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 1-20 of 471 results.
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ID:
566
Year: 2021
Name: Zonghao Zou
Institution: Santa Clara University
Subject area(s):
Title of Talk: Helical trajectories of swimming cells with a flexible flagellar hook
Abstract: The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum in Stokes flow are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.
Year: 2021
Name: Zonghao Zou
Institution: Santa Clara University
Subject area(s):
Title of Talk: Helical trajectories of swimming cells with a flexible flagellar hook
Abstract: The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum in Stokes flow are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.
ID:
543
Year: 2019
Name: Valorie Zonnefeld
Institution: Dordt University
Subject area(s): Pedagogy of Mathematics
Title of Talk: Classroom Environments that Nurture a Growth Mindset
Abstract: Carol Dweck and Jo Boaler's landmark research regarding the importance of a growth mindset for learning and specifically mathematics is a game changer for professors and teachers. Learn what a growth mindset is and how to foster it in your classroom.
Year: 2019
Name: Valorie Zonnefeld
Institution: Dordt University
Subject area(s): Pedagogy of Mathematics
Title of Talk: Classroom Environments that Nurture a Growth Mindset
Abstract: Carol Dweck and Jo Boaler's landmark research regarding the importance of a growth mindset for learning and specifically mathematics is a game changer for professors and teachers. Learn what a growth mindset is and how to foster it in your classroom.
ID:
159
Year: 2006
Name: WEN ZHOU
Institution: Iowa State University
Subject area(s):
Title of Talk: Chemotactic Collapse in Keller-Segel Equation
Abstract: Chemotaxis phenomenon is one of the most fundamental phenomenons in the biology field. In 1970s, Keller and Segel characterize this phenomenon with two coupled equations. Study on the blow up of the solutions of the this equation is one of the key part of the research on this equation. This short talk will briefly introduce some recent results of the study on this equation, including Nagai, Velazquez, Stevens, Levine, and Hortsman's work, etc.
Year: 2006
Name: WEN ZHOU
Institution: Iowa State University
Subject area(s):
Title of Talk: Chemotactic Collapse in Keller-Segel Equation
Abstract: Chemotaxis phenomenon is one of the most fundamental phenomenons in the biology field. In 1970s, Keller and Segel characterize this phenomenon with two coupled equations. Study on the blow up of the solutions of the this equation is one of the key part of the research on this equation. This short talk will briefly introduce some recent results of the study on this equation, including Nagai, Velazquez, Stevens, Levine, and Hortsman's work, etc.
ID:
527
Year: 2019
Name: Hongyuan Zhang
Institution: Grinnell College
Subject area(s): applied topology
Title of Talk: Artworks and Articles Meet Mapper and Persistent Homology
Abstract: Since its recent birth, topological data analysis (TDA) has proven to be a very useful tool when studying large and high-dimensional data sets. We will talk about the application of two TDA tools, persistent homology and the Mapper algorithm, to the Metropolitan Museum of Art (MET) artwork data set and two scholarly literature databases: arXiv and Google Scholar. For the MET data, we use the Mapper Algorithm to guide feature selection in building a logistic regression model for classifying certain artworks. Then we use persistent homology to help differentiate between two subsets of artwork. For the arXiv data, we use persistent homology to derive a general sense of the shape of the data. With help of the Mapper Algorithm, we further explore the point cloud by analyzing trends and features in visualizations. For the Google Scholar data, we find that there are interesting correlations between academic category of the paper and number of pages, number of references, and published date.
Year: 2019
Name: Hongyuan Zhang
Institution: Grinnell College
Subject area(s): applied topology
Title of Talk: Artworks and Articles Meet Mapper and Persistent Homology
Abstract: Since its recent birth, topological data analysis (TDA) has proven to be a very useful tool when studying large and high-dimensional data sets. We will talk about the application of two TDA tools, persistent homology and the Mapper algorithm, to the Metropolitan Museum of Art (MET) artwork data set and two scholarly literature databases: arXiv and Google Scholar. For the MET data, we use the Mapper Algorithm to guide feature selection in building a logistic regression model for classifying certain artworks. Then we use persistent homology to help differentiate between two subsets of artwork. For the arXiv data, we use persistent homology to derive a general sense of the shape of the data. With help of the Mapper Algorithm, we further explore the point cloud by analyzing trends and features in visualizations. For the Google Scholar data, we find that there are interesting correlations between academic category of the paper and number of pages, number of references, and published date.
