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Cycles And Bases Of Graphs And Matroids, Ping Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

The objective of this dissertation is to investigate the properties of cycles and bases in matroids and in graphs. In [62], Tutte defined the circuit graph of a matroid and proved that a matroid is connected if and only if its circuit graph is connected. Motivated by Tutte's result, we introduce the 2nd order circuit graph of a matroid, and prove that for any connected matroid M other than U1,1, the second order circuit graph of M has diameter at most 2 if and only if M does not have a restricted minor isomorphic to U2,6.;Another research conducted in this …

Stable Tameness Of Two-Dimensional Polynomial Automorphisms Over A Regular Ring, Joost Berson, Arno Van Den Essen, David Wright

Mathematics Faculty Research

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. This results from the main theorem of this paper, which asserts that an automorphism in any dimension n is stably tame if said condition holds point-wise over Spec R. A key element in the proof is a theorem which yields the following corollary: over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local …

Shining A Hilbertian Lamp On The Bidisk, John E. Mccarthy

Mathematics Faculty Research

Four lectures on how different aspects of the function theory of the bidisk can be illuminated by using Hilbert spaces and operator theory.

Relations Between Twisted Derivations And Twisted Cyclic Homology, Jack M. Shapiro

Mathematics Faculty Research

For a given endomorphism on a unitary κ-algebra, Α, with κ in the center of Α, there are definitions of twisted cyclic and Hochschild homology. This paper will show that the method used to define them can be used to define twisted de Rham homology. The main result is that twisted de Rham homology can be thought of as the kernel of the Connes map from twisted cyclic homology to twisted Hochschild homology.

A Carathéodory Theorem For The Bidisk Via Hilbert Space Methods, Jim Agler, John E. Mccarthy, N J. Young

Mathematics Faculty Research

If φ is an analytic function bounded by 1 on the bidisk D 2 and τ∈∂(D 2 ) is a point at which φ has an angular gradient ∇φ(τ) then ∇φ(λ)→∇φ(τ) as λ → τ nontangentially in D 2 . This is an analog for the bidisk of a classical theorem of Carathéodory for the disk. For φ as above, if τ∈∂(D 2 ) is such that the lim inf of (1−|φ(λ)|)/(1−∥λ∥) as λ → τ is finite then the directional derivative D−δφτ) exists for all appropriate directions δ∈C 2 . Moreover, one can associate with φ and τ an …

Use Of A Clay Modeling Task To Reduce Chocolate Craving., Jackie Andrade, Sally Pears, Jon May, David J. Kavanagh

School of Psychology

Elaborated Intrusion theory (EI theory; Kavanagh, Andrade, & May, 2005) posits two main cognitive components in craving: associative processes that lead to intrusive thoughts about the craved substance or activity, and elaborative processes supporting mental imagery of the substance or activity. We used a novel visuospatial task to test the hypothesis that visual imagery plays a key role in craving. Experiment 1 showed that spending 10 min constructing shapes from modeling clay (plasticine) reduced participants' craving for chocolate compared with spending 10 min 'letting your mind wander'. Increasing the load on verbal working memory using a mental arithmetic task (counting …

The Determinant Formula In The Inverse Scattering Procedure For Steplike Potentials, Odile R. Bastille

Mathematics and Statistics

No abstract provided.

Integrating Mathematical Modeling For Undergraduate Pre-Service Science Education Learning And Instruction In The Middle School Classroom, William Robertson, David Carrejo

Selected Works Temporary Series

El Paso is a bicultural, bilingual community with a 76.6% Hispanic population. Combining El Paso’s population with that of its sister city, Ciudad Juárez, Mexico, our community is the largest metropolitan area on any international border in the world. Students at the University of Texas at El Paso (UTEP) are mostly female, and 50% of the total student population is made up of first-generation college students. These demographics are accompanied by low socioeconomic and educational factors: 23.6% of local families live below the poverty level, compared to 12.5% nationally; 32.9% of 25-year-olds have not graduated from high school; 19% of …

Integrating Mathematical Modeling For Undergraduate Pre-Service Science Education Learning And Instruction In The Middle School Classroom, William Robertson, David Carrejo

Departmental Papers (TE)

El Paso is a bicultural, bilingual community with a 76.6% Hispanic population. Combining El Paso’s population with that of its sister city, Ciudad Juárez, Mexico, our community is the largest metropolitan area on any international border in the world. Students at the University of Texas at El Paso (UTEP) are mostly female, and 50% of the total student population is made up of first-generation college students. These demographics are accompanied by low socioeconomic and educational factors: 23.6% of local families live below the poverty level, compared to 12.5% nationally; 32.9% of 25-year-olds have not graduated from high school; 19% of …

Algebra Knowledge In Early Elementary School Supporting Later Mathematics Ability., Scott A. Strother 1979-

