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.
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ID:
404
Year: 2014
Name: Jonathan White
Institution: Coe College
Subject area(s): Pedagogy/Transition to Proof
Title of Talk: Constructing the Naturals -- An Inquiry-Based Approach
Abstract: The construction of the natural numbers via the Peano Axioms is a strangely neglected backwater of the undergraduate curriculum. It deserves more attention. Meanwhile, although inquiry-based learning has gained some traction, it usually is considered a binary decision, where a course either is or is not taught using an IBL approach. I propose a standalone unit, giving our number systems the foundation they deserve, and offering a "trial size" taste of IBL.
Year: 2014
Name: Jonathan White
Institution: Coe College
Subject area(s): Pedagogy/Transition to Proof
Title of Talk: Constructing the Naturals -- An Inquiry-Based Approach
Abstract: The construction of the natural numbers via the Peano Axioms is a strangely neglected backwater of the undergraduate curriculum. It deserves more attention. Meanwhile, although inquiry-based learning has gained some traction, it usually is considered a binary decision, where a course either is or is not taught using an IBL approach. I propose a standalone unit, giving our number systems the foundation they deserve, and offering a "trial size" taste of IBL.
ID:
562
Year: 2021
Name: Russ Goodman
Institution: Central College
Subject area(s): pedagogy, sports analytics
Title of Talk: Sports Analytics: Soccer -- An Honors Seminar Utilizing Cutting-Edge Technology for Course-Based Student Research
Abstract: In 2020, the speakers received a Moore Family Foundation grant to purchase 20 Catapult-brand GPS/accelerometer devices for use in student research. Subsequently, the speakers designed an honors seminar entitled Sports Analytics: Soccer to enable enrolled students to have a research experience with this new technology, studying aspects of “physical load” on the Central College women’s soccer team. This presentation will describe the structure of the course, the successes and challenges of the course, and what the future holds for this type of sports analytics undergraduate research at Central College.
Year: 2021
Name: Russ Goodman
Institution: Central College
Subject area(s): pedagogy, sports analytics
Title of Talk: Sports Analytics: Soccer -- An Honors Seminar Utilizing Cutting-Edge Technology for Course-Based Student Research
Abstract: In 2020, the speakers received a Moore Family Foundation grant to purchase 20 Catapult-brand GPS/accelerometer devices for use in student research. Subsequently, the speakers designed an honors seminar entitled Sports Analytics: Soccer to enable enrolled students to have a research experience with this new technology, studying aspects of “physical load” on the Central College women’s soccer team. This presentation will describe the structure of the course, the successes and challenges of the course, and what the future holds for this type of sports analytics undergraduate research at Central College.
ID:
439
Year: 2016
Name: Henry Walker
Institution: Grinnell College
Subject area(s): Pedagogy, collaborative learning, student engagement
Title of Talk: A Lab-based Pedagoy that Emphasizes Collaboration
Abstract: Following pedagogy pioneered by mathematician Eugene Herman at Grinnell College, this talk describes my experiences with a lab-based pedagogy in which students work collaboratively in pairs for each class session. As an instructor, I lecture about 4 hours per month, usually in 5-10 minute mini-lectures. Elements of this approach have been studied extensively by others to show effectiveness. Further, my own experience shows I can cover about 20% more material with this pedagogy over a traditional format, and test scores are better. Since this talk will focus upon pedagogy, the talk will largely be content-free.
Year: 2016
Name: Henry Walker
Institution: Grinnell College
Subject area(s): Pedagogy, collaborative learning, student engagement
Title of Talk: A Lab-based Pedagoy that Emphasizes Collaboration
Abstract: Following pedagogy pioneered by mathematician Eugene Herman at Grinnell College, this talk describes my experiences with a lab-based pedagogy in which students work collaboratively in pairs for each class session. As an instructor, I lecture about 4 hours per month, usually in 5-10 minute mini-lectures. Elements of this approach have been studied extensively by others to show effectiveness. Further, my own experience shows I can cover about 20% more material with this pedagogy over a traditional format, and test scores are better. Since this talk will focus upon pedagogy, the talk will largely be content-free.
