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 161-180 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:
403
Year: 2014
Name: Brian Diaz
Institution: Cornell College
Subject area(s):
Title of Talk: An Elementary Solution to a Problem of Ramanujan's Interest
Abstract: In the early 1900's, Srinivasa Ramanujan discovered an intriguing, yet exotic, integral that he believed could have a 'simple', beautiful closed form. However, he never gave a simple solution to this integral. It wouldn't be until the mid-1950's when Russian mathematician V. I. Levin revisited Ramanujan's integral. He used non-elementary calculus techniques to prove that the integral, indeed, had a closed form for a single parameter; however, that parameter was only defined for positive integers. The integral would not be fully explored for the sake of itself until half a century later. Recently, V. Adamchik found that exact same integral that Ramanujan had encountered nearly a century ago. He showed a closed form using methods of Euler sums and related non-elementary techniques. This presentation will show a closed form of the integral does exist, but use only methods of elementary calculus. In addition, these techniques can be used to extend the result to double parameters!
Year: 2014
Name: Brian Diaz
Institution: Cornell College
Subject area(s):
Title of Talk: An Elementary Solution to a Problem of Ramanujan's Interest
Abstract: In the early 1900's, Srinivasa Ramanujan discovered an intriguing, yet exotic, integral that he believed could have a 'simple', beautiful closed form. However, he never gave a simple solution to this integral. It wouldn't be until the mid-1950's when Russian mathematician V. I. Levin revisited Ramanujan's integral. He used non-elementary calculus techniques to prove that the integral, indeed, had a closed form for a single parameter; however, that parameter was only defined for positive integers. The integral would not be fully explored for the sake of itself until half a century later. Recently, V. Adamchik found that exact same integral that Ramanujan had encountered nearly a century ago. He showed a closed form using methods of Euler sums and related non-elementary techniques. This presentation will show a closed form of the integral does exist, but use only methods of elementary calculus. In addition, these techniques can be used to extend the result to double parameters!
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:
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:
400
Year: 2014
Name: Debasis Mandal
Institution: Iowa State University
Subject area(s): Complexity Theory
Title of Talk: Separation of NP-Completeness Notions
Abstract: Informally speaking, reductions translate instances of one problem to instances of another problem; a problem A is polynomial-time reducible to a problem B if A can be solved in polynomial-time by making queries to problem B. By varying the manner in which the queries are allowed to make, we obtain a wide spectrum of reductions. At one end of the spectrum is Cook/Turing reduction where multiple queries are allowed and the i-th query made depends on answers to previous queries. On the other end is the most restrictive reduction, Karp-Levin/many-one reduction, where each positive instance of problem A is mapped to a positive instance of problem B, and so are the negative instances. This raises the following question: For complexity class NP, is there a Turing complete language that is not many-one complete? The first result that achieves such separation, under a reasonable hypothesis, is due to Lutz and Mayordomo. We show this separation for NP, under a believable worst-case hardness hypothesis. This is a joint work with A. Pavan and Rajeswari Venugopalan.
Year: 2014
Name: Debasis Mandal
Institution: Iowa State University
Subject area(s): Complexity Theory
Title of Talk: Separation of NP-Completeness Notions
Abstract: Informally speaking, reductions translate instances of one problem to instances of another problem; a problem A is polynomial-time reducible to a problem B if A can be solved in polynomial-time by making queries to problem B. By varying the manner in which the queries are allowed to make, we obtain a wide spectrum of reductions. At one end of the spectrum is Cook/Turing reduction where multiple queries are allowed and the i-th query made depends on answers to previous queries. On the other end is the most restrictive reduction, Karp-Levin/many-one reduction, where each positive instance of problem A is mapped to a positive instance of problem B, and so are the negative instances. This raises the following question: For complexity class NP, is there a Turing complete language that is not many-one complete? The first result that achieves such separation, under a reasonable hypothesis, is due to Lutz and Mayordomo. We show this separation for NP, under a believable worst-case hardness hypothesis. This is a joint work with A. Pavan and Rajeswari Venugopalan.