Electronic Theses and Dissertations

The current study explored the impact that algebra knowledge in 1st and 2nd grade can have in growth and achievement in mathematics through 5th grade. Previous studies have shown the positive impact of teaching algebra in middle school (e.g. Smith, 1996). Other studies have shown that students can learn and apply fundamental algebra concepts even earlier, including early elementary grades (e.g. Schifter et al., 2008; Brizuela and Earnest, 2008). The current study aimed to expand upon this research by showing students' knowledge of early algebra concepts can predict positive longitudinal outcomes. This would support cognitive and education theories that students …

Acquisition Of Mathematical Vocabulary Using Constant Time Delay With Individuals With Moderate And Severe Disabilities., Connie Elaine Morrison 1974-

Electronic Theses and Dissertations

Constant Time Delay (CST) has been used extensively as a procedure to teach children with disabilities a variety of skills. There is a preponderance of evidence that this instructional strategy is a highly effective (Handen & Zane, 1987; Koscinski & Gast, 1993; & Schuster, Stevens, & Doak, 1990). However, there appears to be a lack of research regarding the use of CTD with children with moderate and/or severe disabilities in learning core content vocabulary. Therefore, the primary purpose of this study was to determine if students with moderate and severe disabilities could acquire core mathematical vocabulary content through the use …

Analyzing Common Algebra-Related Misconceptions And Errors Of Middle School Students., Sarah B. Bush

Electronic Theses and Dissertations

The purpose of this study was to examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebra-related misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used …

The Effects Of Changing From A Traditional Mathematics Curriculum To An Integrated Mathematics Curriculum On Student Mathematics Learning In Georgia, Catherine Lynn Mallanda

Dissertations

In 2005, the state of Georgia adopted a new integrated mathematics curriculum, the Georgia Performance Standards (GPS), which included a task-based approach for instruction. The purpose of this study was to determine if the new Georgia Performance Standards for mathematics increased students’ mean mathematics Preliminary SAT/National Merit Scholarship Qualifying Test (PSAT/NMSQT) scores or induced changes in the distribution of students’ scores on the PSAT/NMSQT. In addition, it was determined whether the level of course the student took, the type of implementation of the GPS curriculum or the preparation for implementation affected the PSAT/NMSQT scores. The results of the study indicated …

Accuracy Of The Teacherinsight Online Perceiver Tool In Determining The Effectiveness Of High Rated And Low Rated Math And Science New Hire Teachers Following One Year And Three Years Of Single School District Employment, Nicole A. Regan

Student Work

The purpose of this study is to explore the accuracy of the TeacherInsight online perceiver tool (Gallup University, 2007) in determining the effectiveness of high rated (n =14) and low rated ( n =36) math and science new hire teachers summative appraisal ratings, completed graduate coursework, and retention status following one year and three years of single school district employment.

Performance Comparison Between Ib School Students And Non-Ib School Students On The International Schools’ Assessment (Isa) And On The Social And Emotional Wellbeing Questionnaire, Ling Tan, Yan Bibby

Monitoring Learning

This report examines the performance of students enrolled in the IB Primary Years Programme (PYP) and the IB Middle Years Programme (MYP) on the ACER International Schools’ Assessment (ISA) compared with non-IB students from the same ISA cohorts. The ISA is an assessment created especially for students in international schools in Grades 3 to 10. The assessment asks both multiple-choice and open-ended questions in the areas of writing, reading and mathematics, and provides international normative information about student performance. The Reading and Mathematical Literacy are based on the internationally endorsed frameworks of the OECD's Programme for International Student Assessment (PISA). …

Elementary Teachers’ Mathematical Content Knowledge, Efficacy, And Problem Solving Abilities In Alternative Certification, Brian R. Evans

NERA Conference Proceedings 2011

The purpose of this study was to understand teachers’ mathematical content knowledge, self-efficacy, problem solving abilities, and teacher beliefs in an elementary education mathematics methods course for special education teachers in the New York City Teaching Fellows and Teach for America alternative certification programs. Findings revealed a significant increase in mathematical knowledge and self-efficacy. Additionally, teachers were found to have high self-efficacy and strong problem solving abilities. Teachers generally found that helping students with disabilities learn mathematics was the biggest issue in their teaching, and that the use of technology and manipulatives were the most important topics in their learning.

A Comparison Of Two Alternative Pathway Programs In Secondary Mathematics Teacher Certification, Brian R. Evans

NERA Conference Proceedings 2011

The purpose of this study was to compare the mathematics content knowledge, attitudes toward mathematics, and concepts of self-efficacy held by teachers in two alternative pathways to mathematics teacher certification: New York City Teaching Fellows and Teach for America. Findings revealed that there were no differences between Teaching Fellows and TFA teachers in mathematics content knowledge, attitudes toward mathematics, and concepts of self-efficacy. However, learning and teaching journals revealed several differences between Teaching Fellows and TFA teachers.

