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 401-420 of 471 results.
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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.
ID:
498
Year: 2018
Name: Wako Bungula
Institution: University of Iowa
Subject area(s): Topological Data Analysis
Title of Talk: Filtration and Stability of Mapper Graph for Point Cloud Data
Abstract: Filtration and stability of TDA Mapper graph for topological spaces have been studied; and using a generalization of the Bottleneck distance called interleaving distance, the stability of Mapper graph for the topological spaces has been proven. A problem arises when trying to extend this stability theorem to the point cloud data case because clustering algorithms do not usually give filtration. I will be talking about the conditions required for the stability theorem to be extended to point cloud data case.
Year: 2018
Name: Wako Bungula
Institution: University of Iowa
Subject area(s): Topological Data Analysis
Title of Talk: Filtration and Stability of Mapper Graph for Point Cloud Data
Abstract: Filtration and stability of TDA Mapper graph for topological spaces have been studied; and using a generalization of the Bottleneck distance called interleaving distance, the stability of Mapper graph for the topological spaces has been proven. A problem arises when trying to extend this stability theorem to the point cloud data case because clustering algorithms do not usually give filtration. I will be talking about the conditions required for the stability theorem to be extended to point cloud data case.
ID:
499
Year: 2018
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Upper division mathematics teaching
Title of Talk: Tips and Tricks for Tracking a Student Centered Class
Abstract: Teaching an IBL mathematics class can often feel like transitioning from trying to herd cats to sitting in the kitten room and watching appreciating watching them crawl all over each other. When it works, this brings a warm and fuzzy feeling to your heart, but then you realize that you need to keep track of all this chaos and have something for the assessment gurus at the end of the term. Fear not, this is possible to do and in such a way that your students will become more engaged and not less. The trick is to include discussion tracking as part of the responsibility of the student and not solely that of the teacher. This talk will go over a variety of successful and not-so-successful ways to include students in the tasks of classroom management and discussion tracking. I will give you at least one, concrete method that you could use in your class and a variety of things you could do to personalize the technique for your personality. Finally, I will explain how this works to create a more student-owned learning space where the emphasis is on mathematics and learning and not on grades.
Year: 2018
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Upper division mathematics teaching
Title of Talk: Tips and Tricks for Tracking a Student Centered Class
Abstract: Teaching an IBL mathematics class can often feel like transitioning from trying to herd cats to sitting in the kitten room and watching appreciating watching them crawl all over each other. When it works, this brings a warm and fuzzy feeling to your heart, but then you realize that you need to keep track of all this chaos and have something for the assessment gurus at the end of the term. Fear not, this is possible to do and in such a way that your students will become more engaged and not less. The trick is to include discussion tracking as part of the responsibility of the student and not solely that of the teacher. This talk will go over a variety of successful and not-so-successful ways to include students in the tasks of classroom management and discussion tracking. I will give you at least one, concrete method that you could use in your class and a variety of things you could do to personalize the technique for your personality. Finally, I will explain how this works to create a more student-owned learning space where the emphasis is on mathematics and learning and not on grades.
ID:
500
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?
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?
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:
501
Year: 2018
Name: Joy Becker
Institution: Wartburg College
Subject area(s):
Title of Talk: Writing Across the Mathematics Curriculum
Abstract: Providing students multiple ways to practice mathematical communication skills aids in their development. In particular, writing can be infused into math courses at various levels, across a wide range of assignments. This talk will give examples of such assignments and ways to incorporate different levels of writing in a variety of mathematics courses.
Year: 2018
Name: Joy Becker
Institution: Wartburg College
Subject area(s):
Title of Talk: Writing Across the Mathematics Curriculum
Abstract: Providing students multiple ways to practice mathematical communication skills aids in their development. In particular, writing can be infused into math courses at various levels, across a wide range of assignments. This talk will give examples of such assignments and ways to incorporate different levels of writing in a variety of mathematics courses.
