Digital Commons Network^™

Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner

Pitzer Faculty Publications and Research

Sir Isaac Newton revolutionized physics and astronomy in his Principia. How did he do it? Would his method work on any area of inquiry, not only in science, but also about society and religion? We look at how some Newtonians, most notably Colin Maclaurin, combined sophisticated mathematical modeling and empirical data in what has come to be called the "Newtonian Style." We argue that this style was responsible not only for Maclaurin’s scientific success but for his ability to solve problems ranging from taxation to insurance to theology. We show how Maclaurin’s work strengthened the prestige of Newtonianism and …

What Factors Contribute To The Success Of African American Women In Science And Mathematics: Do Teaching Techniques Matter, Sheryl Mcglamery

Teacher Education Faculty Proceedings & Presentations

The session content will focus on the author's research about effective teaching techniques that engage and assist African American women (and others) in succeeding in science and mathematics courses. Several case studies will highlight the effective practice focus of this session.

Outerplanar Crossing Numbers, The Circular Arrangement Problem And Isoperimetric Functions, Eva Czabarka, Ondrej Sykora, Laszlo A. Szekely, Imrich Vrt'o

Faculty Publications

We extend the lower bound in [15] for the outerplanar crossing number (in other terminologies also called convex, circular and one-page book crossing number) to a more general setting. In this setting we can show a better lower bound for the outerplanar crossing number of hypercubes than the best lower bound for the planar crossing number. We exhibit further sequences of graphs, whose outerplanar crossing number exceeds by a factor of log n the planar crossing number of the graph. We study the circular arrangement problem, as a lower bound for the linear arrangement problem, in a general fashion. We …

Division Of Science And Math Topics Courses 10/25/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Math 2993 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Math 1993 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Stat 4631 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Stat 4611 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Math 4993 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Math 3993 Course Proposal 10/07/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

To Journey Beyond Infinity, Kent A. Bessey

BYU Studies Quarterly

The notion of infinity has fascinated philosophers, scientists, and mathematicians for millennia. Its enigmatic nature seemed to thwart all attempts to unlock its secrets. Scriptural allusions to the infinite evoke a similar sense of mystery. Few have been as intrigued by the concept of infinity—or as tenacious in trying to understand it—as the German mathematician Georg Cantor. Between 1874 and 1884, Cantor published numerous papers that illuminated some of the shadowy regions of the infinite. He discovered a remarkable realm where half of a pie is as large as the whole, infinity comes in different sizes, and miracles are mathematically …

The Relationships Of Teachers' Levels Of Technology Integration On Student Achievement In Reading And Mathematics, Valerie S. Fields

Doctoral Dissertations

The purpose of this study was to determine to what extent the level of technology integration of fourth and eighth grade teachers in eleven rural school districts in northeastern Louisiana related to student achievement in reading and mathematics.

The sample consisted of 123 fourth and eighth grade teachers and their students from the eleven rural school districts in northeastern Louisiana. Fifty-eight percent of the teachers represented the fourth grade and 42% of the teachers represented the eighth grade. The teachers served a school age population in which 20% or more was from families with incomes below the poverty line.

Mean …

Math Anxiety: Causes, Effects, And Preventative Measures, Megan R. Smith

Senior Honors Theses

Math anxiety is a real problem facing students and teachers today. The mathematics teacher especially needs to understand the causes and effects of math anxiety as well as ways to help students overcome it. There are many symptoms of math anxiety including an unwillingness to attempt mathematics problems, a fear of taking advanced mathematics classes, and being unusually nervous when in mathematics class. Math anxiety hinders students' working memory (Perina, 2002). It occurs at different ages in different people for different reasons. The main cause of math anxiety is the teacher himself It has been shown that students tend to …

Statistics Form B: Discipline Objectives And Requirements 09/10/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Statistics Form A: Discipline Summary 09/10/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Mathematics Form B: Discipline Objectives And Requirements 09/03/2004, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Some Statistical Contributions To The Analysis Of Human Genome Diversity And Evolution., Analabha Basu Dr.

Doctoral Theses

The work embodied in this thesis pertains to human population genetics. In particular, the overarching goals of this thesis are to contribute to the understanding of genomic diversity of human populations and to the development of statistical methods for making inferences in genome diversity studies. With these two goals in mind, we have carried out a detailed statistical analysis of genomic data on a large number of ethnic populations of India, generated in the laboratory of the Anthropology & Human Genetics Unit, Indian Statistical Institute, Kolkata. Additionally, wherever relevant, we have compared our data with those collated from the published …

Results On Hyperspaces, Jorge M. Martinez-Montejano

Graduate Theses, Dissertations, and Problem Reports

A characterization of Cp(X), the family of subcontinua of X containing a fixed point of X, when X is an atriodic continuum is given as follows. Assume Z is a continuum and consider the following three conditions: (1) Z is a planar absolute retract; (2) cut points of Z have component number two; (3) any true cyclic element of Z contains at most two cut points of Z. If X is an atriodic continuum and p ∈ X, then Cp(X) satisfies (1)--(3) and, conversely, if Z satisfies (1)--(3), then there exist an arc-like continuum (hence, atriodic) X and a point …