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:
462
Year: 2016
Name: ypmvqq ypmvqq
Institution: raCweZrhMNjKxbics
Subject area(s): UvVwwTilpXhZkD
Title of Talk: VgMIpGhcdwlkdWXBUw
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Year: 2016
Name: ypmvqq ypmvqq
Institution: raCweZrhMNjKxbics
Subject area(s): UvVwwTilpXhZkD
Title of Talk: VgMIpGhcdwlkdWXBUw
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ID:
155
Year: 2006
Name: Di Wu
Institution: Iowa State University
Subject area(s): Computational Biology and Applied Mathematics
Title of Talk: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data
Abstract: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data Di Wu and Zhijun Wu Program on Bioinformatics and Computational Biology Department of Mathematics Iowa State University Ames, Iowa 50011 Abstract. Given a set of distances for certain pairs of atoms in a protein, the coordinates of the atoms and hence the protein structure can then be determined through solving a so-called distance geometry problem. However, it has been proved to be a NP hard problem when only a set of partial distances given. Previously, we used a so-called geometric build-up approach to develop several algorithms for solving the distance geometry problem with a set of sparse distance data. In this method, the coordinates of the atoms in a protein are determined as one atom at a time, with the distances from four base atoms to the atom to be determined. However, the requirement for four base atoms for the unique determination of each atom is sufficient, but unnecessary and even redundant for rigid structural determination. Here we investigate a rigid geometric build-up algorithm, which requires three base atoms instead of four base atoms for the determination of each atom. It could generate rigid structures, even a unique structure for very sparse distance data of a protein eventually. Due to the reflection in the determination for some atoms, this algorithm may also produce multiple structures satisfying given distances. We present the results obtained by using the algorithm for the determination of the structures, which suggests the potential of applying the algorithm to the distance based protein structural modeling.
Year: 2006
Name: Di Wu
Institution: Iowa State University
Subject area(s): Computational Biology and Applied Mathematics
Title of Talk: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data
Abstract: Protein Structure Determination: A Rigid Geometric Build-up Algorithm for Solving a Distance Geometry Problem with Sparse Exact Distance Data Di Wu and Zhijun Wu Program on Bioinformatics and Computational Biology Department of Mathematics Iowa State University Ames, Iowa 50011 Abstract. Given a set of distances for certain pairs of atoms in a protein, the coordinates of the atoms and hence the protein structure can then be determined through solving a so-called distance geometry problem. However, it has been proved to be a NP hard problem when only a set of partial distances given. Previously, we used a so-called geometric build-up approach to develop several algorithms for solving the distance geometry problem with a set of sparse distance data. In this method, the coordinates of the atoms in a protein are determined as one atom at a time, with the distances from four base atoms to the atom to be determined. However, the requirement for four base atoms for the unique determination of each atom is sufficient, but unnecessary and even redundant for rigid structural determination. Here we investigate a rigid geometric build-up algorithm, which requires three base atoms instead of four base atoms for the determination of each atom. It could generate rigid structures, even a unique structure for very sparse distance data of a protein eventually. Due to the reflection in the determination for some atoms, this algorithm may also produce multiple structures satisfying given distances. We present the results obtained by using the algorithm for the determination of the structures, which suggests the potential of applying the algorithm to the distance based protein structural modeling.
ID:
336
Year: 2012
Name: Kelly Woodard
Institution: Simpson College
Subject area(s): Combinatorics
Title of Talk: Beggar Your Neighbor, The Search for an Infinite Game
Abstract: In this talk we will present the work completed in the summer of 2012 during the Dr. Albert H. and Greta A. Bryan Summer Research Program at Simpson College. We furthered the analysis of the card game Beggar-My-Neighbor specifically with the intent of discovering a deal that leads to an infinite game in a 52-card deck. We used combinatorics and programs written in Mathematica to examine and refine the large number of possible deals based on structures that lead to cyclic behavior.
Year: 2012
Name: Kelly Woodard
Institution: Simpson College
Subject area(s): Combinatorics
Title of Talk: Beggar Your Neighbor, The Search for an Infinite Game
Abstract: In this talk we will present the work completed in the summer of 2012 during the Dr. Albert H. and Greta A. Bryan Summer Research Program at Simpson College. We furthered the analysis of the card game Beggar-My-Neighbor specifically with the intent of discovering a deal that leads to an infinite game in a 52-card deck. We used combinatorics and programs written in Mathematica to examine and refine the large number of possible deals based on structures that lead to cyclic behavior.
