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 221-240 of 471 results.
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ID:
208
Year: 2007
Name: James Fiedler
Institution: Iowa State University
Subject area(s):
Title of Talk: On a Group Associated With Projective Planes
Abstract: A pair of orthogonal Latin squares of order n is equivalent to a permutation on the set of ordered pairs of integers 1, ..., n. Since a projective plane of order n exists if and only if there exists a set of n-1 mutually orthogonal Latin squares of order n, the group generated by the above permutations may be of some interest in the study of projective planes. Relevant definitions and results of some investigations concerning these groups will be presented.
Year: 2007
Name: James Fiedler
Institution: Iowa State University
Subject area(s):
Title of Talk: On a Group Associated With Projective Planes
Abstract: A pair of orthogonal Latin squares of order n is equivalent to a permutation on the set of ordered pairs of integers 1, ..., n. Since a projective plane of order n exists if and only if there exists a set of n-1 mutually orthogonal Latin squares of order n, the group generated by the above permutations may be of some interest in the study of projective planes. Relevant definitions and results of some investigations concerning these groups will be presented.
ID:
210
Year: 2007
Name: Stephen Willson
Institution: Iowa State University
Subject area(s):
Title of Talk: On the Mathematics of Juggling
Abstract: The mathematical analysis of juggling gives interesting examples of permutations and uses of modular arithmetic. Simple mathematical notation can be used to describe many different ways of juggling. The descriptions can tell which periodic patterns give valid juggling methods.
Year: 2007
Name: Stephen Willson
Institution: Iowa State University
Subject area(s):
Title of Talk: On the Mathematics of Juggling
Abstract: The mathematical analysis of juggling gives interesting examples of permutations and uses of modular arithmetic. Simple mathematical notation can be used to describe many different ways of juggling. The descriptions can tell which periodic patterns give valid juggling methods.
ID:
211
Year: 2007
Name: Rana Mikkelson
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to Minimum Rank of a Graph
Abstract: Given a graph, we can associate a set of matrices therewith: the set of all symmetric matrices A over R where aij = 0 ? G has an edge between vertex i and j . We define the minimum rank of a graph is then the minimum among the ranks of all the matrices in this set. There is no one easy formula for computing this value given any graph, but for certain types graphs we can find the minimum rank exactly, and for others we can at least determine a few bounds. This talk introduces the topic and begins to explore the known results.
Year: 2007
Name: Rana Mikkelson
Institution: Iowa State University
Subject area(s):
Title of Talk: An Introduction to Minimum Rank of a Graph
Abstract: Given a graph, we can associate a set of matrices therewith: the set of all symmetric matrices A over R where aij = 0 ? G has an edge between vertex i and j . We define the minimum rank of a graph is then the minimum among the ranks of all the matrices in this set. There is no one easy formula for computing this value given any graph, but for certain types graphs we can find the minimum rank exactly, and for others we can at least determine a few bounds. This talk introduces the topic and begins to explore the known results.
ID:
212
Year: 2007
Name: Siu-Hung (Richard) Ng
Institution: Iowa State University
Subject area(s):
Title of Talk: Counting the number of solutions in a finite group
Abstract: The notion of Frobenius-Schur (FS)-indicators of a finite group representation has been developed for more than a century. These indicators can be obtained by counting the number of solutions x of the equation x^n=g in a finite group. Moreover, the second indicators can be used to construct topological invariants of surfaces. It was not known until recently that they are invariants of the tensor categories of finite group representations. In the talk, we will give a brief history of these indicators and their new developments.
Year: 2007
Name: Siu-Hung (Richard) Ng
Institution: Iowa State University
Subject area(s):
Title of Talk: Counting the number of solutions in a finite group
Abstract: The notion of Frobenius-Schur (FS)-indicators of a finite group representation has been developed for more than a century. These indicators can be obtained by counting the number of solutions x of the equation x^n=g in a finite group. Moreover, the second indicators can be used to construct topological invariants of surfaces. It was not known until recently that they are invariants of the tensor categories of finite group representations. In the talk, we will give a brief history of these indicators and their new developments.
