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 321-340 of 471 results.
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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:
343
Year: 2012
Name: Mary Therese Padberg
Institution: University of Iowa
Subject area(s): Mathematical Biology
Title of Talk: The Twisted Tale of Protein-bound DNA
Abstract: DNA is important for our cells to function and grow, but it cannot accomplish this alone. DNA is just the blueprint and its information must be read and expressed by proteins. Understanding the shape of DNA when protein has bound to it (protein-bound DNA) is important for biological and medical research. Laboratory techniques exist which allow scientists to find the geometric structure for some protein-bound DNA complexes. When these techniques fail, we can often experimentally determine a topology for the complex, but topology alone is not enough. In order to understand the structure of protein-bound DNA at a scientifically useful level we need to know the geometry of the structure. In this talk we will create a mathematical model based on the DNA topology from laboratory experiments to describe the geometry of the DNA. We will discuss the flexibility of this model to accept user modifications in order to model the protein-bound DNA sample under variable conditions. Thus, by combining geometric and topological solutions we will be able to more accurately describe the shape of large protein-bound DNA complexes.
Year: 2012
Name: Mary Therese Padberg
Institution: University of Iowa
Subject area(s): Mathematical Biology
Title of Talk: The Twisted Tale of Protein-bound DNA
Abstract: DNA is important for our cells to function and grow, but it cannot accomplish this alone. DNA is just the blueprint and its information must be read and expressed by proteins. Understanding the shape of DNA when protein has bound to it (protein-bound DNA) is important for biological and medical research. Laboratory techniques exist which allow scientists to find the geometric structure for some protein-bound DNA complexes. When these techniques fail, we can often experimentally determine a topology for the complex, but topology alone is not enough. In order to understand the structure of protein-bound DNA at a scientifically useful level we need to know the geometry of the structure. In this talk we will create a mathematical model based on the DNA topology from laboratory experiments to describe the geometry of the DNA. We will discuss the flexibility of this model to accept user modifications in order to model the protein-bound DNA sample under variable conditions. Thus, by combining geometric and topological solutions we will be able to more accurately describe the shape of large protein-bound DNA complexes.
ID:
282
Year: 2010
Name: Brian Patterson
Institution: Iowa State University
Subject area(s): Real Analysis, Computability Theory
Title of Talk: Multi-Resolution Cellular Automata for Real Computation
Abstract: We will first briefly review cellular automata and why representing and computing with real numbers with a computer is problematic. Then we will discuss a new approach that uses the concept of fissioning cells to approximate real-valued regions. I will close with a brief explanation of my simulator.
Year: 2010
Name: Brian Patterson
Institution: Iowa State University
Subject area(s): Real Analysis, Computability Theory
Title of Talk: Multi-Resolution Cellular Automata for Real Computation
Abstract: We will first briefly review cellular automata and why representing and computing with real numbers with a computer is problematic. Then we will discuss a new approach that uses the concept of fissioning cells to approximate real-valued regions. I will close with a brief explanation of my simulator.
ID:
417
Year: 2015
Name: Catherine Patterson
Institution: University of Iowa
Subject area(s): Mathematical biology, applied math, modeling
Title of Talk: Modeling the Effects of Multiple Myeloma Bone Disease
Abstract: Cancer is a lot like a hurricane; you can see it coming, but you don't know exactly where it will go or how much damage it will do. However, by combining a mathematical model with patient data, we can make predictions about the development of a patient's cancer. My research focuses on multiple myeloma, a plasma cell cancer that disrupts the bone remodeling process. In multiple myeloma patients, bone destruction outpaces bone replacement, producing bone lesions. This talk will describe the cell dynamics that regulate bone remodeling and explain how they are impacted by multiple myeloma. I will then discuss techniques used to model this system, including Savageau's power law approximations.
Year: 2015
Name: Catherine Patterson
Institution: University of Iowa
Subject area(s): Mathematical biology, applied math, modeling
Title of Talk: Modeling the Effects of Multiple Myeloma Bone Disease
Abstract: Cancer is a lot like a hurricane; you can see it coming, but you don't know exactly where it will go or how much damage it will do. However, by combining a mathematical model with patient data, we can make predictions about the development of a patient's cancer. My research focuses on multiple myeloma, a plasma cell cancer that disrupts the bone remodeling process. In multiple myeloma patients, bone destruction outpaces bone replacement, producing bone lesions. This talk will describe the cell dynamics that regulate bone remodeling and explain how they are impacted by multiple myeloma. I will then discuss techniques used to model this system, including Savageau's power law approximations.
