Mathematics Commons^™

Paper Abstracts (2015), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Introduction (2015), Thomas Price, Derek Schuurman, Kevin Vander Meulen

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Subject-Centered Approach To Integrate Faith And Learning, Valorie L. Zonnefeld

Faculty Work Comprehensive List

No abstract provided.

Table Of Contents (2015), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Proceedings Of The Twentieth Conference Of The Association Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

The proceedings of the twentieth conference of the Associate of Christians in the Mathematical Sciences held at Redeemer University College from May 27-30, 2015.

Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali

Pomona Faculty Publications and Research

At the beginning of last summer I wrote about a neat trick to make your summer a productive one. And I heard from some of you who took me up on this suggestion; it seems that this actually works for many people! So, this year, for those who are willing to experiment with new ideas, I have another summer recommendation: Let us clean!

How Does Tutoring To Develop Conceptual Understanding Impact Student Understanding?, Kelsey Cummings

Honors Program Theses and Projects

No abstract provided.

Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

Boise State University Theses and Dissertations

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major …

Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

Undergraduate Honors Theses

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

The Relationship Between Elementary Teachers' Self-Efficacy For Teaching Mathematics And Their Mathematical Knowledge For Teaching, Meagan Mckinney

Boise State University Theses and Dissertations

This study examined the relationship between elementary teachers’ mathematical knowledge for teaching (MKT) and their self-efficacy for teaching mathematics. Self-efficacy and MKT are of high importance with implications in regards to quality of instruction and the Common Core State Standards for mathematics. Using the Content Knowledge for Teaching Mathematics (CKT-M) instrument, data for this study were collected from thirty-five elementary school teachers participating in the Improving Teachers’ Monitoring of Learning Grant at the time. The data were concerned with these teachers’ self-efficacy with the pedagogy and content of mathematics using the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Qualitative data were …

Bohr Density Of Simple Linear Group Orbits, Roger Howe, Francois Ziegler

Mathematical Sciences: Faculty Publications

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Families Of Weighted Sum Formulas For Multiple Zeta Values, Li Guo, Peng Lei, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.

Estimation In The Exponentiated Kumaraswamy Dagum Distribution With Censored Samples, Broderick O. Oluyede, Shujiao Huang

Mathematical Sciences: Faculty Publications

In a recent note, Huang and Oluyede (2014) proposed a new model called the exponentiated Kumaraswamy Dagum (EKD) distribution with applications to income and lifetime data. In this note, this distribution is shown to be a very competitive model for describing censored observations in lifetime reliability problems. This work shows that in certain cases, the EKD distribution performs better than other parametric model such as the exponentiated Kumaraswamy Weibull distribution and its sub-models, which include some of the commonly used models in survival analysis and reliability analysis, such as the exponentiated Weibull, Weibull and exponential distributions.

Fostoria Intermediate Elementary School Family Math Night, Chelsea Nye

Honors Projects

This is a Family Math Night that was planned and held at Fostoria Intermediate Elementary School in Fostoria, Ohio. It includes the Research Questions, Literature Review, Proposed Activity, Methodology, and Expected Results as well as the Annotated Bibliography and Timeline for Completion from my research and planning. Following the Proposal are 20 mathematical activity or game lesson plans and direction sheets that were planned for the Family Math Night. There are 5 different mathematical activities or games for each grade level 3-6, each meeting a different domain in the Common Core State Standards. At the end there is two general …

How Visualization Can Improve The Understanding Of Mathematics, Mariah Martin

Undergraduate Research Conference

High school students have a difficult time taking the new End-Of-Course exams in math. Why are students having this difficulty? This could be because students lack the understanding of visualization in mathematics. Visualization can be helpful to certain students who think this way, while also confusing to those same students, and others as well. However, to what extent do high stakes tests, such as the End-Of-Course exams in Algebra I and II, incorporate mathematical visualization? How can visualization help improve the understanding of mathematics? This review will explain the advantages and disadvantages of incorporating visualization in these exams, how students …

Does Being Bilingual Make You Better At Math?, Enxhi Elezi

Honors Projects in Mathematics

The purpose of this study is to examine if there is any relationship between being bilingual, defined as speaking your native language at home and another language in school, and your mathematical ability. Data from the National Longitudinal Study of Adolescent Health was used to compare the math grades of students who were not born in the US and speak English, Spanish, or Other at home. Also, data from the Bryant University first year students was used to test if students who speak a different language at home have a higher mathematical average than their monolingual peers. Results show that …

Transforming Precalculus Instruction: Evidence-Based Course Design, Wendy M. Smith

Discipline-Based Education Research Group Speaker Series

The UNL Mathematics Department has been focused on transforming precalculus instruction since 2012, with a goal of greater levels of student success. A short-term measure of student success is the passing rate (C or better), which has jumped from an average of 62% (2007-2011) to 80% for the past two falls. A longer-term measure of student success is recruiting and retaining undergraduates to STEM disciplines and careers. In this talk I will share specifics of the reform efforts (the who-what-when-where-why-and-how), and also share preliminary results from the research we have simultaneously been conducting into the reform efforts.