ID:
502
Year: 2018
Name: Kristopher Lee
Institution: Iowa State University
Subject area(s):
Title of Talk: Characterizing Isometries: A Long Running Undergraduate Research Project
Abstract: In 2010, my adviser Aaron Luttman began an undergraduate research project with an honors student at Clarkson University. The goal was to investigate a decomposition for isometries between normed vector spaces; specifically, to prove that the domain of the isometry had to be the direct sum of ``nice'' subspaces. The project ended in 2011 when my adviser (and the student) left academia. I revived the project in 2015 with an honors student here at Iowa State University, and while significant progress was made, we did not fully resolve it. This semester, I am approaching the problem again with a new student. We'll talk about the ins, outs, and what-have-yous of the project, where we currently stand, and the plan going forward.
Year: 2018
Name: Kristopher Lee
Institution: Iowa State University
Subject area(s):
Title of Talk: Characterizing Isometries: A Long Running Undergraduate Research Project
Abstract: In 2010, my adviser Aaron Luttman began an undergraduate research project with an honors student at Clarkson University. The goal was to investigate a decomposition for isometries between normed vector spaces; specifically, to prove that the domain of the isometry had to be the direct sum of ``nice'' subspaces. The project ended in 2011 when my adviser (and the student) left academia. I revived the project in 2015 with an honors student here at Iowa State University, and while significant progress was made, we did not fully resolve it. This semester, I am approaching the problem again with a new student. We'll talk about the ins, outs, and what-have-yous of the project, where we currently stand, and the plan going forward.
ID:
503
Year: 2018
Name: Justin Hoffmeier
Institution: Northwest Missouri State University
Subject area(s): Algebra
Title of Talk: Exact Zero Divisor Graphs
Abstract: Zero divisor graphs of rings identify the elements of the annihilators. Is it possible to identify the generators of the annihilators from these graphs? We work examples for which the answer is yes. Our explanation uses exact zero divisor graphs. For this talk, rings will be only the integers modulo n and we will assume very little background knowledge.
Year: 2018
Name: Justin Hoffmeier
Institution: Northwest Missouri State University
Subject area(s): Algebra
Title of Talk: Exact Zero Divisor Graphs
Abstract: Zero divisor graphs of rings identify the elements of the annihilators. Is it possible to identify the generators of the annihilators from these graphs? We work examples for which the answer is yes. Our explanation uses exact zero divisor graphs. For this talk, rings will be only the integers modulo n and we will assume very little background knowledge.
ID:
504
Year: 2018
Name: Charles Ashbacher
Institution: Charles Ashbacher Technologies
Subject area(s): Recreational mathematics
Title of Talk: Mathematical Venery and Other Humor
Abstract: In modern usage, the term “venery” refers to the pursuit of sexual pleasure, yet in medieval times it referred to the act of game hunting. The terms of venery refers to the rather unusual words used to describe a collection of animals of the same species. Charles W. Trigg composed a paper published in Journal of Recreational Mathematics that used this term to refer to the naming of collections of math people and objects. He listed some examples and this paper opens with additional examples created by the author. It concludes with some additional examples of mathematical humor.
Year: 2018
Name: Charles Ashbacher
Institution: Charles Ashbacher Technologies
Subject area(s): Recreational mathematics
Title of Talk: Mathematical Venery and Other Humor
Abstract: In modern usage, the term “venery” refers to the pursuit of sexual pleasure, yet in medieval times it referred to the act of game hunting. The terms of venery refers to the rather unusual words used to describe a collection of animals of the same species. Charles W. Trigg composed a paper published in Journal of Recreational Mathematics that used this term to refer to the naming of collections of math people and objects. He listed some examples and this paper opens with additional examples created by the author. It concludes with some additional examples of mathematical humor.
