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 41-60 of 471 results.
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ID:
548
Year: 2019
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Balanced Numbers and Balanced Primes
Abstract: Balanced numbers are odd natural numbers n which have an equal number of 0s and 1s in the periodic part of the base-2 representation of their reciprocal 1/n. We present some insights about balanced numbers that use just elementary Number Theory like the Quadratic Reciprocity Theorem. In particular, if a prime p is congruent to 3 or 5 modulo 8, then p is balanced. If a prime p is congruent to 7 modulo 8, then p is not balanced. All powers of p are balanced iff p is. The case of primes congruent to 1 modulo 8 is much more difficult. Hasse made a breakthrough in 1966, showing that the balanced primes have a Dirichlet density of 17/24. We have refined Hasse's result slightly. Another question is how big is the set of balanced numbers (not only primes) less than x? Using a method due to Landau, we can show that this is bounded above by C x/log^(1/4) (x) and below by D x / log^(3/4)(x), with constants C, D > 0. I solemnly promise that I won't go into the gory detail, only highlight the beautiful and accessible parts of the subject. The second part of the talk is joint work with Joshua Zelinsky.
Year: 2019
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Balanced Numbers and Balanced Primes
Abstract: Balanced numbers are odd natural numbers n which have an equal number of 0s and 1s in the periodic part of the base-2 representation of their reciprocal 1/n. We present some insights about balanced numbers that use just elementary Number Theory like the Quadratic Reciprocity Theorem. In particular, if a prime p is congruent to 3 or 5 modulo 8, then p is balanced. If a prime p is congruent to 7 modulo 8, then p is not balanced. All powers of p are balanced iff p is. The case of primes congruent to 1 modulo 8 is much more difficult. Hasse made a breakthrough in 1966, showing that the balanced primes have a Dirichlet density of 17/24. We have refined Hasse's result slightly. Another question is how big is the set of balanced numbers (not only primes) less than x? Using a method due to Landau, we can show that this is bounded above by C x/log^(1/4) (x) and below by D x / log^(3/4)(x), with constants C, D > 0. I solemnly promise that I won't go into the gory detail, only highlight the beautiful and accessible parts of the subject. The second part of the talk is joint work with Joshua Zelinsky.
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:
551
Year: 2019
Name: Angela Kohlhaas
Institution: Loras College
Subject area(s):
Title of Talk: Iowa Mathematics Pathway Forum
Abstract: This fall, members of the Iowa Department of Education started a statewide conversation with the goal of improving student success in transitioning from high school to college math, with a focus on low income students and underrepresented minorities. This conversation is taking place through a series of monthly online discussions connecting representatives from various professional Iowa math organizations across high schools, community colleges, Regents institutions, and private four-year colleges and universities. As our representative from the Iowa MAA, I will share the background for this initiative as well as our current progress defining challenges and brainstorming solutions. I will also invite discussion and continued brainstorming from the audience.
Year: 2019
Name: Angela Kohlhaas
Institution: Loras College
Subject area(s):
Title of Talk: Iowa Mathematics Pathway Forum
Abstract: This fall, members of the Iowa Department of Education started a statewide conversation with the goal of improving student success in transitioning from high school to college math, with a focus on low income students and underrepresented minorities. This conversation is taking place through a series of monthly online discussions connecting representatives from various professional Iowa math organizations across high schools, community colleges, Regents institutions, and private four-year colleges and universities. As our representative from the Iowa MAA, I will share the background for this initiative as well as our current progress defining challenges and brainstorming solutions. I will also invite discussion and continued brainstorming from the audience.
ID:
554
Year: 2019
Name: Susan Crook
Institution: Loras College
Subject area(s):
Title of Talk: Why Aren't We All Using IBL?
Abstract: Inquiry-based learning has been a buzzword in college mathematics teaching circles for years. By having students have more ownership over their own learning, IBL has been shown to begin closing the achievement gap for minority students. Anecdotal evidence of its success abounds…so, with all this positive data, why isn't every math classroom taught using IBL methods? In this interactive talk, we'll discuss some of the common obstacles and challenges professors experience when they use IBL and brainstorm some ways to overcome these issues.
Year: 2019
Name: Susan Crook
Institution: Loras College
Subject area(s):
Title of Talk: Why Aren't We All Using IBL?
