John Horton Conway: A Puzzle Game,
2014
Butler University
John Horton Conway: A Puzzle Game, Jeremiah Farrell, Karen Farrell
Scholarship and Professional Work - LAS
There are 10 different letters in the name JOHN HORTON CONWAY and we use each of these exactly three times each to form the following ten words: JHC, COW, NYC, JAN, RON, WRY, RAT, JOT, HWT, HAY.
The Efficacy Of Mathematics Education,
2014
University of South Florida; Sarasota-Manatee
The Efficacy Of Mathematics Education, Eric Geimer
The Transdisciplinary STEAM+ Journal
Evidence supports the notion that mathematics education in the United States is inadequate. There is also evidence that mathematics education deficiencies extend internationally. The worldwide mathematics education deficit appears large enough that improving student performance in this educational problem area could yield great economic benefit. To improve the efficacy of mathematics education, education’s root problems must first be understood. Often supposed educational root problems are considered and contrasted against potential deficiencies of mathematics methodologies and curricula that are based on mainstream educational philosophies. The educational philosophies utilized to form early-grade mathematics methodologies and related curricula are judged to be the …
The Nature And Nurture Of Intuition,
2014
College of Saint Benedict/Saint John's University
The Nature And Nurture Of Intuition, Thomas Q. Sibley
Forum Lectures
Are people just innately good at mathematics or not? My teaching experience suggests mathematical ability is not just fate: Students develop their mathematical abilities by doing mathematics. In particular we discuss geometric intuition, its connection with geometric reasoning and the possibility of developing them, using examples to get the listeners actively thinking about their own geometric thinking.
The Spacetime Geometry Of A Null Electromagnetic Field,
2014
Department of Physics, Utah State University
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Presentations and Publications
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein–Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance,
2014
Harvey Mudd College
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek
HMC Senior Theses
The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.
Symmetries Of Embedded Complete Bipartite Graphs,
2014
Loyola Marymount University
Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn
Mathematics, Statistics and Data Science Faculty Works
We characterize which automorphisms of an arbitrary complete bipartite graph Kn,m can be induced by a homeomorphism of some embedding of the graph in S3.
Promoting Reu Participation From Students In Underrepresented Groups,
2014
University of Richmond
Promoting Reu Participation From Students In Underrepresented Groups, Heather M. Russell, Heather A. Dye
Department of Math & Statistics Faculty Publications
Research experiences for undergraduates (REUs) are an important component of undergraduate education. However, at the 2012 Trends in Undergraduate Research in the Mathematical Sciences conference, questions were raised about why many REU programs see few applications from students that are members of underrepresented groups. We examine the benefits of REUs and factors preventing or promoting participation in REUs.
Finding Zeros Of Rational Quadratic Forms,
2014
Claremont McKenna College
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
CMC Senior Theses
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.
Groupoids Of Type I And Ii Using [0, N),
2014
University of New Mexico
Groupoids Of Type I And Ii Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Study of algebraic structures built using [0, n) happens to be one of an interesting and innovative research. Here in this book authors define non associative algebraic structures using the interval [0, n). Here we define two types of groupoids using [0, n) both of them are of infinite order. It is an open conjecture to find whether these new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity or Bruck identity or so on. We know on [0, n) we cannot build rings only pseudo rings, however in this book we use these …
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces,
2014
University of New Mexico
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, A. A. Salama, Florentin Smarandache, Valeri Kroumov
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we generalize the crisp topological space to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.