ID:
505
Year: 2018
Name: Mitchel T. Keller
Institution: Morningside College
Subject area(s): Mathematical writing/publishing
Title of Talk: PreTeXt: One Input, Many Beautiful Outputs
Abstract: In this talk, we will take a look at some of the features of PreTeXt (formerly MathBook XML), which is a language designed for authors to be able to use a master source file to produce a variety of output formats. A PreTeXt source file marks up the structure of the document (theorems, proofs, exercises, examples, figures, etc.) using an XML syntax that may remind users of HTML, but with a total focus on structure and not presentation. Mathematical expressions in the source are marked up using LaTeX notation. Support for including a variety of interactive elements in the document is available, with additional interactive features planned. While most existing PreTeXt projects are book-length, the system is now mature and stable enough that interested individuals are encouraged to use it for developing materials for their courses, regardless of whether they might eventually develop into a larger project. PreTeXt source files are easily converted to HTML that looks good on both desktops and mobile devices and LaTeX for producing print versions. A conversion from PreTeXt to the EPUB format used by Apple's iBooks is under development, and a PreTeXt to Kindle conversion will follow. The speaker is the author of one open-source text written in PreTeXt (Applied Combinatorics with W.T. Trotter), co-editor of the PreTeXt edition of Bogart's Combinatorics through Guided Discovery (with Oscar Levin and Kent E. Morrison), Production Editor for Active Calculus by Boelkins et al., and is a core member of the group guiding further development of PreTeXt.
Year: 2018
Name: Mitchel T. Keller
Institution: Morningside College
Subject area(s): Mathematical writing/publishing
Title of Talk: PreTeXt: One Input, Many Beautiful Outputs
Abstract: In this talk, we will take a look at some of the features of PreTeXt (formerly MathBook XML), which is a language designed for authors to be able to use a master source file to produce a variety of output formats. A PreTeXt source file marks up the structure of the document (theorems, proofs, exercises, examples, figures, etc.) using an XML syntax that may remind users of HTML, but with a total focus on structure and not presentation. Mathematical expressions in the source are marked up using LaTeX notation. Support for including a variety of interactive elements in the document is available, with additional interactive features planned. While most existing PreTeXt projects are book-length, the system is now mature and stable enough that interested individuals are encouraged to use it for developing materials for their courses, regardless of whether they might eventually develop into a larger project. PreTeXt source files are easily converted to HTML that looks good on both desktops and mobile devices and LaTeX for producing print versions. A conversion from PreTeXt to the EPUB format used by Apple's iBooks is under development, and a PreTeXt to Kindle conversion will follow. The speaker is the author of one open-source text written in PreTeXt (Applied Combinatorics with W.T. Trotter), co-editor of the PreTeXt edition of Bogart's Combinatorics through Guided Discovery (with Oscar Levin and Kent E. Morrison), Production Editor for Active Calculus by Boelkins et al., and is a core member of the group guiding further development of PreTeXt.
ID:
506
Year: 2018
Name: Joshua Zelinsky
Institution: ISU
Subject area(s): Number theory
Title of Talk: Lower and upper bounds in integer complexity.
Abstract: Define ||n|| to be the complexity of n, the smallest number of 1's needed to write n using an arbitrary combination of addition and multiplication. John Selfridge showed that ||n|| is at least 3log3n for all n, and this lower bound is obtained exactly when n is a power of 3. Richard Guy noted the trivial upper bound of 3log_2 n for all n bigger than 1, by writing n in base 2. This talk will discuss work improving the upper bound, as well as work leading to a complete classification of numbers whose complexity is close to the lower bound. Along the way, we'll develop connections to both ordinal numbers and the p-adics.
Year: 2018
Name: Joshua Zelinsky
Institution: ISU
Subject area(s): Number theory
Title of Talk: Lower and upper bounds in integer complexity.
Abstract: Define ||n|| to be the complexity of n, the smallest number of 1's needed to write n using an arbitrary combination of addition and multiplication. John Selfridge showed that ||n|| is at least 3log3n for all n, and this lower bound is obtained exactly when n is a power of 3. Richard Guy noted the trivial upper bound of 3log_2 n for all n bigger than 1, by writing n in base 2. This talk will discuss work improving the upper bound, as well as work leading to a complete classification of numbers whose complexity is close to the lower bound. Along the way, we'll develop connections to both ordinal numbers and the p-adics.