ID:
213
Year: 2007
Name: Krishna B. Athreya
Institution: Iowa State University
Subject area(s):
Title of Talk: Preferential Attachment Random Graphs with General Weight Function
Abstract: Start with a graph G_0 = {V_1 , V_2} with one edge connecting the two vertices V_1, V_2. Now create a new vertex V_3 and attach it (i.e. add an edge) to V_1 or V_2 with equal probability. Set G_3={V_1 , V_2, V_3}. Let G_n={V_1,
Year: 2007
Name: Krishna B. Athreya
Institution: Iowa State University
Subject area(s):
Title of Talk: Preferential Attachment Random Graphs with General Weight Function
Abstract: Start with a graph G_0 = {V_1 , V_2} with one edge connecting the two vertices V_1, V_2. Now create a new vertex V_3 and attach it (i.e. add an edge) to V_1 or V_2 with equal probability. Set G_3={V_1 , V_2, V_3}. Let G_n={V_1,
ID:
214
Year: 2007
Name: Kliemann Wolfgang
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
Year: 2007
Name: Kliemann Wolfgang
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
ID:
215
Year: 2007
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
Year: 2007
Name: Wolfgang Kliemann
Institution: Iowa State University
Subject area(s):
Title of Talk: Linear Differential Equations
Abstract: Spectral properties of matrices can be characterized in various ways: The algebraic approach via the characteristic polynomial yields the eigenvalues and corresponding (generalized) eigenspaces resulting in the Jordan normal form. The linear-algebraic approach using similarity of matrices again re- sults in a characterization via the Jordan form. Furthermore, the dynamical approach via di
ID:
219
Year: 2008
Name: Haseena Ahmed
Institution: Iowa State University
Subject area(s): Applied Mathematics, Numerical Analysis
Title of Talk: Alternating evolution (AE) schemes for hyperbolic conservation laws
Abstract: An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes.
Year: 2008
Name: Haseena Ahmed
Institution: Iowa State University
Subject area(s): Applied Mathematics, Numerical Analysis
Title of Talk: Alternating evolution (AE) schemes for hyperbolic conservation laws
Abstract: An alternating evolution (AE) system is proposed which is an accurate approximation to systems of hyperbolic conservation laws. We develop a class of local Alternating Evolution (AE) schemes, where we take advantage of high accuracy of the proposed AE approximation. Our approach is based on a sliding average of the AE system over an interval of [x − \Delta x, x + \Delta x]. The numerical scheme is then constructed by sampling the averaged system over alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial reconstruction from the obtained averages and a stable Runge-Kutta discretization in time. The AE schemes have the advantage of easier formulation and implementation, and efficient computation of the solution. For the first and second order local AE schemes applied to scalar laws, we prove the numerical stability in the sense of satisfying the maximum principle and total variation diminishing (TVD) property. Numerical tests for both scalar conservation laws and compressible Euler equations are presented to demonstrate the high order accuracy and capacity of these AE schemes.
ID:
220
Year: 2008
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: Bloch Band Based Level Set Method for the Schrodinger Equation
Abstract: We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method.
Year: 2008
Name: Zhongming WANG
Institution: Iowa State University
Subject area(s):
Title of Talk: Bloch Band Based Level Set Method for the Schrodinger Equation
Abstract: We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method.
ID:
478
Year: 2017
Name: Diego Rojas
Institution: Iowa State University
Subject area(s): Computability Theory, Analysis
Title of Talk: Differentiation of Functions on the Cantor Space and Connections to Real-Valued Functions
Abstract: The notion of online functions of the Cantor space $2^{\mathbb{N}}$, and more generally, of continuous and of computable functions on $2^{\mathbb{N}}$, have been studied recently in connection with algorithmic randomness. In this talk, we present a notion of the derivative of functions on $2^{\mathbb{N}}$, and we establish some connections between functions and their derivatives on $2^{\mathbb{N}}$ and on $\mathbb{R}$, where we can represent real-valued functions as functions acting on the dyadic representation of real numbers. This is joint work with Douglas Cenzer.
