Mathematics Commons^™

Using The Pert Exponential Growth Model: Predicting Past And Future Chinese Populations Involving Their Famous Population Control Policies, Greg Gancarz

A with Honors Projects

This project serves to examine the hypothetical effects of the implementation and repeal of China’s famous One Child Policy on the rate of population growth in that country through the use and applications of the basic exponential growth model. Calculates growth in three different scenarios and estmates the population for China in the year 2045.

Distribution Of Permutation Statistics Across Pattern Avoidance Classes, And The Search For A Denert-Associated Condition Equivalent To Pattern Avoidance, Joshua Thomas Agustin Davies

Dissertations, Master's Theses and Master's Reports

We begin with a discussion of the symmetricity of $\maj$ over $\des$ in pattern avoidance classes, and its relationship to $\maj$-Wilf equivalence. From this, we explore the distribution of permutation statistics across pattern avoidance for patterns of length 3 and 4.

We then begin discussion of Han's bijection, a bijection on permutations which sends the major index to Denert's statistic and the descent number to the (strong) excedance number. We show the existence of several infinite families of fixed points for Han's bijection.

Finally, we discuss the image of pattern avoidance classes under Han's bijection, for the purpose of finding …

Distance Magic-Type And Distance Antimagic-Type Labelings Of Graphs, Bryan Freyberg

Dissertations, Master's Theses and Master's Reports

Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection f from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized …

Hamiltonian Dynamics Of Cosmological Quintessence Models, Rossen Ivanov, Emil Prodanov

Articles

The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for …

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan M. Mcgovern, Owen Killian, Shruti Narashimham, Brendan Quinlivan, John Butler, Rebecca Beck, Ines Beiser, Laura W. Williams, Ronan P. Killeen, Michael Farrell, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures affecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in affected patients and in relatives harbouring a disease-specific endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unaffected first-degree relatives with abnormal temporal discrimination, 16 unaffected …

Investigating The Role Of The Written Curriculum On Lesson Planning For First-Year Elementary Mathematics Teachers, Anna Kron

Honors Program Theses

While studies have previously explored aspects of lesson planning from the perspective of experienced teachers, there is a lack of research investigating how this process is different for brand new educators. The researcher, a preservice elementary teacher studying at the University of Northern Iowa, wanted to learn more about the available resources and how she would utilize them when planning for mathematics instruction in her first elementary classroom. At the completion of this project, the researcher hoped to have a better understanding of the process first-year elementary teachers experience when transforming written textbook materials into a mathematics lesson plan. The …

Complexity Of Linear Summary Statistics, Micah G. Pedrick

HMC Senior Theses

Families of linear functionals on a vector space that are mapped to each other by a group of symmetries of the space have a significant amount of structure. This results in computational redundancies which can be used to make computing the entire family of functionals at once more efficient than applying each in turn. This thesis explores asymptotic complexity results for a few such families: contingency tables and unranked choice data. These are used to explore the framework of Radon transform diagrams, which promise to allow general theorems about linear summary statistics to be stated and proved.

Emergence And Complexity In Music, Zoe Tucker

HMC Senior Theses

How can we apply mathematical notions of complexity and emergence to music, and how can these mathematical ideas then inspire new musical works? Using Steve Reich's Clapping Music as a starting point, we look for emergent patterns in music by considering cases where a piece's complexity is significantly different from the total complexity of each of the individual parts. Definitions of complexity inspired by information theory, data compression, and musical practice are considered. We also consider the number of distinct musical pieces that could be composed in the same manner as Clapping Music. Finally, we present a new musical …

Platonismes, Marco Panza

MPP Published Research

Selon la vulgata philosophique, le platonisme concernant un certain domaine de recherche est la thèse affirmant que ce domaine concerne des objets qui lui sont propres, dont l’existence est indépendante de l’activité cognitive humaine. Souvent, dans la même vulgata on parle aussi de platonisme pour se référer à une thèse un peu différente, d’après laquelle ce qu’on dit concernant ce domaine est vrai ou faux indépendamment de toute justification ou réfutation que l’on puisse apporter. Naturellement, si parmi les énoncées ayant trait à ce demain, il y en a qu’on peut prendre comme particulièrement surs du fait d’en avoir une …