Abstract: Inquiry-based learning has been a buzzword in college mathematics teaching circles for years. By having students have more ownership over their own learning, IBL has been shown to begin closing the achievement gap for minority students. Anecdotal evidence of its success abounds…so, with all this positive data, why isn't every math classroom taught using IBL methods? In this interactive talk, we'll discuss some of the common obstacles and challenges professors experience when they use IBL and brainstorm some ways to overcome these issues.
ID:
555
Year: 2019
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: The Math of Data Science
Abstract: Data Science is one of the buzzwordiest fields right now. In this talk, I will try to define Data Science out of my work implementing it as an undergraduate major at Loras. Then I will go on to talk about where Mathematics, both from the undergraduate and graduate curricula, is integral to the development and perhaps practice of Data Science.
Year: 2019
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: The Math of Data Science
Abstract: Data Science is one of the buzzwordiest fields right now. In this talk, I will try to define Data Science out of my work implementing it as an undergraduate major at Loras. Then I will go on to talk about where Mathematics, both from the undergraduate and graduate curricula, is integral to the development and perhaps practice of Data Science.
ID:
512
Year: 2018
Name: Katherine Vance
Institution: Simpson College
Subject area(s):
Title of Talk: Sine, Cosine, and Euler
Abstract: In mid-September, I attended a training workshop for the TRIUMPHS project. The goal of the project is to develop materials to teach core mathematical content using primary historical sources and active learning techniques. At the end of September, I site-tested one of the TRIUMPHS Primary Source Projects, ``The Derivatives of the Sine and Cosine Functions," in my Calculus 1 class. I will give a little bit of background on the TRIUMPHS project and share my experience as a site tester.
Year: 2018
Name: Katherine Vance
Institution: Simpson College
Subject area(s):
Title of Talk: Sine, Cosine, and Euler
Abstract: In mid-September, I attended a training workshop for the TRIUMPHS project. The goal of the project is to develop materials to teach core mathematical content using primary historical sources and active learning techniques. At the end of September, I site-tested one of the TRIUMPHS Primary Source Projects, ``The Derivatives of the Sine and Cosine Functions," in my Calculus 1 class. I will give a little bit of background on the TRIUMPHS project and share my experience as a site tester.
ID:
513
Year: 2018
Name: Theron Hitchman
Institution: University of Northern Iowa
Subject area(s): topology
Title of Talk: Playing with topology: knots and branched covers
Abstract: In joint work with undergraduate Dan Tarnow, we played with lifting knot diagrams from the sphere to other surfaces using branched covers and a combinatorial construction called a 'butterfly diagram.' We played with many examples, including finding many lifts of the trefoil. I'll share our small collection of results, some of the 3d printed knots that Dan made, and how I am pretty sure we asked the wrong questions.
Year: 2018
Name: Theron Hitchman
Institution: University of Northern Iowa
Subject area(s): topology
Title of Talk: Playing with topology: knots and branched covers
Abstract: In joint work with undergraduate Dan Tarnow, we played with lifting knot diagrams from the sphere to other surfaces using branched covers and a combinatorial construction called a 'butterfly diagram.' We played with many examples, including finding many lifts of the trefoil. I'll share our small collection of results, some of the 3d printed knots that Dan made, and how I am pretty sure we asked the wrong questions.
ID:
514
Year: 2018
Name: Brittney Miller
Institution: Coe College
Subject area(s):
Title of Talk: Using Playdough and 3D Prints to Visualize Volumes
Abstract: Using two-dimensional images to visualize three-dimensional objects can be challenging. Instead, playdough and 3D prints can help us better understand different shapes and their cross sections. Let’s have some fun with these physical representations of objects to more clearly illustrate and help our students learn how to, for example, set up volume integrals.
Year: 2018
Name: Brittney Miller
Institution: Coe College
Subject area(s):
Title of Talk: Using Playdough and 3D Prints to Visualize Volumes
Abstract: Using two-dimensional images to visualize three-dimensional objects can be challenging. Instead, playdough and 3D prints can help us better understand different shapes and their cross sections. Let’s have some fun with these physical representations of objects to more clearly illustrate and help our students learn how to, for example, set up volume integrals.