ID:
288
Year: 2010
Name: Travis Peters
Institution: Iowa State University
Subject area(s):
Title of Talk: Minimum rank, maximum nullity and zero forcing number for selected graph families
Abstract: The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This talk discusses the graph families ciclos and estrellas. In particular, these families provide the examples showing that the maximum nullity of a graph and its dual may differ, and similarly for zero forcing number.
Year: 2010
Name: Travis Peters
Institution: Iowa State University
Subject area(s):
Title of Talk: Minimum rank, maximum nullity and zero forcing number for selected graph families
Abstract: The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This talk discusses the graph families ciclos and estrellas. In particular, these families provide the examples showing that the maximum nullity of a graph and its dual may differ, and similarly for zero forcing number.
ID:
305
Year: 2011
Name: Travis Peters
Institution: Iowa State University
Subject area(s):
Title of Talk: Zero forcing number, maximum nullity, and path cover number of complete edge subdivision graphs
Abstract: The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. The path cover number is the fewest number of vertex disjoint induced paths that cover all the vertices of the graph. We study the effect of edge subdivisions of a graph on the zero forcing number, maximum nullity, and path cover number.
Year: 2011
Name: Travis Peters
Institution: Iowa State University
Subject area(s):
Title of Talk: Zero forcing number, maximum nullity, and path cover number of complete edge subdivision graphs
Abstract: The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. The path cover number is the fewest number of vertex disjoint induced paths that cover all the vertices of the graph. We study the effect of edge subdivisions of a graph on the zero forcing number, maximum nullity, and path cover number.
ID:
256
Year: 2009
Name: Donald Peterson
Institution: Iowa State University
Subject area(s): Encryption, Number Theory
Title of Talk: The 1/P Pseudo-Random Number Generator
Abstract: Seemingly suitable for encryption, the 1/P pseudo-random number generator quickly outputs a long, well-distributed sequence of digits from a small seed. However, without any prior knowledge of the seed, it can be determined and the sequence can be predicted both forwards and backwards by careful examination of 2|P| + 1 digits of the sequence. This article examines how to develop the generator, and more importantly given a small bit of any sequence, how to predict the remaining sequence.
Year: 2009
Name: Donald Peterson
Institution: Iowa State University
Subject area(s): Encryption, Number Theory
Title of Talk: The 1/P Pseudo-Random Number Generator
Abstract: Seemingly suitable for encryption, the 1/P pseudo-random number generator quickly outputs a long, well-distributed sequence of digits from a small seed. However, without any prior knowledge of the seed, it can be determined and the sequence can be predicted both forwards and backwards by careful examination of 2|P| + 1 digits of the sequence. This article examines how to develop the generator, and more importantly given a small bit of any sequence, how to predict the remaining sequence.
ID:
345
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Art & Geometry
Title of Talk: Geometreks
Abstract: Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and M_bius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, Montreal, New Orleans, and many other locales.
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Art & Geometry
Title of Talk: Geometreks
Abstract: Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and M_bius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, Montreal, New Orleans, and many other locales.
ID:
346
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Counting
Title of Talk: Pancake Sorting, Prefix Reversals, and DNA Rearrangements
Abstract: The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements.
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Counting
Title of Talk: Pancake Sorting, Prefix Reversals, and DNA Rearrangements
Abstract: The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements.
ID:
541
Year: 2019
Name: Christina Pospisil
Institution: University of Massachusetts Boston
Subject area(s):
Title of Talk: Generalization Theory for Linear Algebra I: An Embedding Algorithm and an appropriate Inverse for non-injective mappings in one dimension
Abstract: An algorithm for multiplying and adding matrices regardless of dimensions via an embedding is presented. An equivalent embedding for a general determinant theory is also investigated (Part I: Appropriate Inverses for non-injective mappings in one dimension are presented). In future work there will be applications to physics and other natural sciences be explored.
Year: 2019
Name: Christina Pospisil
Institution: University of Massachusetts Boston
Subject area(s):
Title of Talk: Generalization Theory for Linear Algebra I: An Embedding Algorithm and an appropriate Inverse for non-injective mappings in one dimension
Abstract: An algorithm for multiplying and adding matrices regardless of dimensions via an embedding is presented. An equivalent embedding for a general determinant theory is also investigated (Part I: Appropriate Inverses for non-injective mappings in one dimension are presented). In future work there will be applications to physics and other natural sciences be explored.