ID:
440
Year: 2016
Name: Henry Walker
Institution: Grinnell College
Subject area(s): Pedagogy, collaborative learning, student engagement
Title of Talk: A Lab-based Pedagoy that Emphasizes Collaboration
Abstract: Following pedagogy pioneered by mathematician Eugene Herman at Grinnell College, this talk describes my experiences with a lab-based pedagogy in which students work collaboratively in pairs for each class session. As an instructor, I lecture about 4 hours per month, usually in 5-10 minute mini-lectures. Elements of this approach have been studied extensively by others to show effectiveness. Further, my own experience shows I can cover about 20% more material with this pedagogy over a traditional format, and test scores are better. Since this talk will focus upon pedagogy, the talk will largely be content-free.
Year: 2016
Name: Henry Walker
Institution: Grinnell College
Subject area(s): Pedagogy, collaborative learning, student engagement
Title of Talk: A Lab-based Pedagoy that Emphasizes Collaboration
Abstract: Following pedagogy pioneered by mathematician Eugene Herman at Grinnell College, this talk describes my experiences with a lab-based pedagogy in which students work collaboratively in pairs for each class session. As an instructor, I lecture about 4 hours per month, usually in 5-10 minute mini-lectures. Elements of this approach have been studied extensively by others to show effectiveness. Further, my own experience shows I can cover about 20% more material with this pedagogy over a traditional format, and test scores are better. Since this talk will focus upon pedagogy, the talk will largely be content-free.
ID:
543
Year: 2019
Name: Valorie Zonnefeld
Institution: Dordt University
Subject area(s): Pedagogy of Mathematics
Title of Talk: Classroom Environments that Nurture a Growth Mindset
Abstract: Carol Dweck and Jo Boaler's landmark research regarding the importance of a growth mindset for learning and specifically mathematics is a game changer for professors and teachers. Learn what a growth mindset is and how to foster it in your classroom.
Year: 2019
Name: Valorie Zonnefeld
Institution: Dordt University
Subject area(s): Pedagogy of Mathematics
Title of Talk: Classroom Environments that Nurture a Growth Mindset
Abstract: Carol Dweck and Jo Boaler's landmark research regarding the importance of a growth mindset for learning and specifically mathematics is a game changer for professors and teachers. Learn what a growth mindset is and how to foster it in your classroom.
ID:
358
Year: 2013
Name: Paul Muhly
Institution: University of Iowa
Subject area(s): pedagogy
Title of Talk: TeX in the Classroom
Abstract: In this talk I will advocate for and share my experiences when requiring students to write their homework in LaTeX. The experiences I have had when requiring students to TeX their homework have been surprisingly positive. I will explain what I have done and offer suggestions, especially suggestions about how to get students started using TeX.
Year: 2013
Name: Paul Muhly
Institution: University of Iowa
Subject area(s): pedagogy
Title of Talk: TeX in the Classroom
Abstract: In this talk I will advocate for and share my experiences when requiring students to write their homework in LaTeX. The experiences I have had when requiring students to TeX their homework have been surprisingly positive. I will explain what I have done and offer suggestions, especially suggestions about how to get students started using TeX.
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:
438
Year: 2016
Name: Meghan Stevens
Institution: Drake University
Subject area(s): Ordinary Differential Equations, Mathematical Biology, Global Dynamics
Title of Talk: Global Dynamics of a Breast Cancer Competition System
Abstract: In this talk I present a system of five ordinary differential equations to model the competition for space and resources between breast cancer cells and healthy cells. Included is the cancer stem cell hypothesis, which states that there exist proliferating cancer stem cells that repopulate non-proliferating tumor cells and can lead to tumor recurrence. These cancer stem cells exist in a smaller population, making them harder to detect. Additionally, the system contains an equation for the immune system in order to show how the body naturally defends itself from invading tumors. Finally, because the majority of breast cancer cells are estrogen-receptor positive, the role of excess estrogen in the body introduced through birth control in included. Estrogen increases the amount of cancer cells while hindering the effectiveness of the immune system. Its presence also increases the likelihood that healthy cells will mutate.Through stability analysis of sub-models in addition to the full model, states in which cancer is eradicated are found, as well as states in which cancer persists, given certain parameter values.
