Other Mathematics Commons^™

Vertex Weighted Spectral Clustering, Mohammad Masum

Electronic Theses and Dissertations

Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to ...

Disciple, Jessica K. Sklar

Journal of Humanistic Mathematics

This is a love poem for mathematics.

Discrete And Continuous: A Fundamental Dichotomy In Mathematics, James Franklin

Journal of Humanistic Mathematics

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

Journal of Humanistic Mathematics

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.

Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, Victor J. Ricchezza, H. L. Vacher

Numeracy

Building on suggestions from alumni from a recent interview project, students in Computational Geology at the University of South Florida were tasked with reading a popular non-fiction book on mathematics and writing about the book and their feelings about math. The book, The Math Instinct by Keith Devlin, was chosen because we believed it would give the students something interesting to write about and not because we had any expectations in particular about what it might reveal about or do for their math anxiety. The nature of the responses received from the students led to the performance of a post-hoc ...

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added ...

Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

Electronic Journal of Linear Algebra

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.

Rainbow Copies Of C4 In Edge-Colored Hypercubes, József Balogh, Michelle Delcourt, Bernard Lidický, Cory Palmer

Bernard Lidický

For positive integers k and d such that 4≤k4in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.

Entropy In Topological Groups, Part 2, Dikran Dikranjan

Summer Conference on Topology and Its Applications

Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.

Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be ...

Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill

Dialogue & Nexus

Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.

Mathematical Evolution, Jeremiah Farrell, William Johnston

Scholarship and Professional Work - LAS

Crossword puzzle featured in the May 2017 issue of American Mathematical Monthly.

The Loewner Equation And Weierstrass' Function, Gavin Ainsley Glenn

University of Tennessee Honors Thesis Projects

No abstract provided.

On Some One-Complex Dimensional Slices Of The Boundedness Locus Of A Multi-Parameter Rational Family, Matthew Hoeppner

Theses and Dissertations

Complex dynamics involves the study of the behavior of complex-valued functions when they are composed with themselves repeatedly. We observe the orbits of a function by passing starting values through the function iteratively. Of particular interest are the orbits of any critical points of the function, called critical orbits. The behavior of a family of functions can be determined by examining the change in the critical orbit(s) of the functions as the values of the associated parameters vary. These behaviors are often separated into two categories: parameter values where one or more critical orbits remain bounded, and parameter values ...

Asymptotic Expansion Of The L^2-Norm Of A Solution Of The Strongly Damped Wave Equation, Joseph Silvio Barrera

Theses and Dissertations

The Fourier transform, F, on R^N (N≥1) transforms the Cauchy problem for the strongly damped wave equation u_tt(t,x) - Δu_t(t,x) - Δu(t,x) = 0 to an ordinary differential equation in time t. We let u(t,x) be the solution of the problem given by the Fourier transform, and v(t,ƺ) be the asymptotic profile of F(u)(t,ƺ) = û(t,ƺ) found by Ikehata in [4].

In this thesis we study the asymptotic expansions of the squared L^2-norms of u(t,x), û(t,ƺ) - v(t,ƺ), and v(t ...

Cocompact Cubulations Of Mixed 3-Manifolds, Joseph Dixon Tidmore

Theses and Dissertations

In this dissertation, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold M is mixed if its JSJ decomposition has at least one JSJ torus and at least one hyperbolic block. We show the fundamental group of M is virtually compact special iff M is chargeless, i.e. each interior Seifert fibered block has a trivial Euler number relative to the fibers of adjacent blocks.

Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson

Dissertations

As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval ...

Sum-Defined Colorings In Graphs, James Hallas

Honors Theses

There have been numerous studies using a variety of methods for the purpose of uniquely distinguishing every two adjacent vertices of a graph. Many of these methods have involved graph colorings. The most studied colorings are proper colorings. A proper coloring of a graph G is an assignment of colors to the vertices of G such that adjacent vertices are assigned distinct colors. The minimum number of colors required in a proper coloring of G is the chromatic number of G. In our work, we introduce a new coloring that induces a (nearly) proper coloring. Two vertices u and v ...

Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

Zea E-Books

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics ...

The Value Of A Win: Analysis Of Playoff Structures, Matthew Orsi

Honors Projects in Mathematics

The purpose of this Senior Capstone project is to analyze the distinctions between existing playoff systems. In particular, we are looking to analyze the differences between the standard single-elimination tournament (which the NCAA has used since the inception of the tournament) and other potential options: double-elimination and multiple game series. Popular sports such as Major League Baseball and the National Basketball Association all use multiple game series for their playoffs. This project will use probability theory and simulation to determine the likelihood of different seeds winning a championship as well as the expected number of victories by seed in each ...

Your Nsf Mathematical Sciences Institutes, Jason Grout, Leslie Hogben

Leslie Hogben

No abstract provided.