ID:
515
Year: 2018
Name: Michael Dorff
Institution: Brigham Young University
Subject area(s):
Title of Talk: How Mathematics Is Making Hollywood Movies Better
Abstract: What’s your favorite movie? Star Wars? Avatar? The Avengers? Frozen? What do these and all the highest earning Hollywood movies since 2000 have in common? Mathematics! You probably didn’t think about it while watching these movies, but math was used to help make them. In this presentation, we will discuss how math is being used to create better and more realistic movies. Along the way we will discuss some specific movies and the mathematics behind them. We will include examples from Disney’s 2013 movie Frozen (how to use math to create realistic looking snow) to Pixar’s 2004 movie The Incredibles (how to use math to make an animated character move faster). Come and join us and get a better appreciation of mathematics and movies.
Year: 2018
Name: Michael Dorff
Institution: Brigham Young University
Subject area(s):
Title of Talk: How Mathematics Is Making Hollywood Movies Better
Abstract: What’s your favorite movie? Star Wars? Avatar? The Avengers? Frozen? What do these and all the highest earning Hollywood movies since 2000 have in common? Mathematics! You probably didn’t think about it while watching these movies, but math was used to help make them. In this presentation, we will discuss how math is being used to create better and more realistic movies. Along the way we will discuss some specific movies and the mathematics behind them. We will include examples from Disney’s 2013 movie Frozen (how to use math to create realistic looking snow) to Pixar’s 2004 movie The Incredibles (how to use math to make an animated character move faster). Come and join us and get a better appreciation of mathematics and movies.
ID:
516
Year: 2018
Name: Carlos Castillo-Chavez
Institution: Arizona State University
Subject area(s):
Title of Talk: Epidemiology: Role of dynamic individual decisions during ongoing epidemic outbreaks
Abstract: The lecture begins with a historical review of epidemic models and the concept of tipping point. We then revisit phenomenologically inspired modeling frameworks that account for the impact that single disease outbreaks have on the decisions that individuals make in response to real or perceived risk of infection. Finally, a behavioral framework where individual decisions are modeled as a function of tradeoffs made in response to self-assessed costs tied to present or future risks of infection, including those resulting from potential loss of benefits due to risk aversion decisions is introduced and implemented on a simplified population-level epidemic model. The impact of these decisions is illustrated in the context of a single influenza outbreak.
Year: 2018
Name: Carlos Castillo-Chavez
Institution: Arizona State University
Subject area(s):
Title of Talk: Epidemiology: Role of dynamic individual decisions during ongoing epidemic outbreaks
Abstract: The lecture begins with a historical review of epidemic models and the concept of tipping point. We then revisit phenomenologically inspired modeling frameworks that account for the impact that single disease outbreaks have on the decisions that individuals make in response to real or perceived risk of infection. Finally, a behavioral framework where individual decisions are modeled as a function of tradeoffs made in response to self-assessed costs tied to present or future risks of infection, including those resulting from potential loss of benefits due to risk aversion decisions is introduced and implemented on a simplified population-level epidemic model. The impact of these decisions is illustrated in the context of a single influenza outbreak.
ID:
517
Year: 2018
Name: Chris Spicer
Institution: Morningside College
Subject area(s):
Title of Talk: On Sheldon Primes
Abstract: In a 2015 MAA Math Horizons article, the authors introduced the concept of a Sheldon prime, based on a conversation between several characters in the CBS sitcom The Big Bang Theory. The authors left open whether or not any number other than 73 satisfied the specific properties. Recent work has proven that it is in fact unique. We will introduce Sheldon primes and the number theory behind them, and demonstrate its uniqueness.
Year: 2018
Name: Chris Spicer
Institution: Morningside College
Subject area(s):
Title of Talk: On Sheldon Primes
Abstract: In a 2015 MAA Math Horizons article, the authors introduced the concept of a Sheldon prime, based on a conversation between several characters in the CBS sitcom The Big Bang Theory. The authors left open whether or not any number other than 73 satisfied the specific properties. Recent work has proven that it is in fact unique. We will introduce Sheldon primes and the number theory behind them, and demonstrate its uniqueness.
ID:
518
Year: 2018
Name: Angela Kohlhaas
Institution: Loras College
Subject area(s):
Title of Talk: Data Reasoning: Changing our General Math Requirement
Abstract: At Loras College, we have had a mathematical modeling requirement in our general education for some time. Traditional courses like college algebra, precalculus, and calculus satisfy the requirement, as do a variety of “math for liberal arts” type courses. Though all of them use data, none of them deeply engage students in reasoning with data. This means we are not really preparing our students to engage with our data-driven world. We have also had an increased demand for statistics, which barely satisfies our math modeling outcomes. So, whether we are sages or fools, we have decided to essentially change our general education math requirement to a statistics requirement. In this talk, we will share our hopes, our steps in this direction, and our concerns so far.