Topological Duality And Lattice Expansions, Ii: Lattice Expansions With Quasioperators,
2014
Chapman University
Topological Duality And Lattice Expansions, Ii: Lattice Expansions With Quasioperators, M. Andrew Moshier, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The main objective of this paper (the second of two parts) is to show that quasioperators can be dealt with smoothly in the topological duality established in Part I. A quasioperator is an operation on a lattice that either is join preserving and meet reversing in each argument or is meet preserving and join reversing in each argument. The paper discusses several common examples, including orthocomplementation on the closed subspaces of a fixed Hilbert space (sending meets to joins), modal operators auS and a- on a bounded modal lattice (preserving joins, resp. meets), residuation on a bounded residuated lattice (sending …
Spin Cobordism And Quasitoric Manifolds,
2014
University of Kentucky
Spin Cobordism And Quasitoric Manifolds, Clinton M. Hines
Theses and Dissertations--Mathematics
This dissertation demonstrates a procedure to view any quasitoric manifold as a “minimal” sub-manifold of an ambient quasitoric manifold of codimension two via the wedge construction applied to the quotient polytope. These we term wedge quasitoric manifolds. We prove existence utilizing a construction on the quotient polytope and characteristic matrix and demonstrate conditions allowing the base manifold to be viewed as dual to the first Chern class of the wedge manifold. Such dualization allows calculations of KO characteristic classes as in the work of Ochanine and Fast. We also examine the Todd genus as it relates to two types of …
Using Topology To Explore Mathematics Education Reform,
2014
Harvey Mudd College
Using Topology To Explore Mathematics Education Reform, Carling Sugarman
HMC Senior Theses
Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, …
Transitions In Line Bitangency Submanifolds For A One-Parameter Family Of Immersion Pairs,
2014
University of North Florida
Transitions In Line Bitangency Submanifolds For A One-Parameter Family Of Immersion Pairs, William Edward Olsen
UNF Graduate Theses and Dissertations
Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each …
Some Properties Of The Harmonic Quadrilateral,
2014
University of New Mexico
Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.
On Clifford Analysis For Holomorphic Mappings,
2014
Instituto Politécnico Nacl
On Clifford Analysis For Holomorphic Mappings, M. E. Luna-Elizarrarás, M. Shapiro, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In the classical theory of several complex variables, holomorphic mappings are just n-tuples of holomorphic functions in m variables, with arbitrary n and m, and no relations between these functions are assumed. Some 30 years ago John Ryan introduced complex, or complexified, Clifford analysis which is, in a sense, the study of certain classes of holomorphic mappings where the components are not independent, and instead obey the relations generated by the Cauchy– Riemann and Dirac-type operators. In this paper, we take a closer look at this theory emphasizing some additional properties that holomorphic mappings satisfy in this context. Our attention …
Topological Duality And Lattice Expansions, I: A Topological Construction Of Canonical Extensions,
2014
Chapman University
Topological Duality And Lattice Expansions, I: A Topological Construction Of Canonical Extensions, M. Andrew Moshier, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The two main objectives of this paper are (a) to prove purely topological duality theorems for semilattices and bounded lattices, and (b) to show that the topological duality from (a) provides a construction of canonical extensions of bounded lattices. In previously known dualities for semilattices and bounded lattices, the dual spaces are compact 0-dimensional spaces with additional algebraic structure. For example, semilattices are dual to 0-dimensional compact semilattices. Here we establish dual categories in which the spaces are characterized purely in topological terms, with no additional algebraic structure. Thus the results can be seen as generalizing Stone's duality for distributive …
Hom Quandles,
2014
Loyola Marymount University
Hom Quandles, Alissa S. Crans, Sam Nelson
Mathematics, Statistics and Data Science Faculty Works
If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q to A has a natural quandle structure. We exploit this fact to enhance the quandle counting invariant, providing an example of links with the same counting invariant values but distinguished by the hom quandle structure. We generalize the result to the case of biquandles, collect observations and results about abelian quandles and the hom quandle, and show that the category of abelian quandles is symmetric monoidal closed.
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups,
2014
Georgia Southern University
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko
College of Graduate Studies: Theses & Dissertations
The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$.
The Behavior Of Normality When Iteratively Finding The Normal To A Line In An Lp Geometry,
2013
Rochester Institute of Technology
The Behavior Of Normality When Iteratively Finding The Normal To A Line In An Lp Geometry, David L. Farnsworth, Joshua M. Fitzhugh
Articles
The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in lp geometries with p > 1 repeatedly finding the normal line through the origin gives sequences of lines that monotonically approach specific lines of symmetry of the unit circle. Which lines of symmetry that are approached depends upon the value of p and the slope of the initial line.