Bifurcation From Infinity And Multiplicity Of Solutions For Nonlinear Periodic Boundary Value Problems, Nsoki Mavinga, M. N. Nkashama

Mathematics & Statistics Faculty Works

We are concerned with multiplicity and bifurcation results for solutions of nonlinear second order differential equations with general linear part and periodic boundary conditions. We impose asymptotic conditions on the nonlinearity and let the parameter vary. We then proceed to establish a priori estimates and prove multiplicity results (for large-norm solutions) when the parameter belongs to a (nontrivial) continuum of real numbers. Our results extend and complement those in the literature. The proofs are based on degree theory, continuation methods, and bifurcation from infinity techniques.

Use Of Sex-Specific Clinical And Exercise Risk Scores To Identify Patients At Increased Risk For All-Cause Mortality, Paul C. Cremer, Yuping Wu, Haitham M. Ahmed, Lee M. Pierson, Danielle M. Brennan, Mouaz H. Al-Mallah, Clinton A. Brawner, Jonathan K. Ehrman, Steven J. Keteyian, Roger S. Blumenthal, Michael J. Blaha, Leslie Cho

Mathematics and Statistics Faculty Publications

Importance Risk assessment tools for exercise treadmill testing may have limited external validity. Cardiovascular mortality has decreased in recent decades, and women have been underrepresented in prior cohorts.

Objectives To determine whether exercise and clinical variables are associated with differential mortality outcomes in men and women and to assess whether sex-specific risk scores better estimate all-cause mortality.

Design, Setting, and Participants This retrospective cohort study included 59 877 patients seen at the Cleveland Clinic Foundation (CCF cohort) from January 1, 2000, through December 31, 2010, and 49 278 patients seen at the Henry Ford Hospital (FIT cohort) from January 1, …

Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher

Mathematics and Statistics Faculty Publications and Presentations

System Dynamics (SD) modeling is a powerful analytical method used by professional scientists, academics, and governmental officials to study the behavior patterns of complex systems. Specifically through use of the Stella software, it is a method that I and others have used for over two decades with high school, and even middle school, math and science students. In this paper I describe an introduction to SD modeling intended for an algebra class (in either middle or high school). In the body of the paper, a nested sequence of simple bank account examples, increasing in complexity, is used to demonstrate a …

Mind The Gap: An Initial Analysis Of The Transition Of A Second Level Curriculum Reform To Higher Education, Michael Carr, Fiona Faulkner, Cormac Breen, Mark Prendergast

Articles

This article details an initial analysis of the transition of a second level curriculum reform to higher education in Ireland. The reform entitled ‘Project Maths’ involved changes to what second level students learn in mathematics, how they learn it, and how they are assessed. Changes were rolled out nationally on a phased basis in September 2010. Students who were taught and assessed through the new curriculum first entered third level education in September 2012. It is important that third level mathematics lecturers are aware of the changes to the curriculum since certain topics such as vectors and matrices are no …

13: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.

08: Sine Transformations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SineTransformations.nb allows you to use sliders to see the effects of parameters on the amplitude, period, phase shift, and vertical shift.

15: Koch Snowflakes, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.

04: Domain And Range, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DomainAndRange.nb allows you to graph various types of functions and shows the domain and/or range along the appropriate axis.

08: Accumulator, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

Accumulator.nb takes a function ƒ and other information to sketch both the graph of ƒ and the graph of F(x) = Integral of ƒ(t) from a to x. Use the slider for the x-value to see how the accumulated area under ƒ helps to create the graph of F.

11: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.

10: Slope Fields + Solns, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SlopeFields+Solns.nb follows similarly from the previous notebook. Here, however, there is a 2D slider that shows a specific solution function as you move the initial point.