ID:
376
Year: 2014
Name: Kenneth Price
Institution: University of Wisconsin Oshkosh
Subject area(s):
Title of Talk: Arrowgrams: Tips and Pointers
Abstract: An arrowgram is a type of puzzle based on the transitive relation, directed graphs, and groups. To solve the puzzle a group element is assigned to each arrow of a directed graph. This is called a grading and the group element assigned to an arrow is called its grade. Grades for some arrows are given. The rest of the arrows are assigned grades using a rule which is based on transitivity. Arrowgrams also contain secret messages. The words are formed by pairs of letters which stand for the arrows. The puzzle is solved when every arrow is graded and the secret message is revealed. We answer some mathematical questions related to constructing and solving arrowgrams. How many arrows have to be given grades? Which arrows can be used? Can the same set of arrows be used for different groups?
Year: 2014
Name: Kenneth Price
Institution: University of Wisconsin Oshkosh
Subject area(s):
Title of Talk: Arrowgrams: Tips and Pointers
Abstract: An arrowgram is a type of puzzle based on the transitive relation, directed graphs, and groups. To solve the puzzle a group element is assigned to each arrow of a directed graph. This is called a grading and the group element assigned to an arrow is called its grade. Grades for some arrows are given. The rest of the arrows are assigned grades using a rule which is based on transitivity. Arrowgrams also contain secret messages. The words are formed by pairs of letters which stand for the arrows. The puzzle is solved when every arrow is graded and the secret message is revealed. We answer some mathematical questions related to constructing and solving arrowgrams. How many arrows have to be given grades? Which arrows can be used? Can the same set of arrows be used for different groups?
ID:
353
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Fibonacci's Flower Garden
Abstract: It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden.
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Fibonacci's Flower Garden
Abstract: It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden.
ID:
354
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Mathematics to DIE for: The Battle Between Counting and Matching
Abstract: Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Mathematics to DIE for: The Battle Between Counting and Matching
Abstract: Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
ID:
285
Year: 2010
Name: Reza Rastegar
Institution: Iowa State University
Subject area(s): Probability
Title of Talk: Random walks in a sparse ``cookie" environment
Abstract: ``Cookie random walks" is a popular model of self-interacting random walks. Several variations of this model have been studied during the last decade. In this talk we will focus on the random walk on the integer lattice, where the ``cookies" perturbing the random walk are placed in a regular random sub-lattice of Z. We will present the model, briefly discuss an associated branching process, and then state criteria for transience and recurrence for this random walk.
Year: 2010
Name: Reza Rastegar
Institution: Iowa State University
Subject area(s): Probability
Title of Talk: Random walks in a sparse ``cookie" environment
Abstract: ``Cookie random walks" is a popular model of self-interacting random walks. Several variations of this model have been studied during the last decade. In this talk we will focus on the random walk on the integer lattice, where the ``cookies" perturbing the random walk are placed in a regular random sub-lattice of Z. We will present the model, briefly discuss an associated branching process, and then state criteria for transience and recurrence for this random walk.
ID:
547
Year: 2019
Name: Patrick Rault
Institution: University of Nebraska at Omaha
Subject area(s):
Title of Talk: A Dozen National and Regional Mini-grant opportunities for Undergraduate Faculty
Abstract: A wide range of mini-grants are available to support both teaching and research. The Inquiry-Based Learning Iowa-Nebraska Community (IBLINC) is now offering mini-grants for a wide range of peer-collaboration activities ranging from attending events to collaborating on course materials. This builds on a national momentum to offer mini-grants from the MAA for a wide variety of teaching activities, from CURM for an academic-year REU-style project with our students, and from AIM for a weeklong research retreat for your faculty team. While most of these programs are grant funded, the MAA’s Project NExT program has raised substantial continuing funds to provide professional development and a supportive community for new faculty. Join us to hear about a dozen such funding sources, learn what the aforementioned acronyms stand for, or share your own experiences.
Year: 2019
Name: Patrick Rault
Institution: University of Nebraska at Omaha
Subject area(s):
Title of Talk: A Dozen National and Regional Mini-grant opportunities for Undergraduate Faculty
Abstract: A wide range of mini-grants are available to support both teaching and research. The Inquiry-Based Learning Iowa-Nebraska Community (IBLINC) is now offering mini-grants for a wide range of peer-collaboration activities ranging from attending events to collaborating on course materials. This builds on a national momentum to offer mini-grants from the MAA for a wide variety of teaching activities, from CURM for an academic-year REU-style project with our students, and from AIM for a weeklong research retreat for your faculty team. While most of these programs are grant funded, the MAA’s Project NExT program has raised substantial continuing funds to provide professional development and a supportive community for new faculty. Join us to hear about a dozen such funding sources, learn what the aforementioned acronyms stand for, or share your own experiences.