ID:
399
Year: 2014
Name: Tyler Skorczewski
Institution: Cornell College
Subject area(s): math biology, fluid dynamics
Title of Talk: Toward an integrative model of suction feeding using the immersed boundary method
Abstract: Suction feeding is among the most common forms of aquatic prey capture. During a suction feeding strike a fish rapidly opens its mouth creating a fluid flow that draws in the prey. This is an example of indirect prey capture; the fish does not directly manipulate the prey, but rather the fluid flow around the prey. Previous studies of suction feeding have either studied jaw mechanics or the flow field in isolation, or have only considered rigid jaw motions (think of a fish mouth as a collection of metal plates). In this talk I will describe work in progress to develop a new methodology to study fish suction feeding that relaxes some of these conditions. In particular we will allow for more realistic flexible jaws and examine how the kinematics of the jaw motion affects the resultant flow field and subsequent prey capture.
Year: 2014
Name: Tyler Skorczewski
Institution: Cornell College
Subject area(s): math biology, fluid dynamics
Title of Talk: Toward an integrative model of suction feeding using the immersed boundary method
Abstract: Suction feeding is among the most common forms of aquatic prey capture. During a suction feeding strike a fish rapidly opens its mouth creating a fluid flow that draws in the prey. This is an example of indirect prey capture; the fish does not directly manipulate the prey, but rather the fluid flow around the prey. Previous studies of suction feeding have either studied jaw mechanics or the flow field in isolation, or have only considered rigid jaw motions (think of a fish mouth as a collection of metal plates). In this talk I will describe work in progress to develop a new methodology to study fish suction feeding that relaxes some of these conditions. In particular we will allow for more realistic flexible jaws and examine how the kinematics of the jaw motion affects the resultant flow field and subsequent prey capture.
ID:
398
Year: 2014
Name: Olena Ostapyuk
Institution: University of Northern Iowa
Subject area(s): Mathematics Education
Title of Talk: How can i be more than Imaginary for Future HIgh School Mathematics Teachers
Abstract: High school teachers introduce i as a solution to the equation x^2=-1 without understanding the geometry of complex numbers. This results in students not understanding the role of complex numbers in other contexts. The purpose of this talk is to share an introduction to complex numbers used in a mathematics course for future secondary mathematics teachers to demystify i and provide a rationale for its use in both pure and applied mathematics.
Year: 2014
Name: Olena Ostapyuk
Institution: University of Northern Iowa
Subject area(s): Mathematics Education
Title of Talk: How can i be more than Imaginary for Future HIgh School Mathematics Teachers
Abstract: High school teachers introduce i as a solution to the equation x^2=-1 without understanding the geometry of complex numbers. This results in students not understanding the role of complex numbers in other contexts. The purpose of this talk is to share an introduction to complex numbers used in a mathematics course for future secondary mathematics teachers to demystify i and provide a rationale for its use in both pure and applied mathematics.
ID:
397
Year: 2014
Name: Charles Ashbacher
Institution: Upper Iowa University
Subject area(s):
Title of Talk: Teaching Managers to Think Of All Factors When Making Decisions
Abstract: Abstract: Major management decisions are often made without the proper analysis of all the details and consequences of the actions. The current wave known as 'reshoring' is where companies that transferred production facilities to other countries are now returning that production to the United States. This is a consequence of rising costs of labor and materials in other countries coupled with additional factors such as lax IP laws. Proper training of managers includes cost projections that incorporate all factors and two major projects in a management science class at Upper Iowa University where these aspects are included will be presented.
Year: 2014
Name: Charles Ashbacher
Institution: Upper Iowa University
Subject area(s):
Title of Talk: Teaching Managers to Think Of All Factors When Making Decisions
Abstract: Abstract: Major management decisions are often made without the proper analysis of all the details and consequences of the actions. The current wave known as 'reshoring' is where companies that transferred production facilities to other countries are now returning that production to the United States. This is a consequence of rising costs of labor and materials in other countries coupled with additional factors such as lax IP laws. Proper training of managers includes cost projections that incorporate all factors and two major projects in a management science class at Upper Iowa University where these aspects are included will be presented.
ID:
396
Year: 2014
Name: Dave Renfro
Institution: #business/industry/government
Subject area(s): calculus, real analysis
Title of Talk: Calculus Curiosities
Abstract: Over the years I have collected a lot of little-known mathematical curiosities and minutia from various books and journal articles. This talk is intended to be a "show and tell" for some of this material, mostly restricted to things that could be of use in first year calculus courses, or at least to things likely to be of interest to teachers of such courses.
