Mathematics Commons^™

Introduction (2011), Russell Howell

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2011), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2011), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences

Acms 18th Biennial Conference Proceedings, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Association of Christians in the Mathematical Sciences 18th Biennial Conference Proceedings, June 1-4, 2011, Westmont College, Santa Barbara, CA.

Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame

Honors Projects in Mathematics

This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon …

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

The Impact Of Manipulatives On Learning In The Elementary And Middle School Mathematics Classroom, Laura Dahl

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in the elementary and middle school mathematics classrooms. It embodies the logic behind using manipulative materials in the classroom setting and the impact their use will have on student understanding and enjoyment for learning mathematical concepts. This research paper will identify the struggles and concerns of manipulative use along with the need of increased professional development and training for teachers to be better prepared for the daunting, yet rewarding challenges of successfully teaching mathematics.

Groups And Semigroups Generated By Automata, David Mccune

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups ``expanding automaton semigroups''. We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups …

Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer

Department of Mathematics: Dissertations, Theses, and Student Research

This work is primarily concerned with the study of artinian modules over commutative noetherian rings.

We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for mini-max modules.

In the last chapter we prove that if the Betti …

Hilbert–Samuel And Hilbert–Kunz Functions Of Zero-Dimensional Ideals, Lori A. Mcdonnell

Department of Mathematics: Dissertations, Theses, and Student Research

The Hilbert-Samuel function measures the length of powers of a zero-dimensional ideal in a local ring. Samuel showed that over a local ring these lengths agree with a polynomial, called the Hilbert-Samuel polynomial, for sufficiently large powers of the ideal. We examine the coefficients of this polynomial in the case the ideal is generated by a system of parameters, focusing much of our attention on the second Hilbert coefficient. We also consider the Hilbert-Kunz function, which measures the length of Frobenius powers of an ideal in a ring of positive characteristic. In particular, we examine a conjecture of Watanabe and …

On Morrey Spaces In The Calculus Of Variations, Kyle Fey

Department of Mathematics: Dissertations, Theses, and Student Research

We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫_Ω f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(|·|)^α(x), where h is an N-function.

Following this, we provide a characterization of the class of Young measures that can be generated by a sequence …

On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wiener-type measures on spaces of continuous functions; our generalizations include an extension to multiple parameters, and a method of adjusting the distribution and covariance structure of the measure on the underlying function space.

In the second chapter, we consider single-parameter function spaces and extend a fundamental integration formula of Paley, Wiener, and Zygmund for an important class of functionals on this space. In the third chapter, we discuss measures on very general function spaces and introduce the specific example of a generalized …

Packings And Realizations Of Degree Sequences With Specified Substructures, Tyler Seacrest

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation focuses on the intersection of two classical and fundamental areas in graph theory:  graph packing and degree sequences.  The question of packing degree sequences lies naturally in this intersection, asking when degree sequences have edge-disjoint realizations on the same vertex set.  The most significant result in this area is Kundu's k-Factor Theorem, which characterizes when a degree sequence packs with a constant sequence.  We prove a series of results in this spirit, and we particularly search for realizations of degree sequences with edge-disjoint 1-factors.  

Perhaps the most fundamental result in degree sequence theory is the Erdos-Gallai Theorem, characterizing …

Extremal Trees And Reconstruction, Andrew Ray

Department of Mathematics: Dissertations, Theses, and Student Research

Problems in two areas of graph theory will be considered.

First, I will consider extremal problems for trees. In these questions we examine the trees that maximize or minimize various invariants. For instance the number of independent sets, the number of matchings, the number of subtrees, the sum of pairwise distances, the spectral radius, and the number of homomorphisms to a fixed graph. I have two general approaches to these problems. To find the extremal trees in the collection of trees on n vertices with a fixed degree bound I use the certificate method. The certificate is a branch invariant, …

Annihilators Of Local Cohomology Modules, Laura Lynch

Department of Mathematics: Dissertations, Theses, and Student Research

In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider the annihilators of local cohomology modules. We examine these annihilators at various cohomological degrees, in particular at the cohomological dimension and at the height or the grade of the defining ideal. We also investigate the dimension of these annihilators at various degrees and we refine our results by specializing to particular types of rings, for example, Cohen Macaulay rings, unique factorization domains, and rings of small dimension.