ID:
314
Year: 2011
Name: Bill Wood
Institution: University of Northern Iowa
Subject area(s): calculus
Title of Talk: Squigonometry: Developing non-euclidean trigonometry with elementary calculus
Abstract: Differential equations offers one approach to defining the classical trigonometric functions sine and cosine that parameterize the unit circle. We adapt this approach to develop analogous functions that parameterize the unit "squircle" defined by $x^4+y^4=1$. As we develop our new theory of "squigonometry" using only elementary calculus, we will catch glimpses of some very interesting and deep ideas in elliptic integrals, non-euclidean geometry, number theory, and complex analysis.
Year: 2011
Name: Bill Wood
Institution: University of Northern Iowa
Subject area(s): calculus
Title of Talk: Squigonometry: Developing non-euclidean trigonometry with elementary calculus
Abstract: Differential equations offers one approach to defining the classical trigonometric functions sine and cosine that parameterize the unit circle. We adapt this approach to develop analogous functions that parameterize the unit "squircle" defined by $x^4+y^4=1$. As we develop our new theory of "squigonometry" using only elementary calculus, we will catch glimpses of some very interesting and deep ideas in elliptic integrals, non-euclidean geometry, number theory, and complex analysis.
ID:
147
Year: 2006
Name: Scott Wood
Institution: University of Iowa
Subject area(s): Bayesian statistics, spatial statistics, medical geography
Title of Talk: Model Fitting and Selection for County-Level Depression Hospitalization Rates Using Bayesian Statistical Methods
Abstract: Researchers in the health sciences are interested in identifying and modeling the risk factors that are associated with high rates of hospitalization for depression. Being able to identify U.S. counties with high standardized hospitalization rates (SHR) would be useful in allocating federal resources. This project analyzes and critiques three potential Bayesian statistical models that can be implemented using WinBUGS software. Ordinary least squares, Poisson regression, and Bayesian conditional autoregressive (CAR) models are considered in detail. Though each has its advantages and disadvantages, qualitative and quantitative evidence suggest that the Bayesian CAR model is the optimal choice for this data. While a Bayesian CAR model will be shown to account for spatial autocorrelation and Poisson response variables, it was not as reliable as hoped for making accurate predictions at the county level.
Year: 2006
Name: Scott Wood
Institution: University of Iowa
Subject area(s): Bayesian statistics, spatial statistics, medical geography
Title of Talk: Model Fitting and Selection for County-Level Depression Hospitalization Rates Using Bayesian Statistical Methods
Abstract: Researchers in the health sciences are interested in identifying and modeling the risk factors that are associated with high rates of hospitalization for depression. Being able to identify U.S. counties with high standardized hospitalization rates (SHR) would be useful in allocating federal resources. This project analyzes and critiques three potential Bayesian statistical models that can be implemented using WinBUGS software. Ordinary least squares, Poisson regression, and Bayesian conditional autoregressive (CAR) models are considered in detail. Though each has its advantages and disadvantages, qualitative and quantitative evidence suggest that the Bayesian CAR model is the optimal choice for this data. While a Bayesian CAR model will be shown to account for spatial autocorrelation and Poisson response variables, it was not as reliable as hoped for making accurate predictions at the county level.
ID:
133
Year: 2005
Name: Phil Wood
Institution:
Subject area(s): Calculus
Title of Talk: Simple Teaching of Differential Calculus
Abstract: Calculus may be taught more understandably by first describing its practical uses and then presenting it as simple algebra and geometry. In doing this all mention of infinitesimals, increments, theory of limits and formal proofs has been eliminated.
Year: 2005
Name: Phil Wood
Institution:
Subject area(s): Calculus
Title of Talk: Simple Teaching of Differential Calculus
Abstract: Calculus may be taught more understandably by first describing its practical uses and then presenting it as simple algebra and geometry. In doing this all mention of infinitesimals, increments, theory of limits and formal proofs has been eliminated.