Restricted Sum Formula Of Alternating Euler Sums, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

In this paper, we study restricted sum formulas involving alternating Euler sums which are defined by ζ(s1,…,sd;ε1,…,εd)=∑n1>⋯>nd≥1εn11⋯εnddns11⋯nsdd,

for all positive integers s 1,…,s d and ε 1=±1,…,ε d =±1 with (s 1,ε 1)≠(1,1). We call w=s 1+⋯+s d the weight and d the depth. When ε j =−1 we say the jth component is alternating. We first consider Euler sums of the following special type: ξ(2s1,…,2sd)=ζ(2s1,…,2sd;(−1)s1,…,(−1)sd).

For d≤n, let Ξ(2n,d) be the sum of all ξ(2s 1,…,2s d ) …

Local Well-Posedness Of Periodic Fifth Order Kdv-Type Equations, Yi Hu, Xiaochun Li

Mathematical Sciences: Faculty Publications

In this paper, the local well-posedness of periodic fifth order dispersive equation with nonlinear term P1(u)∂xu + P2(u)∂xu∂xu. Here P1(u) and P2(u) are polynomials of u. We also get some new Strichartz estimates.

A Comparison Of Mathematics Content In The 2002 And 2014 Ged Test, Genice Cox

All Capstone Projects

As society changes and competition grows, the skilled worker becomes hard to find. For these reasons, secondary education is the starting point for pursuing college, a trade, and a career. For more than 60 years individuals have been given a second chance to complete their high school education by taking the General Education Development (GED) exam. This exam has been updated to correspond to changes in society and the workforce. As of 2014, the GED test was changed dramatically. This research project traced from past to present the intent of the assessment, teaching methods, curriculum, statistics, and overall preparation of …

Labeling And Comparison Of Isomeric Tree-Like Polyphenyl Systems, Tabitha Williford, Alex Collins, Shainaz Landge, Hua Wang

Mathematical Sciences: Faculty Publications

Tree-like polyphenyl systems form an important class of compounds in chemistry, in particular material science and polymers. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are the sub-categories of such systems with extremal Wiener indices. In this article, we provide a labelling of the vertices on each hexagon (i.e., the corresponding benzene ring), which facilitates the illustration of a treelike polyphenyl system with its corresponding tree structure. This approach helps to characterize the extremal tree-like polyphenyl systems with respect to the …

Cohen Factorizations: Weak Functoriality And Applications, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a “weak functoriality” result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen–Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.

Existence Of Solutions For A Variable Exponent System Without Ps Conditions, Li Yin, Yuan Liang, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u| p(x)−2∇u) + |u| p(x)−2u = λa(x)|u| γ(x)−2u + Fu(x, u, v) in R N , − div |∇v| q(x)−2∇v) + |v| q(x)−2 v = λb(x)|v| δ(x)−2 v + Fv(x, u, v) in R N , u ∈ W1,p(·) (R N ), v ∈ W1,q(·) (R N ), where the corresponding functional does not satisfy PS conditions. We obtain a sufficient condition for the existence of solution and also present a result on asymptotic behavior of solutions at …

Session B-1: Pipelines And Oil Spills!, Patrick Young

Professional Learning Day

Don’t miss this hands-on approach to middle school math. Participants will construct an actual pipeline from inexpensive materials and record evidence of leakage. They will then conduct an experiment and create a model relating liquid volume and spill area. They will apply their model to determine how much liquid leaked from their pipeline.

Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie

Professional Learning Day

Delve into the exciting world of math through games, puzzles and other sources! Participants shall try their luck and test their skill at these diversions. Participants will leave this session with a wealth of mathematical activities appropriate for students of all ages.

Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse

Professional Learning Day

The common core practice standards ask us to teach students to propose mathematical models and test their viability. Participants will do an experiment, collect data and use technological tools to combine modeling, analysis and basic statistics. Participants should bring a laptop, if possible; otherwise, bring a graphing calculator.

Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover

Professional Learning Day

Ah HA! Making the connection between polynomial functions, rational functions and using reciprocals! Join us to flip, not flop, with trig for your classroom.

Session C-2: Problem-Based Mathematics: You Reap What You Sow, Nicole Ross, Lindsey Herlehy

Professional Learning Day

Approach problem-based mathematics through a historical perspective! Join us to learn a fun, hands-on approach to examining the science behind crop rotation systems originally implemented during the Medieval Period. This activity requires students to mathematically evaluate the efficiency of a crop rotation system, strategically complete an integers-based crop puzzle, and evaluate crop yield and profit through data analysis. This activity integrates a variety of middle school mathematics concepts.

Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti

Professional Learning Day

This session will focus on implementing Common Core Middle-School Mathematics Standards using student-centered activities. Participants will receive three hands-on activities (one each at grades six, seven, and eight) to take back to their classrooms.

Density Of Gallai Multigraphs, Colton Magnant

Mathematical Sciences: Faculty Publications

Diwan and Mubayi asked how many edges of each color could be included in a 33-edge-colored multigraph containing no rainbow triangle. We answer this question under the modest assumption that the multigraphs in question contain at least one edge between every pair of vertices. We also conjecture that this assumption is, in fact, without loss of generality.