Year: 2017
Name: Diego Rojas
Institution: Iowa State University
Subject area(s): Computability Theory, Analysis
Title of Talk: Differentiation of Functions on the Cantor Space and Connections to Real-Valued Functions
Abstract: The notion of online functions of the Cantor space $2^{\mathbb{N}}$, and more generally, of continuous and of computable functions on $2^{\mathbb{N}}$, have been studied recently in connection with algorithmic randomness. In this talk, we present a notion of the derivative of functions on $2^{\mathbb{N}}$, and we establish some connections between functions and their derivatives on $2^{\mathbb{N}}$ and on $\mathbb{R}$, where we can represent real-valued functions as functions acting on the dyadic representation of real numbers. This is joint work with Douglas Cenzer.
ID:
224
Year: 2008
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): geometry, teacher education, proof
Title of Talk: Proofs in elementary geometry - what IS the sum of angles in a triangle?
Abstract: One textbook for future teachers gives no less than four 'arguments' for this theorem. It is not claimed that they are proofs, and indeed they are not (all involve some circular reasoning). But the difference between such arguments and proofs is never made clear. We'll discover the flaws in the logic here, which are not obvious at all. Then we'll look at a number of examples from standard elementary geometry - some rock-solid one-line proofs, some examples where we all skip the proof and eyeball it, and finally an example which shows how 'eyeballing it' can lead to a 'proof' of 64=65.
Year: 2008
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): geometry, teacher education, proof
Title of Talk: Proofs in elementary geometry - what IS the sum of angles in a triangle?
Abstract: One textbook for future teachers gives no less than four 'arguments' for this theorem. It is not claimed that they are proofs, and indeed they are not (all involve some circular reasoning). But the difference between such arguments and proofs is never made clear. We'll discover the flaws in the logic here, which are not obvious at all. Then we'll look at a number of examples from standard elementary geometry - some rock-solid one-line proofs, some examples where we all skip the proof and eyeball it, and finally an example which shows how 'eyeballing it' can lead to a 'proof' of 64=65.
ID:
481
Year: 2017
Name: Alex Nowak
Institution: Iowa State University
Subject area(s): quasigroups, universal algebra, design theory
Title of Talk: Semisymmetric quasigroups
Abstract: Specified by Latin squares, quasigroups, often referred to as the ``nonassociative groups," seem, on the surface at least, to be objects of strictly combinatorial interest. However, quasigroups may also be specified as type (2, 2, 2) algebras satisfying equational identities, thus forming a variety in the universal algebraic sense. After introducing quasigroups through basic definitions and examples, we'll move into a discussion of the class of semisymmetric quasigroups. This class provides some nice illustrations of the interplay between algebra, combinatorics (in particular, design theory), and geometry that is provoked by quasigroup theory.
Year: 2017
Name: Alex Nowak
Institution: Iowa State University
Subject area(s): quasigroups, universal algebra, design theory
Title of Talk: Semisymmetric quasigroups
Abstract: Specified by Latin squares, quasigroups, often referred to as the ``nonassociative groups," seem, on the surface at least, to be objects of strictly combinatorial interest. However, quasigroups may also be specified as type (2, 2, 2) algebras satisfying equational identities, thus forming a variety in the universal algebraic sense. After introducing quasigroups through basic definitions and examples, we'll move into a discussion of the class of semisymmetric quasigroups. This class provides some nice illustrations of the interplay between algebra, combinatorics (in particular, design theory), and geometry that is provoked by quasigroup theory.