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:
402
Year: 2014
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Teaching techniques
Title of Talk: Using short "lecture challenge questions" in large lecture courses
Abstract: The talk describes my use of daily "lecture challenges" in large lecture courses such as Calculus or Mathematical Ideas. These "lecture challenges" are one-problem quizzes on material presented in the same lecture. Problems are typically easy problems that might be test questions. There is no partial credit. Students get one point for a wrong answer, two points for a correct answer. Absent students get no points, so students are motivated to attend. The problems are very fast to grade. Students may help and teach each other.
Year: 2014
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Teaching techniques
Title of Talk: Using short "lecture challenge questions" in large lecture courses
Abstract: The talk describes my use of daily "lecture challenges" in large lecture courses such as Calculus or Mathematical Ideas. These "lecture challenges" are one-problem quizzes on material presented in the same lecture. Problems are typically easy problems that might be test questions. There is no partial credit. Students get one point for a wrong answer, two points for a correct answer. Absent students get no points, so students are motivated to attend. The problems are very fast to grade. Students may help and teach each other.
ID:
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:
154
Year: 2006
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Graph theory / mathematical biology
Title of Talk: Reconstructing genomes in the presence of hybridizations
Abstract: A homoplasy at a site in the DNA occurs when the value of a character (A, C, G, or T) changes more than once in the evolutionary history. Homoplasies create extra difficulties for reconstructing the evolutionary history of a collection of taxa. Recent interest has grown concerning evolutionary histories that are not described by trees but rather by more general networks that allow for hybridization events. A natural question is, in an idealized situation where homoplasies occur only at hybridization events, whether the characters at the leaves and the root of the network determine the characters at the internal vertices. Mathematically, one has a directed rooted acyclic graph in which the vertices correspond to taxa. At each vertex there is a set of genes. Under appropriate assumptions, the genes at all vertices are determined by the genes at the root and at the leaves.
Year: 2006
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): Graph theory / mathematical biology
Title of Talk: Reconstructing genomes in the presence of hybridizations
Abstract: A homoplasy at a site in the DNA occurs when the value of a character (A, C, G, or T) changes more than once in the evolutionary history. Homoplasies create extra difficulties for reconstructing the evolutionary history of a collection of taxa. Recent interest has grown concerning evolutionary histories that are not described by trees but rather by more general networks that allow for hybridization events. A natural question is, in an idealized situation where homoplasies occur only at hybridization events, whether the characters at the leaves and the root of the network determine the characters at the internal vertices. Mathematically, one has a directed rooted acyclic graph in which the vertices correspond to taxa. At each vertex there is a set of genes. Under appropriate assumptions, the genes at all vertices are determined by the genes at the root and at the leaves.
ID:
75
Year: 2004
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): graph theory
Title of Talk: Building supertrees using distances
Abstract: Suppose that a family of rooted phylogenetic trees Ti with different sets Xi of leaves is given. A supertree for the family would be a single rooted tree T whose leaf set is the union of all the Xi, such that the branching information in T corresponds to the branching information in all the trees Ti. This talk proposes a polynomial-time method BUILD-WITH-DISTANCES that makes essential use of distance information provided on the trees Ti to construct a rooted tree T. When a supertree containing also the distance information exists, then the method produces a supertree T. This supertree often shows increased resolution over the trees found by methods that utilize only the topology of the input trees.
Year: 2004
Name: Stephen Willson
Institution: Iowa State University
Subject area(s): graph theory
Title of Talk: Building supertrees using distances
Abstract: Suppose that a family of rooted phylogenetic trees Ti with different sets Xi of leaves is given. A supertree for the family would be a single rooted tree T whose leaf set is the union of all the Xi, such that the branching information in T corresponds to the branching information in all the trees Ti. This talk proposes a polynomial-time method BUILD-WITH-DISTANCES that makes essential use of distance information provided on the trees Ti to construct a rooted tree T. When a supertree containing also the distance information exists, then the method produces a supertree T. This supertree often shows increased resolution over the trees found by methods that utilize only the topology of the input trees.
ID:
297
Year: 2010
Name: Daniel Willis
Institution: Loras College
Subject area(s): K-12 Teaching; Geometry
Title of Talk: An Introduction to Logo
Abstract: An introduction to Logo (Turtle Geometry) using MSWLogo, a freeware version of Logo for 32-bit Windows. The talk will introduce basic commands, loops, procedures, and the use of variables, with applications to regular polygons, stars, tessellations, rotations, translations, reflections, and symmetry. The speaker has used Logo with teachers (and pre-service teachers) of elementary school, middle school, and high school mathematics.