Year: 2016
Name: Meghan Stevens
Institution: Drake University
Subject area(s): Ordinary Differential Equations, Mathematical Biology, Global Dynamics
Title of Talk: Global Dynamics of a Breast Cancer Competition System
Abstract: In this talk I present a system of five ordinary differential equations to model the competition for space and resources between breast cancer cells and healthy cells. Included is the cancer stem cell hypothesis, which states that there exist proliferating cancer stem cells that repopulate non-proliferating tumor cells and can lead to tumor recurrence. These cancer stem cells exist in a smaller population, making them harder to detect. Additionally, the system contains an equation for the immune system in order to show how the body naturally defends itself from invading tumors. Finally, because the majority of breast cancer cells are estrogen-receptor positive, the role of excess estrogen in the body introduced through birth control in included. Estrogen increases the amount of cancer cells while hindering the effectiveness of the immune system. Its presence also increases the likelihood that healthy cells will mutate.Through stability analysis of sub-models in addition to the full model, states in which cancer is eradicated are found, as well as states in which cancer persists, given certain parameter values.
ID:
279
Year: 2010
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): ODE, recurrence, power series, experimental mathematics
Title of Talk: Recurrences, power series, and ODE
Abstract: A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects.
Year: 2010
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): ODE, recurrence, power series, experimental mathematics
Title of Talk: Recurrences, power series, and ODE
Abstract: A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects.
ID:
286
Year: 2010
Name: Jitka Stehnova
Institution: Mt. Mercy College
Subject area(s): Number Theory, Representation Theory
Title of Talk: Representation Theory
Abstract: In this talk, we first give an introduction to the representation theory of p-adic groups. We will then focus on the subset of unitary groups, specifically U(1,1) and U(2) and show a process of parametrization of irreducible admissible supercuspidal representations.
Year: 2010
Name: Jitka Stehnova
Institution: Mt. Mercy College
Subject area(s): Number Theory, Representation Theory
Title of Talk: Representation Theory
Abstract: In this talk, we first give an introduction to the representation theory of p-adic groups. We will then focus on the subset of unitary groups, specifically U(1,1) and U(2) and show a process of parametrization of irreducible admissible supercuspidal representations.
ID:
64
Year: 2004
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, exponential sums
Title of Talk: Uniform distribution and invertible matrices
Abstract: Uniform distribution is usually known as a property of sequences xn in the unit interval, like n alpha modulo 1, where alpha is irrational. We will present an example of uniform distribution in the unit square, explain the handy Weyl criterion used to prove uniform distribution, and conclude with an application to invertible 2x2 - matrices over the integers.
Year: 2004
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, exponential sums
Title of Talk: Uniform distribution and invertible matrices
Abstract: Uniform distribution is usually known as a property of sequences xn in the unit interval, like n alpha modulo 1, where alpha is irrational. We will present an example of uniform distribution in the unit square, explain the handy Weyl criterion used to prove uniform distribution, and conclude with an application to invertible 2x2 - matrices over the integers.
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:
372
Year: 2013
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Diophantine Geometry, L-functions
Title of Talk: Geometric distribution of primes in Z[sqrt(2)]
Abstract: It all starts with the question: what can we say about integers a, b such that a^2 - 2b^2 is a prime? We will show some ways to make this question more precise - in particular, we study the distribution of the corresponding points (a,b) in the plane. The fundamental tool is the ring Z[sqrt(2)], and from there we make connections to analytic number theory (L-functions, Hecke characters) which arise very naturally - this is the context where Hecke invented 'Hecke characters', and they are much easier to understand here than when you read about them in MathWorld.