ID:
482
Year: 2017
Name: Alex Nowak
Institution: Iowa State University
Subject area(s):
Title of Talk: Semisymmetric quasigroups
Abstract: Specified by Latin squares, quasigroups, often referred to as the ``nonassociative groups," seem, on the surface at least, to be objects of strictly combinatorial interest. However, quasigroups may also be specified as type (2, 2, 2) algebras satisfying equational identities, thus forming a variety in the universal algebraic sense. After introducing quasigroups through basic definitions and examples, we'll move into a discussion of the class of semisymmetric quasigroups. This class provides some nice illustrations of the interplay between algebra, combinatorics (in particular, design theory), and geometry that is provoked by quasigroup theory.
Year: 2017
Name: Alex Nowak
Institution: Iowa State University
Subject area(s):
Title of Talk: Semisymmetric quasigroups
Abstract: Specified by Latin squares, quasigroups, often referred to as the ``nonassociative groups," seem, on the surface at least, to be objects of strictly combinatorial interest. However, quasigroups may also be specified as type (2, 2, 2) algebras satisfying equational identities, thus forming a variety in the universal algebraic sense. After introducing quasigroups through basic definitions and examples, we'll move into a discussion of the class of semisymmetric quasigroups. This class provides some nice illustrations of the interplay between algebra, combinatorics (in particular, design theory), and geometry that is provoked by quasigroup theory.
ID:
492
Year: 2017
Name: Alex Schulte
Institution: Iowa State University
Subject area(s):
Title of Talk: Anti-Van der Waerden number of 3-term arithmetic progression
Abstract: A set is rainbow if each element of the set is a di erent color. The anti-van der Waerden number of the integers from 1 to n, denoted by aw([n]; k), is the least positive integer r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. The exact value of the anti-van der Waerden number of the integers where k = 3 is given by aw([n]; 3) = dlog3 ne+2. The anti-van der Waerden number can also be de ned on graphs, where aw(G; k) is the least number of colors such that every coloring contains a rainbow k-term arithmetic progression. Bounds on the anti-van der Wareden number of graphs have been established and exact values are known for certain families of graphs. Keywords: Rainbow, r
Year: 2017
Name: Alex Schulte
Institution: Iowa State University
Subject area(s):
Title of Talk: Anti-Van der Waerden number of 3-term arithmetic progression
Abstract: A set is rainbow if each element of the set is a di erent color. The anti-van der Waerden number of the integers from 1 to n, denoted by aw([n]; k), is the least positive integer r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. The exact value of the anti-van der Waerden number of the integers where k = 3 is given by aw([n]; 3) = dlog3 ne+2. The anti-van der Waerden number can also be de ned on graphs, where aw(G; k) is the least number of colors such that every coloring contains a rainbow k-term arithmetic progression. Bounds on the anti-van der Wareden number of graphs have been established and exact values are known for certain families of graphs. Keywords: Rainbow, r
ID:
244
Year: 2008
Name: Elgin Johnston
Institution: Iowa State University
Subject area(s):
Title of Talk: Running a Math Circle
Abstract: For the last ten years I have been running a Math Circle for local middle and high school students. I will talk a little about the organization of the circle, how the circle is conducted, and about the mathematics we investigate.
Year: 2008
Name: Elgin Johnston
Institution: Iowa State University
Subject area(s):
Title of Talk: Running a Math Circle
Abstract: For the last ten years I have been running a Math Circle for local middle and high school students. I will talk a little about the organization of the circle, how the circle is conducted, and about the mathematics we investigate.
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:
252
Year: 2009
Name: Elgin Johnston
Institution: Iowa State University
Subject area(s): Math education, out reach
Title of Talk: A Teachers Circle for Middle School Math Teachers
Abstract: Last year I partnered with Jean Krusi, an Ames Middle School Mathematics teacher, and Gail Johnston, ISU Mathematics Lecturer, to organize and run a Teachers Circle for Middle School Mathematics Teachers. We followed up with a one week Teachers' Circle workshop in June 2009. This talk will describe our experience and supply good references for those interested in trying something like this in their own areas.