Year: 2010
Name: Daniel Willis
Institution: Loras College
Subject area(s): K-12 Teaching; Geometry
Title of Talk: An Introduction to Logo
Abstract: An introduction to Logo (Turtle Geometry) using MSWLogo, a freeware version of Logo for 32-bit Windows. The talk will introduce basic commands, loops, procedures, and the use of variables, with applications to regular polygons, stars, tessellations, rotations, translations, reflections, and symmetry. The speaker has used Logo with teachers (and pre-service teachers) of elementary school, middle school, and high school mathematics.
ID:
232
Year: 2008
Name: Dan Willis
Institution: Loras College
Subject area(s): Preservice Teachers
Title of Talk: Math for Elementary Teachers
Abstract: The speaker will survey some of the available research on the mathematics content needs of elementary school teachers and future teachers. He will also discuss the impact this research has had on the development of a two-course 8-credit sequence "Math for Elementary Teachers I/II" at Loras College. This new two-course sequence is a program requirement for all Elementary Education majors at Loras College.
Year: 2008
Name: Dan Willis
Institution: Loras College
Subject area(s): Preservice Teachers
Title of Talk: Math for Elementary Teachers
Abstract: The speaker will survey some of the available research on the mathematics content needs of elementary school teachers and future teachers. He will also discuss the impact this research has had on the development of a two-course 8-credit sequence "Math for Elementary Teachers I/II" at Loras College. This new two-course sequence is a program requirement for all Elementary Education majors at Loras College.
ID:
560
Year: 2021
Name: Marshall Whittlesey
Institution: California State University San Marcos
Subject area(s): Geometry
Title of Talk: Using quaternions to prove theorems in spherical geometry
Abstract: It is well known that the complex numbers can be used to do transformation geometry in the plane. In particular, rotation by angle ϴ about the origin is accomplished via multiplication by the complex number e^iϴ=cos ϴ+ i sin ϴ. It is less well known that the quaternion algebra (consisting of expressions of the form a+bi+cj+dk with i^2=j^2=k^2=ijk=-1) can be used to do similar transformations in three dimensional space. In this talk we show how to use quaternions to prove an interesting classical theorem in spherical geometry. These methods are featured in the speaker's new book with CRC Press, "Spherical Geometry and its Applications", which the author hopes will be attractive for use in topics courses in geometry.
Year: 2021
Name: Marshall Whittlesey
Institution: California State University San Marcos
Subject area(s): Geometry
Title of Talk: Using quaternions to prove theorems in spherical geometry
Abstract: It is well known that the complex numbers can be used to do transformation geometry in the plane. In particular, rotation by angle ϴ about the origin is accomplished via multiplication by the complex number e^iϴ=cos ϴ+ i sin ϴ. It is less well known that the quaternion algebra (consisting of expressions of the form a+bi+cj+dk with i^2=j^2=k^2=ijk=-1) can be used to do similar transformations in three dimensional space. In this talk we show how to use quaternions to prove an interesting classical theorem in spherical geometry. These methods are featured in the speaker's new book with CRC Press, "Spherical Geometry and its Applications", which the author hopes will be attractive for use in topics courses in geometry.
ID:
404
Year: 2014
Name: Jonathan White
Institution: Coe College
Subject area(s): Pedagogy/Transition to Proof
Title of Talk: Constructing the Naturals -- An Inquiry-Based Approach
Abstract: The construction of the natural numbers via the Peano Axioms is a strangely neglected backwater of the undergraduate curriculum. It deserves more attention. Meanwhile, although inquiry-based learning has gained some traction, it usually is considered a binary decision, where a course either is or is not taught using an IBL approach. I propose a standalone unit, giving our number systems the foundation they deserve, and offering a "trial size" taste of IBL.
Year: 2014
Name: Jonathan White
Institution: Coe College
Subject area(s): Pedagogy/Transition to Proof
Title of Talk: Constructing the Naturals -- An Inquiry-Based Approach
Abstract: The construction of the natural numbers via the Peano Axioms is a strangely neglected backwater of the undergraduate curriculum. It deserves more attention. Meanwhile, although inquiry-based learning has gained some traction, it usually is considered a binary decision, where a course either is or is not taught using an IBL approach. I propose a standalone unit, giving our number systems the foundation they deserve, and offering a "trial size" taste of IBL.