Year: 2018
Name: Angela Kohlhaas
Institution: Loras College
Subject area(s):
Title of Talk: Data Reasoning: Changing our General Math Requirement
Abstract: At Loras College, we have had a mathematical modeling requirement in our general education for some time. Traditional courses like college algebra, precalculus, and calculus satisfy the requirement, as do a variety of “math for liberal arts” type courses. Though all of them use data, none of them deeply engage students in reasoning with data. This means we are not really preparing our students to engage with our data-driven world. We have also had an increased demand for statistics, which barely satisfies our math modeling outcomes. So, whether we are sages or fools, we have decided to essentially change our general education math requirement to a statistics requirement. In this talk, we will share our hopes, our steps in this direction, and our concerns so far.
ID:
519
Year: 2018
Name: Eric Canning
Institution: Morningside College
Subject area(s): Mathematics Pedagogy
Title of Talk: The Use of Projects in Calculus II and Linear Algebra
Abstract: I will share my experiences having students, in small groups, create posters and make presentations in Calculus II and Linear Algebra courses. Several students gave poster presentations of their projects at an undergraduate research symposium.
Year: 2018
Name: Eric Canning
Institution: Morningside College
Subject area(s): Mathematics Pedagogy
Title of Talk: The Use of Projects in Calculus II and Linear Algebra
Abstract: I will share my experiences having students, in small groups, create posters and make presentations in Calculus II and Linear Algebra courses. Several students gave poster presentations of their projects at an undergraduate research symposium.
ID:
520
Year: 2018
Name: Laura McCauley
Institution: Peru State College
Subject area(s): Graph Theory
Title of Talk: Spot It! with Combinatorics
Abstract: The game of Spot It! consists of 55 game cards, each card has 8 symbols, and each pair of cards has exactly one symbol in common. The idea is to 'spot' the match on your card before the other players 'spot' their match. There are many ways to approach the mathematics behind designing a game of Spot It!. Different fields of mathematics are considered and applied to the problem, ultimately resulting in a beautiful interconnectedness within concepts of Combinatorics.
Year: 2018
Name: Laura McCauley
Institution: Peru State College
Subject area(s): Graph Theory
Title of Talk: Spot It! with Combinatorics
Abstract: The game of Spot It! consists of 55 game cards, each card has 8 symbols, and each pair of cards has exactly one symbol in common. The idea is to 'spot' the match on your card before the other players 'spot' their match. There are many ways to approach the mathematics behind designing a game of Spot It!. Different fields of mathematics are considered and applied to the problem, ultimately resulting in a beautiful interconnectedness within concepts of Combinatorics.
ID:
521
Year: 2018
Name: Amanda Matson
Institution: Clarke University
Subject area(s):
Title of Talk: MAAthfest Roundup
Abstract: Bringing MAAthfest to Iowa, Dr. Matson will recap some of the happenings at MAAthfest and invite others to build on that information.
Year: 2018
Name: Amanda Matson
Institution: Clarke University
Subject area(s):
Title of Talk: MAAthfest Roundup
Abstract: Bringing MAAthfest to Iowa, Dr. Matson will recap some of the happenings at MAAthfest and invite others to build on that information.
ID:
522
Year: 2018
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s):
Title of Talk: Feynman Operational Calculus
Abstract: The forthcoming paper "Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a $(C_0)$ semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures" (by L. Nielsen, to appear in Integral Equations and Operator Theory) contains, as its main result, an evolution equation which serves to describe how Feynman's operational calculus evolves with time in the presence of a $(C_0)$ semigroup of linear operators. There are several examples in this paper which give rise to so-called, Feynman-Kac formulas with Lebesgue- Stieltjes measures (first investigated from a function space integral point of view by M. L. Lapidus in the late 1980s). However, due to the different approach, the Feynman-Kac formulas obtained in the paper by Nielsen have some significant differences from those obtained by Lapidus. An associated operator differential equation (essentially a nonhomogeneous Schrodinger's equation) is also obtained in Nielsen's paper. This talk will concentrate on the explanation of the newly-found Feynman-Kac formulas and some associated results.