Year: 2014
Name: Dave Renfro
Institution: #business/industry/government
Subject area(s): calculus, real analysis
Title of Talk: Calculus Curiosities
Abstract: Over the years I have collected a lot of little-known mathematical curiosities and minutia from various books and journal articles. This talk is intended to be a "show and tell" for some of this material, mostly restricted to things that could be of use in first year calculus courses, or at least to things likely to be of interest to teachers of such courses.
ID:
395
Year: 2014
Name: Adam Case
Institution: Iowa State University
Subject area(s): Algorithmic Information Theory
Title of Talk: Mutual Dimension
Abstract: The mutual (shared) information between two random variables is a well-understood concept in Shannon information theory, but how do we think about mutual information between other kinds of objects such as strings or real numbers? In this talk, we discuss various notions of mutual information from the perspective of algorithmic information theory. First we explore the algorithmic information content of a binary string. We then discuss the notion of the dimension (density of algorithmic information) of a real number. Finally, we explain our recent solution to an open problem: the correct formulation of the mutual information between two real numbers. This is joint work with Jack Lutz. The talk will be accessible to math undergraduates.
Year: 2014
Name: Adam Case
Institution: Iowa State University
Subject area(s): Algorithmic Information Theory
Title of Talk: Mutual Dimension
Abstract: The mutual (shared) information between two random variables is a well-understood concept in Shannon information theory, but how do we think about mutual information between other kinds of objects such as strings or real numbers? In this talk, we discuss various notions of mutual information from the perspective of algorithmic information theory. First we explore the algorithmic information content of a binary string. We then discuss the notion of the dimension (density of algorithmic information) of a real number. Finally, we explain our recent solution to an open problem: the correct formulation of the mutual information between two real numbers. This is joint work with Jack Lutz. The talk will be accessible to math undergraduates.
ID:
394
Year: 2014
Name: Chris Spicer
Institution: Morningside College
Subject area(s): graph theory
Title of Talk: Cops and Robbers on Oriented Graphs
Abstract: Cops and Robbers is a turn-based game traditionally played on graphs. In this talk, we extend this game to oriented graphs. Although a complete characterization of 1-cop-win graphs is known, there is not yet a corresponding characterization for oriented graphs. Necessary conditions are described for an oriented graph to be 1-cop-win, and several results are provided toward finding sufficient conditions.
Year: 2014
Name: Chris Spicer
Institution: Morningside College
Subject area(s): graph theory
Title of Talk: Cops and Robbers on Oriented Graphs
Abstract: Cops and Robbers is a turn-based game traditionally played on graphs. In this talk, we extend this game to oriented graphs. Although a complete characterization of 1-cop-win graphs is known, there is not yet a corresponding characterization for oriented graphs. Necessary conditions are described for an oriented graph to be 1-cop-win, and several results are provided toward finding sufficient conditions.
ID:
393
Year: 2014
Name: Titus Klinge
Institution: Iowa State University
Subject area(s): molecular programming, ODEs
Title of Talk: Exact Analytical Solutions of a Chemical Oscillator
Abstract: A chemical reaction network (CRN) is a mathematical model used extensively in chemistry with deep connections to ordinary differential equations (ODEs). CRNs have been used to model naturally occurring reactions that are periodic such as the Brusselator and the Oreganator. However, the nonlinearity of the underlying ODEs is often complex and a large amount of research has been devoted to approximating the solutions to these ODEs. Recently, Luca Cardelli defined a CRN that has similar desirable periodic behavior. In this talk we present a general analysis of this CRN including exact analytical solutions to the underlying ODEs. This is joint work with James I. Lathrop. This talk will be accessible to both undergraduate and graduate students.
