped by interactions between things that develop slowly over time and things that happen very rapidly. Picture a garden. A bud takes hours to open up into a flower. A bee takes seconds to fly in, pollinate the flower and then depart. It can be difficult to fully consider both fast and slow time scales at the same time---yet it is the interaction between these events that makes the garden work. Mathematicians have developed a number of techniques for analyzing systems that include both fast and slow time scales. We will consider a graphical method for predicting what happens when fast and slow interact.
Year: 2019
Name: Carol Schumacher
Institution: Kenyon College
Subject area(s):
Title of Talk: Fast Forward, Slow Motion
Abstract: A graphical link between fast and slow time scales: The world is shaped by interactions between things that develop slowly over time and things that happen very rapidly. Picture a garden. A bud takes hours to open up into a flower. A bee takes seconds to fly in, pollinate the flower and then depart. It can be difficult to fully consider both fast and slow time scales at the same time---yet it is the interaction between these events that makes the garden work. Mathematicians have developed a number of techniques for analyzing systems that include both fast and slow time scales. We will consider a graphical method for predicting what happens when fast and slow interact.
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:
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:
277
Year: 2010
Name: Scott Searcy
Institution: Waldorf College
Subject area(s): Math Education
Title of Talk: A Survey of Technology Use and District Spending in North Iowa Schools
Abstract: Also presenting: Dr. Jeffrey Biessman. Conventional wisdom holds that technology use in public schools is commonplace and therefore college freshman have wide exposure to and experience with technology. Anecdotal suggest this may not be true. This survey was designed to reveal the extent of technology use in North Iowa school districts. The survey indicates that larger schools are less likely to budget money for technology on a per pupil basis than smaller districts.
Year: 2010
Name: Scott Searcy
Institution: Waldorf College
Subject area(s): Math Education
Title of Talk: A Survey of Technology Use and District Spending in North Iowa Schools
Abstract: Also presenting: Dr. Jeffrey Biessman. Conventional wisdom holds that technology use in public schools is commonplace and therefore college freshman have wide exposure to and experience with technology. Anecdotal suggest this may not be true. This survey was designed to reveal the extent of technology use in North Iowa school districts. The survey indicates that larger schools are less likely to budget money for technology on a per pupil basis than smaller districts.