Year: 2018
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s):
Title of Talk: Feynman Operational Calculus
Abstract: The forthcoming paper "Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a $(C_0)$ semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures" (by L. Nielsen, to appear in Integral Equations and Operator Theory) contains, as its main result, an evolution equation which serves to describe how Feynman's operational calculus evolves with time in the presence of a $(C_0)$ semigroup of linear operators. There are several examples in this paper which give rise to so-called, Feynman-Kac formulas with Lebesgue- Stieltjes measures (first investigated from a function space integral point of view by M. L. Lapidus in the late 1980s). However, due to the different approach, the Feynman-Kac formulas obtained in the paper by Nielsen have some significant differences from those obtained by Lapidus. An associated operator differential equation (essentially a nonhomogeneous Schrodinger's equation) is also obtained in Nielsen's paper. This talk will concentrate on the explanation of the newly-found Feynman-Kac formulas and some associated results.
ID:
523
Year: 2018
Name: Billy Duckworth
Institution: Creighton University
Subject area(s):
Title of Talk: The Randic Index and Average Path Length
Abstract: In graph theory the Randic Index is a number that gives information about the degree of branching within a particular graph. We examined the relationship between the Randic Index and other well known graph properties such as radius, diameter, and average path length. We attempt to bound the Randic Index for families of graphs such as paths, cycles and "methylated" paths and cycles.
Year: 2018
Name: Billy Duckworth
Institution: Creighton University
Subject area(s):
Title of Talk: The Randic Index and Average Path Length
Abstract: In graph theory the Randic Index is a number that gives information about the degree of branching within a particular graph. We examined the relationship between the Randic Index and other well known graph properties such as radius, diameter, and average path length. We attempt to bound the Randic Index for families of graphs such as paths, cycles and "methylated" paths and cycles.
ID:
524
Year: 2018
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s):
Title of Talk: The new MAA Congress, what do you want them to know? (Continued)
Abstract: The (relatively) new MAA Congress is situated to be a strong form of communication with the national MAA elected officers and the Iowa Section members. As your representative, what so you want to know about the new body? the MAA? What do you want the MAA to hear from the section? This is your opportunity to hear and be heard.
Year: 2018
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s):
Title of Talk: The new MAA Congress, what do you want them to know? (Continued)
Abstract: The (relatively) new MAA Congress is situated to be a strong form of communication with the national MAA elected officers and the Iowa Section members. As your representative, what so you want to know about the new body? the MAA? What do you want the MAA to hear from the section? This is your opportunity to hear and be heard.
ID:
497
Year: 2018
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): Commutative Ring Theory, Algebra
Title of Talk: An Exploration of Factorization: Mathematical Atoms
Abstract: The mathematical system of the integers has many useful properties. One of these is unique factorization. For example, we can write the number 14 in a unique way: 14 = 2 * 7. However, the numbers 2 and 7 cannot be factored into "smaller pieces" in a nontrivial way. So in this sense, they could be called atoms of this mathematical system. Other mathematical systems usually do not have all of the nice properties that the integers do. Some useful properties can still be salvaged in certain cases. An atomic domain is a special mathematical system where its members have a factorization into a product of atoms. However, despite the ability to still factor elements into atoms, some are not as well-behaved as the integers were. For example, there are atomic domains where elements have an infinite number of distinct factorizations! We will discuss some important cases of these atomic domains. Of particular interest will be an atomic domain that only has finitely many atoms.
Year: 2018
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): Commutative Ring Theory, Algebra
Title of Talk: An Exploration of Factorization: Mathematical Atoms
Abstract: The mathematical system of the integers has many useful properties. One of these is unique factorization. For example, we can write the number 14 in a unique way: 14 = 2 * 7. However, the numbers 2 and 7 cannot be factored into "smaller pieces" in a nontrivial way. So in this sense, they could be called atoms of this mathematical system. Other mathematical systems usually do not have all of the nice properties that the integers do. Some useful properties can still be salvaged in certain cases. An atomic domain is a special mathematical system where its members have a factorization into a product of atoms. However, despite the ability to still factor elements into atoms, some are not as well-behaved as the integers were. For example, there are atomic domains where elements have an infinite number of distinct factorizations! We will discuss some important cases of these atomic domains. Of particular interest will be an atomic domain that only has finitely many atoms.