Graph Minor, Jianbing Niu

Graduate Theses, Dissertations, and Problem Reports

In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph where k ≥ 2. If G contains three k-cliques, say L 1, L2, L3, such that |Li ∩ Lj| ≤ k - 2 (1 ≤ i < j ≤ 3), then G contains a Kk +2 as a minor. (2) Let G be a 6-connected claw-free graph. If delta(G) ≥ 7 and G contains three disjoint 5-cliques, say Ll, L2, L3, then G contains a K7 as a minor. (3) There is a function h : N → N, such that, for every 4-connected graph G with minimum degree at least five embedded in a surface with Euler genus g and face-width at least h(g), every longest circuit of the graph G has a chord.

Teachers' Handbook For Using Picture Books To Promote/Reinforce Mathematical Concepts In The Early Primary Grades, Andrea Lynn Bannister

All Master's Theses

The purpose of this paper was to design a handbook for early primary grade teachers interested in using picture books to promote/reinforce mathematics. The handbook includes ten lessons based on the National Council of Teachers of Mathematics Standards, 2000.

Reasoning About Motion: A Case Study, Tiffini Lynn Glaze

Theses and Dissertations

Several dance and industrial design students were given the opportunity to attend a non-traditional mathematics course. The nature of this course prompted student interaction and expected collaboration. My research focuses on one dance student, Sara, who did not consider herself a strong mathematics student, but who understood physical motion very well. This paper explores the evolution of Sara's representations for physical motion in a given task, and discusses her reasoning for keeping or dismissing various parts of her representations during the course of this task. I examine first how Sara learns mathematics with understanding in this task, and second how …

Modeling Of Solid Layer Growth At A Constant Speed In A Binary Melt Crystallization Process, Zongwen Feng

Doctoral Dissertations

Melt crystallization is an attractive separation method for the purification of organics at a large scale. Because the geometry of the rigid crystal lattice is peculiar to the particular substance, most crystallization processes form eutectic systems. The kinetics of crystallization limit the rate in which crystal growth can occur without the incorporation of undesired impurity. If the rate of heat transfer exceeds the mass transfer rate of the impurity, the impurity can solidify, contaminating the product. In practice, one would like to specify a crystallization rate and determine the temperature profile of the crystallizer wall that would achieve this rate. …

Contributions To Emerging Techniques In Survey Sampling., Sanghamitra Pal Dr.

Doctoral Theses

This dissertation contains seven Chapters. The contents in the respective Chapters may be briefly recounted as follows.A topic of classical interest in survey sampling is how to ensure the existence of a uniformly non-negative (UNN) unbiased estimator for the mean square error (MSE) of a homogeneous linear estimator (HLE) for a finite survey population total. Hájek (1958), Vijayan (1975), Rao and Vijayan (1977) and Rao (1979) developed a number of results which boil down to the folowing as narrated in the monograph by Chaudhuri and Stenger (1992).If there exist non-zero constants w, and the unknown values y, of the variable …

Some Studies On Uncertainty Management In Dynamical System Using Fuzzy Techniques With Applications., Kausik Majumdar Dr.

Doctoral Theses

Unceriain information processing by fuzzy if-then rules has received a lot of attention. Here we have taken a different path to model a system. about which we do not have precise information namely. modelling the system by fuzy valued functions without resorting to fuzzy if-then rules. As a result. the phase (state) space of the system becomes a full set and the underlying fuzzy mapping becomes a fuzzy attainability vet mappine. A fuzzy phase space is a collection of special class of furry subsets (fuzsy points) of R&for some positive integral n. Let the collection of all fuzr, real numbers …

Study On Dynamical Process In Boolean Network., Masahiko Kimura

Student Work

This thesis began with a question about how the human brain works and then two type of Boolean Networks , 1-D Cellular Automata and Associate Memory Model are chosen to explore this question. In the first part of this thesis the computability of 1-D Cellular Automata is studied by inventing a simple model, 3 colored balls model and several logical gates are implemented in its space. Although this model is so simple, by implementing three important logical gates, "NOT", "AND" and "OR", 3 colored balls model is proved to be computational universal. Since a common property " annihilation" is seen …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

On Flows Of Graphs, Rui Xu

Graduate Theses, Dissertations, and Problem Reports

Tutte's 3-flow Conjecture, 4-flow Conjecture, and 5-flow Conjecture are among the most fascinating problems in graph theory. In this dissertation, we mainly focus on the nowhere-zero integer flow of graphs, the circular flow of graphs and the bidirected flow of graphs. We confirm Tutte's 3-flow Conjecture for the family of squares of graphs and the family of triangularly connected graphs. In fact, we obtain much stronger results on this conjecture in terms of group connectivity and get the complete characterization of such graphs in those families which do not admit nowhere-zero 3-flows. For the circular flows of graphs, we establish …

Mathematics Discipline Senior Seminar Assessment Report 2003-2004, Mathematics Discipline

Assessment of Student Learning Reports

No abstract provided.