Year: 2014
Name: Titus Klinge
Institution: Iowa State University
Subject area(s): molecular programming, ODEs
Title of Talk: Exact Analytical Solutions of a Chemical Oscillator
Abstract: A chemical reaction network (CRN) is a mathematical model used extensively in chemistry with deep connections to ordinary differential equations (ODEs). CRNs have been used to model naturally occurring reactions that are periodic such as the Brusselator and the Oreganator. However, the nonlinearity of the underlying ODEs is often complex and a large amount of research has been devoted to approximating the solutions to these ODEs. Recently, Luca Cardelli defined a CRN that has similar desirable periodic behavior. In this talk we present a general analysis of this CRN including exact analytical solutions to the underlying ODEs. This is joint work with James I. Lathrop. This talk will be accessible to both undergraduate and graduate students.
ID:
392
Year: 2014
Name: Ruth Charney
Institution: Brandeis University
Subject area(s):
Title of Talk: An Excursion into the Strange World of Singular Geometry
Abstract: In high school we learn about the geometry of the plane. Later, we encounter the geometry of smooth manifolds. In this talk, we take a peek at the mind-bending geometry of singular spaces and their applications.
Year: 2014
Name: Ruth Charney
Institution: Brandeis University
Subject area(s):
Title of Talk: An Excursion into the Strange World of Singular Geometry
Abstract: In high school we learn about the geometry of the plane. Later, we encounter the geometry of smooth manifolds. In this talk, we take a peek at the mind-bending geometry of singular spaces and their applications.
ID:
391
Year: 2014
Name: Robert Devaney
Institution: Boston University
Subject area(s):
Title of Talk: The Fractal Geometry of the Mandelbrot Set
Abstract: In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the "Devaney" sequence. There might even be a joke or two in the talk.
Year: 2014
Name: Robert Devaney
Institution: Boston University
Subject area(s):
Title of Talk: The Fractal Geometry of the Mandelbrot Set
Abstract: In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the "Devaney" sequence. There might even be a joke or two in the talk.
ID:
390
Year: 2014
Name: Theron Hitchman
Institution: University of Northern Iowa
Subject area(s):
Title of Talk: Building Towards Student Ownership
Abstract: Why should a student choose to continue his or her study of mathematics beyond high school? How can we enrich our mathematics classes to make them more interesting and engaging? How can we introduce students to the culture of mathematics, and bring them into the community? I will argue that one way to address these questions is to trust in the students and return to them the ownership of the mathematics, both the content and the process. We might even have some time to discuss how we can pull that off without looking too foolish.
Year: 2014
Name: Theron Hitchman
Institution: University of Northern Iowa
Subject area(s):
Title of Talk: Building Towards Student Ownership
Abstract: Why should a student choose to continue his or her study of mathematics beyond high school? How can we enrich our mathematics classes to make them more interesting and engaging? How can we introduce students to the culture of mathematics, and bring them into the community? I will argue that one way to address these questions is to trust in the students and return to them the ownership of the mathematics, both the content and the process. We might even have some time to discuss how we can pull that off without looking too foolish.
ID:
389
Year: 2014
Name: Jason Smith
Institution: Graceland University
Subject area(s):
Title of Talk: Inquiry Based Learning
Abstract: A discussion about the Inquiry Based Learning(IBL) Workshop I attended this summer as well as my experience using the IBL methods in Probability and Stochastic Processes. I will discuss some early successes and early failures in class. I will mention some of the research in support of IBL.
Year: 2014
Name: Jason Smith
Institution: Graceland University
Subject area(s):
Title of Talk: Inquiry Based Learning
Abstract: A discussion about the Inquiry Based Learning(IBL) Workshop I attended this summer as well as my experience using the IBL methods in Probability and Stochastic Processes. I will discuss some early successes and early failures in class. I will mention some of the research in support of IBL.
ID:
388
Year: 2014
Name: Morgan Fonley
Institution: University of Iowa
Subject area(s):
Title of Talk: Amplification and damping of an oscillating streamflow signal in a river network
Abstract: When river flow is observed under dry conditions (such as late summer), a daily fluctuation can be seen. Without the addition of precipitation, the source of these fluctuations is understood to be evapotranspiration of water from the riparian zone of trees near the river network. The flow at any point in the river network exhibits a time delay between the time of maximal evaporation (around midday) and the minimal streamflow. Several hypotheses suggest reasons for this time delay including different methods by which water moves through the soil. An alternative hypothesis is that the time delay instead comes from constructive and destructive interference that occurs when the oscillating flows of river links undergo different phase shifts and combine their signals. In this way, the flow at a downstream river link can be amplified or damped. I present an analytic solution to the transport equation, a linear ordinary differential equation that can be used to determine the flow at any point in a river network when all hillslopes are assumed to have uniform parameters. I use this solution to demonstrate the extent of amplification or damping that can occur when different parameter values are varied.