Year: 2009
Name: Elgin Johnston
Institution: Iowa State University
Subject area(s): Math education, out reach
Title of Talk: A Teachers Circle for Middle School Math Teachers
Abstract: Last year I partnered with Jean Krusi, an Ames Middle School Mathematics teacher, and Gail Johnston, ISU Mathematics Lecturer, to organize and run a Teachers Circle for Middle School Mathematics Teachers. We followed up with a one week Teachers' Circle workshop in June 2009. This talk will describe our experience and supply good references for those interested in trying something like this in their own areas.
ID:
510
Year: 2018
Name: Anna Aboud
Institution: Iowa State University
Subject area(s): Undergraduate Mathematics Education
Title of Talk: Implementation of Team Based Learning at Iowa State University
Abstract: Team-Based Learning (TBL) is a specific form of active learning designed to collaboratively engage students in significant problem-solving tasks. By means of a flipped classroom, students are able to spend class time working in heterogeneous groups, applying fundamental concepts to a rich applied context. In recent years, the Team-Based Learning structure has been applied with much success to select Calculus sections at Iowa State University. Quantitative data has shown that the TBL students performed better on the midterm and final calculus exams, and gave higher quality explanations. A key component of the success of the TBL method is student attitudes. To this end, a qualitative study was performed in the spring of 2018, examining the mathematical mindsets which influence the experiences and attitudes of students in a TBL classroom. In this talk we will explain how the TBL structure was applied to the Calculus curriculum at Iowa State University, share samples of the rich mathematical tasks implemented, and present the results of quantitative and qualitative studies on the efficacy of this method.
Year: 2018
Name: Anna Aboud
Institution: Iowa State University
Subject area(s): Undergraduate Mathematics Education
Title of Talk: Implementation of Team Based Learning at Iowa State University
Abstract: Team-Based Learning (TBL) is a specific form of active learning designed to collaboratively engage students in significant problem-solving tasks. By means of a flipped classroom, students are able to spend class time working in heterogeneous groups, applying fundamental concepts to a rich applied context. In recent years, the Team-Based Learning structure has been applied with much success to select Calculus sections at Iowa State University. Quantitative data has shown that the TBL students performed better on the midterm and final calculus exams, and gave higher quality explanations. A key component of the success of the TBL method is student attitudes. To this end, a qualitative study was performed in the spring of 2018, examining the mathematical mindsets which influence the experiences and attitudes of students in a TBL classroom. In this talk we will explain how the TBL structure was applied to the Calculus curriculum at Iowa State University, share samples of the rich mathematical tasks implemented, and present the results of quantitative and qualitative studies on the efficacy of this method.
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.
ID:
464
Year: 2017
Name: Michael Heeren
Institution: Kaplan University
Subject area(s): Number Theory
Title of Talk: Sums and Differences of Two Prime Numbers
Abstract: Two unsolved number theory questions are "Is every even whole number greater than 2 the sum of two primes numbers?" and "For every whole even integer, does there exist two prime numbers with that difference?" This presentation will look at these two questions by using a single table created by the addition of integers. The cells that have the sums of odd prime numbers, the opposite of odd prime numbers, or the sum of an odd prime number and the opposite of an odd prime number will be shaded. There will then be two inductive proofs concerning the shaded cells whose results can be used to help answer those two questions.
Year: 2017
Name: Michael Heeren
Institution: Kaplan University
Subject area(s): Number Theory
Title of Talk: Sums and Differences of Two Prime Numbers
Abstract: Two unsolved number theory questions are "Is every even whole number greater than 2 the sum of two primes numbers?" and "For every whole even integer, does there exist two prime numbers with that difference?" This presentation will look at these two questions by using a single table created by the addition of integers. The cells that have the sums of odd prime numbers, the opposite of odd prime numbers, or the sum of an odd prime number and the opposite of an odd prime number will be shaded. There will then be two inductive proofs concerning the shaded cells whose results can be used to help answer those two questions.