Year: 2013
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Diophantine Geometry, L-functions
Title of Talk: Geometric distribution of primes in Z[sqrt(2)]
Abstract: It all starts with the question: what can we say about integers a, b such that a^2 - 2b^2 is a prime? We will show some ways to make this question more precise - in particular, we study the distribution of the corresponding points (a,b) in the plane. The fundamental tool is the ring Z[sqrt(2)], and from there we make connections to analytic number theory (L-functions, Hecke characters) which arise very naturally - this is the context where Hecke invented 'Hecke characters', and they are much easier to understand here than when you read about them in MathWorld.
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:
260
Year: 2009
Name: Eric Errthum
Institution: Winona State University
Subject area(s): Number Theory
Title of Talk: A p-adic Euclidean Algorithm
Abstract: A brief introduction to the p-adic numbers will be given. Then a p-adic Division Algorithm and a p-adic Euclidean Algorithm will be defined in such a way that they mimic the classical algorithms. Lastly these methods are used to compute a generalized GCD and a p-adic simple continued fraction.
Year: 2009
Name: Eric Errthum
Institution: Winona State University
Subject area(s): Number Theory
Title of Talk: A p-adic Euclidean Algorithm
Abstract: A brief introduction to the p-adic numbers will be given. Then a p-adic Division Algorithm and a p-adic Euclidean Algorithm will be defined in such a way that they mimic the classical algorithms. Lastly these methods are used to compute a generalized GCD and a p-adic simple continued fraction.
ID:
46
Year: 2004
Name: Charles Ashbacher
Institution: Mt. Mercy College
Subject area(s): Number theory
Title of Talk: Not All Numbers Are Beautiful
Abstract: In his forthcoming book,
Year: 2004
Name: Charles Ashbacher
Institution: Mt. Mercy College
Subject area(s): Number theory
Title of Talk: Not All Numbers Are Beautiful
Abstract: In his forthcoming book,
ID:
48
Year: 2004
Name: Christopher French
Institution: Grinnell College
Subject area(s): Number Theory
Title of Talk: Fifth roots of Fibonacci Fractions
Abstract: The quotients of consecutive Fibonacci numbers converge to the golden ratio. In fact, the continued fraction expansion for such ratios consists of the nth truncation of the continued fraction expansion for the golden ratio. In a similar way, if F_n denotes the nth Fibonacci number, then the kth root of F_{n+k}/F_n converges to the golden ratio, and one can investigate the continued fraction expansion for these roots. Something rather remarkable happens when k=5.
Year: 2004
Name: Christopher French
Institution: Grinnell College
Subject area(s): Number Theory
Title of Talk: Fifth roots of Fibonacci Fractions
Abstract: The quotients of consecutive Fibonacci numbers converge to the golden ratio. In fact, the continued fraction expansion for such ratios consists of the nth truncation of the continued fraction expansion for the golden ratio. In a similar way, if F_n denotes the nth Fibonacci number, then the kth root of F_{n+k}/F_n converges to the golden ratio, and one can investigate the continued fraction expansion for these roots. Something rather remarkable happens when k=5.
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:
153
Year: 2006
Name: Charles Ashbacher
Institution: Mt. Mercy College
Subject area(s): Number theory
Title of Talk: Some Properties of the Smarandache Fitorial and Supplementary Fitorial Functions
Abstract: The Smarandache Fitorial function FI(N) is defined as the product of all the positive integers less than N that are relatively prime to N and the Smarandache Supplementary Fitorial function SFI(N) as the product of all the positive integers less than or equal to N that are not relatively prime to N. It is clear that FI(N) * SFI(N) = N!. These functions are defined in the book
Year: 2006
Name: Charles Ashbacher
Institution: Mt. Mercy College
Subject area(s): Number theory
Title of Talk: Some Properties of the Smarandache Fitorial and Supplementary Fitorial Functions
Abstract: The Smarandache Fitorial function FI(N) is defined as the product of all the positive integers less than N that are relatively prime to N and the Smarandache Supplementary Fitorial function SFI(N) as the product of all the positive integers less than or equal to N that are not relatively prime to N. It is clear that FI(N) * SFI(N) = N!. These functions are defined in the book
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.