Adviser: Thomas Marley

The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm

Department of Mathematics: Dissertations, Theses, and Student Research

The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.

Adviser: Lynn Erbe and Allan Peterson

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …

Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette

Department of Mathematics: Dissertations, Theses, and Student Research

In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.

Weak Type Inequalities For Maximal Operators Associated To Double Ergodic Sums, Paul Hagelstein, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

Given an approach region Γ ∈ Z₊² and a pair U, V of commuting nonperiodic measure preserving transformations on a probability space (Ω, Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L¹(Ω) converge a.e. or that, given a positive increasing function ϕ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lϕ(L)(Ω) whose associated multiparameter ergodic averages fail to converge a.e.

Year-Round Calendars At The High School Level, Matthew Nohner

Mathematics Graduate Theses

The purpose of this paper is to explore the effects of a year round calendar on math scores at the high school level. Students forget facts, especially math facts, over long extended breaks. Year round calendars aim to address this dilemma by minimizing long breaks from learning. The results of year round calendars have been mixed. Some schools have reported both academic and monetary gains after switching from a traditional calendar, while other schools have seen modest gains in student learning. All studies cited in this paper report that at-risk and low socioeconomic students benefit academically from a year round …

Spectral Asymptotics Of Laplacians Associated To One-Dimensional Iterated Function Systems With Overlaps, Sze-Man Ngai

Mathematical Sciences: Faculty Publications

We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.

Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

We provide finite analogs of a pair of two-variable q-series identities from Ramanujan's lost notebook and a companion identity.

What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker

Journal of Humanistic Mathematics

Mathematical proof lies at the foundations of mathematics, but there are several notions of what mathematical proof is, or might be. In fact, the idea of mathematical proof continues to evolve. In this article, I review the body of literature that argues that there are at least two widely held meanings of proof, and that the standards of proof are negotiated and agreed upon by the members of mathematical communities. The formal view of proof is contrasted with the view of proofs as arguments intended to convince a reader. These views are examined in the context of the various roles …

Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Predictors Of Student Outcomes In Developmental Math At A Public Community And Technical College, Linda Darlene Hunt

Theses, Dissertations and Capstones

With the wide range of abilities of community college students, proper course placement is crucial. Therefore, having better predictors of success can help improve placement of students for their achievement. This study analyzed student predictors, instructor predictors, and classroom predictors in relation to student final exam score and student final grade in Elementary Algebra and Intermediate Algebra classes. Student predictors included gender, ACT math score, SAT math score, community college enrollment, math pretest score, and ASC grade. Instructor predictors included gender, employment status, Mozart music use, and ALEKS software use. Classroom predictors included time of day, number of class meetings …

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Mathematics Faculty Publications

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Tilings, Patterns And Technology, Ma. Louise Antonette N. De Las Peñas, Angela Fatima H. Guzon

Mathematics Faculty Publications

In this paper we discuss various situations where tilings and patterns, with the aid of technology, facilitate the teaching of mathematics and serve as tools in understanding and developing new mathematical ideas. We also illustrate how technology makes possible cultural connections in the study of mathematics using Islamic tilings and patterns.

Connecting Mathematics Students To Philosophy And Faith, Nathan Moyer

ACMS Journal 2010-2011

This paper describes an upper-division class project that helps students wrestle with the deep philosophical questions of mathematics in a relevant way. Through article readings and group discussions, various historical views of mathematical philosophy are examined and critiqued. An emphasis is placed upon students making meaningful connections between their own views of mathematics and their personal Christian faith or worldview.

Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave

Faculty Publications

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …

Spreadsheets Across The Curriculum, 2: Assessing Our Success With Students At Eckerd College, Laura Reiser Wetzel

Numeracy

The Spreadsheets Across the Curriculum (SSAC) library consists of activities to reinforce or teach quantitative literacy or mathematical concepts and skills in context. Each SSAC “module” consists of a PowerPoint presentation with embedded Excel spreadsheets. Each student works through a presentation, thinks about the in-context problem, figures out how to solve it mathematically, and builds spreadsheets to calculate and examine answers.

To assess the effectiveness of SSAC modules, I surveyed Eckerd College undergraduates in two separate studies. Two undergraduate research assistants and I generated pre- and post-tests for 10 SSAC modules. We hired 21 undergraduates who conducted 62 individual module …