ID:
509
Year: 2018
Name: Patrick Rault
Institution: University of Nebraska Omaha
Subject area(s):
Title of Talk: Regional Communities of Practice around Inquiry-Based Learning
Abstract: What began as a small group of professors gathering to discuss implementation of Inquiry-Based Learning (IBL) in our classes has developed into a strong regional community of practice. The Upstate New York IBL consortium was created in 2014 with a mission to create, grow, and maintain a community of instructors across the region. We will discuss how the consortium formed organically, the way that it operates, and several efforts to replicate it in other regions. Suggestions will be provided for creating your own regional community of practice for supporting the adoption and enhancement of active learning techniques.
Year: 2018
Name: Patrick Rault
Institution: University of Nebraska Omaha
Subject area(s):
Title of Talk: Regional Communities of Practice around Inquiry-Based Learning
Abstract: What began as a small group of professors gathering to discuss implementation of Inquiry-Based Learning (IBL) in our classes has developed into a strong regional community of practice. The Upstate New York IBL consortium was created in 2014 with a mission to create, grow, and maintain a community of instructors across the region. We will discuss how the consortium formed organically, the way that it operates, and several efforts to replicate it in other regions. Suggestions will be provided for creating your own regional community of practice for supporting the adoption and enhancement of active learning techniques.
ID:
559
Year: 2021
Name: Jack Rausch
Institution: Creighton University
Subject area(s): Quantum Information Theory, Quantum Computing
Title of Talk: Developing a Quantum Resource Theory for One-Way Information
Abstract: In quantum information theory, the one-way information of the joint evolution of a composite system quantifies the causal relationship between systems. Given a composite two systems, an algorithm is used to create a state $\rho^{A'ABB'} $ which quantifies the one-way information via the measure $R\left(\rho^{A'ABB'} \right) = I\left(\rho^{B} : \rho^{A'AB'} \right) - I\left(\rho^{B} : \rho^{B'} \right)$. A quantum resource theory offers a new perspective to view one-way information. A quantum resource theory examines a problem under a set of physically meaningful limitations which identify certain operations as free (can be used without limitations) and others as resources (operations with limitations or costs). We define a quantum resource theory for one-way information based on the measure $R\left(\rho^{A'ABB'} \right)$, showing that: $R$ is an additive measure, all free states contain $0$ one-way information, the free operations contain all unitary operators $U_{AB} = U_A \otimes U_B$, and $R$ is monotonic under free operations, but not under the restricted operations.
Year: 2021
Name: Jack Rausch
Institution: Creighton University
Subject area(s): Quantum Information Theory, Quantum Computing
Title of Talk: Developing a Quantum Resource Theory for One-Way Information
Abstract: In quantum information theory, the one-way information of the joint evolution of a composite system quantifies the causal relationship between systems. Given a composite two systems, an algorithm is used to create a state $\rho^{A'ABB'} $ which quantifies the one-way information via the measure $R\left(\rho^{A'ABB'} \right) = I\left(\rho^{B} : \rho^{A'AB'} \right) - I\left(\rho^{B} : \rho^{B'} \right)$. A quantum resource theory offers a new perspective to view one-way information. A quantum resource theory examines a problem under a set of physically meaningful limitations which identify certain operations as free (can be used without limitations) and others as resources (operations with limitations or costs). We define a quantum resource theory for one-way information based on the measure $R\left(\rho^{A'ABB'} \right)$, showing that: $R$ is an additive measure, all free states contain $0$ one-way information, the free operations contain all unitary operators $U_{AB} = U_A \otimes U_B$, and $R$ is monotonic under free operations, but not under the restricted operations.
ID:
370
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
ID:
371
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
Year: 2013
Name: Dave Renfro
Institution: ACT, Inc.
Subject area(s): real analysis
Title of Talk: The Upper and Lower Limits of a Function and Semicontinuous Functions
Abstract: A function is continuous on an interval exactly when the function agrees with its "limit function" on the interval, by which we mean the limit (when it exists) of the function at each point. In looking at some examples, we find that limit functions tend to be nicely behaved even when the functions are not. For example, Thomae's function is continuous on a dense set of points and discontinuous on a dense set of points, and yet its limit function is a constant function (identically equal to 0). Of course, the limit function of a function is not always defined, but by considering upper and lower limits (limsup and liminf), we get the upper and lower limit functions of a function. These also tend to be nicely behaved, as is illustrated by the characteristic function of the rationals (discontinuous at every point), whose upper and lower limit functions are constant functions. We will investigate how badly behaved the upper and lower limit functions of a function can be. This will lead to an investigation of semicontinuous functions, which are amazingly ubiquitously omnipresent throughout pure and applied mathematics. This talk should be accessible to most undergraduate math majors, although there will likely be aspects of it that are unfamiliar to nonexperts.
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.