Year: 2014
Name: Morgan Fonley
Institution: University of Iowa
Subject area(s):
Title of Talk: Amplification and damping of an oscillating streamflow signal in a river network
Abstract: When river flow is observed under dry conditions (such as late summer), a daily fluctuation can be seen. Without the addition of precipitation, the source of these fluctuations is understood to be evapotranspiration of water from the riparian zone of trees near the river network. The flow at any point in the river network exhibits a time delay between the time of maximal evaporation (around midday) and the minimal streamflow. Several hypotheses suggest reasons for this time delay including different methods by which water moves through the soil. An alternative hypothesis is that the time delay instead comes from constructive and destructive interference that occurs when the oscillating flows of river links undergo different phase shifts and combine their signals. In this way, the flow at a downstream river link can be amplified or damped. I present an analytic solution to the transport equation, a linear ordinary differential equation that can be used to determine the flow at any point in a river network when all hillslopes are assumed to have uniform parameters. I use this solution to demonstrate the extent of amplification or damping that can occur when different parameter values are varied.
ID:
387
Year: 2014
Name: Debra Czarneski
Institution: Simpson College
Subject area(s):
Title of Talk: Student Presentations in Calculus II
Abstract: In Calculus II, I have student groups teach the integral application sections to the rest of the class. The groups of three students prepare and deliver the lecture, assign homework, and provide feedback on the homework assigned. In this talk, I will discuss the details of the assignment and student responses to the assignment.
Year: 2014
Name: Debra Czarneski
Institution: Simpson College
Subject area(s):
Title of Talk: Student Presentations in Calculus II
Abstract: In Calculus II, I have student groups teach the integral application sections to the rest of the class. The groups of three students prepare and deliver the lecture, assign homework, and provide feedback on the homework assigned. In this talk, I will discuss the details of the assignment and student responses to the assignment.
ID:
386
Year: 2014
Name: Victor Vega
Institution: College of Coastal Georgia
Subject area(s): Topology, Geometry
Title of Talk: Fractals: A Basic Introduction
Abstract: We present a basic introduction to fractals by looking and understand the concept of Hausdorff dimension and Topological dimension by looking at simple examples of classic fractals and geometric constructs. We also define the Julia set and Mandelbrot set as an iterative function on the complex plane and present some examples together with some historical remarks.
Year: 2014
Name: Victor Vega
Institution: College of Coastal Georgia
Subject area(s): Topology, Geometry
Title of Talk: Fractals: A Basic Introduction
Abstract: We present a basic introduction to fractals by looking and understand the concept of Hausdorff dimension and Topological dimension by looking at simple examples of classic fractals and geometric constructs. We also define the Julia set and Mandelbrot set as an iterative function on the complex plane and present some examples together with some historical remarks.
ID:
384
Year: 2014
Name: Susan Crook
Institution: Loras College
Subject area(s):
Title of Talk: Generalized Augmented Happy Numbers
Abstract: What makes a number a happy number? Is it sitting on the beach with no cares in the world or is there more to it than that? In this talk, we'll mathematically define happy numbers and discuss some properties. We'll explore some of their properties and look at variations on the idea of happy numbers to see if we can extend any of these properties. This work was done collaboratively with other undergraduate math faculty at a Research Experience for Undergraduate Faculty this summer at the American Institute for Mathematics, so there will also be a short plug for REUs and the REUF.
Year: 2014
Name: Susan Crook
Institution: Loras College
Subject area(s):
Title of Talk: Generalized Augmented Happy Numbers
Abstract: What makes a number a happy number? Is it sitting on the beach with no cares in the world or is there more to it than that? In this talk, we'll mathematically define happy numbers and discuss some properties. We'll explore some of their properties and look at variations on the idea of happy numbers to see if we can extend any of these properties. This work was done collaboratively with other undergraduate math faculty at a Research Experience for Undergraduate Faculty this summer at the American Institute for Mathematics, so there will also be a short plug for REUs and the REUF.