Eliciting Student Judgments Of Intrinsic Difficulty For Studying Student Misconceptions In Solving Basic Mathematics Items, Eric Magaram, Jean Phanor, Charles Secolsky, Preston Hasbrouck

NERA Conference Proceedings 2011

The misconceptions of developmental mathematics students in solving basic arithmetic problems are becoming a national crisis. If instructors better understood the conceptions that students have that lead to incorrect responses when solving arithmetic problems, instruction of the material presented to the students may improve. Four groups of five students were given five basic math questions for a total of 20 questions, and the only instructions the students were given was to solve the problems out loud and to please continue talking. Their answers were transcribed and the student responses were used to create solution strategies for each of the 20 …

The Impact Of Singapore Math On Student Knowledge And Enjoyment In Mathematics, Jenny Taliaferro Blalock

Doctoral Dissertations

The purpose of this study was to investigate the effect of the Singapore Math curriculum and approach to teaching on enjoyment and knowledge in mathematics in one rural school district in north Louisiana. The quantitative data used were collected from a Math Enjoyment Inventory and a mixed skills pre and posttest. Additional supplemental data were collected from a Teacher Response Form. All data were gathered in the 2010–2011 school year, and an intact population was utilized. Participants were categorized into two groups, the Singapore Math group and the traditional math group. The participating district implemented Singapore Math in the fall …

The Effect Of Single-Gender Education On The Achievement Of Sixth Grade Mathematics Students, Rhonda Lee Hill

Doctoral Dissertations and Projects

The purpose of this study was to investigate the impact on students' academic achievement when served with a single-gender instructional model. Sixth grade students enrolled in single-gender classes were compared to heterogeneous classes utilizing the Measures of Academic Progress (MAP). MAP data from the fall and spring administrations were evaluated to determine academic growth. In the analysis of growth in academic achievement between groups based upon MAP scores, there was no significant difference found between academic growth and gender. While there was group variability that may have impacted achievement scores, overall growth of MAP scores and the amount of achievement …

Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

All HMC Faculty Publications and Research

We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.

Simplicial Bredon-Illman Cohomology With Local Coefficients., Debashis Sen Dr.

Doctoral Theses

The notion of cohomology with local coefficients for topological spaces arose with the work of Steenrod [Ste43, Ste99], in connection with the problem of extending sections of a fibration. This cohomology is built on the notion of fundamental groupoid of the space and can be described by the invariant cochain subcomplex of the cochain complex of the universal cover under the action of the fundamental group of the space. This later description is due to Eilenberg [Eil47]. Cohomology with local coefficients finds applications in many other situations.We focus on one such application of this cohomology which is due to S. …

Spectral Properties Of Large Dimensional Random Circulant Type Matrices., Koushik Saha Dr.

Doctoral Theses

Consider a sequence of matrices whose dimension increases to infinity. Suppose the entries of this sequence of matrices are random. These matrices with increasing dimension are called large dimensional random matrices (LDRM).Practices of random matrices, more precisely the properties of their eigenvalues, has emerged first from data analysis (beginning with Wishart (1928) [132]) and then from statistical models for heavy nuclei atoms (beginning with Wigner (1955) [130]). To insist on its physical applications, a mathematical theory of the spectrum of the random matrices began to emerge with the work of E. P. Wigner, F. J. Dyson, M. L. Mehta, C. …

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Mathematics Faculty Publications

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

Yes We Can Achieve In Mathematics And Why We Don't : African American Female Eleventh And Twelfth Grade Students In A Career And Technical Setting., Courtenay Grace-Rochelle Mayes

Electronic Theses and Dissertations

The underachievement of African American students in the mathematics classroom and the underrepresentation of African Americans in advanced mathematics courses and mathematics related career fields has been a concern for the mathematics education community for many years. The objective of this research was to investigate the perceptions and mathematical experiences of seven African American female high school students who were on a continuum from succeeding at high levels to struggling in mathematics. These particular African American females were eleventh and twelfth grade students enrolled at a career and technical high school located in the Midwestern United States of America. This …

Mathematics: Giving Classical, Christian Education Its Voice, James W. Seidel

Master of Education Program Theses

Classical, Christian education developed in the late twentieth century as the result of the influence of authors and educators such as Dorothy Sayers, Douglas Wilson, and Mortimer Adler. Building upon the educational approach taken in the Middle Ages and earlier, the classical, Christian approach has slowly grown in popularity over the past thirty years. As classical, Christian education has matured, however, some areas of its educational philosophy have developed more slowly than others. In particular, mathematics education within the classical, Christian model has received minimal treatment. This thesis attempts to initiate a more intentional educational philosophy for mathematics in a …

A Smart Approach To Thrive In Mathematics: A Study Of The Relationship Of Attitude And Achievement, Vanessa E. Cleaver

Theses and Dissertations

A mixed-method study was conducted to examine the impact of two locally developed programs, SMART and THRIVE, on student attitudes toward and achievement in Algebra I. SMART is a summer program for students (grades seven through nine) who enrolled in Algebra I the upcoming school year. THRIVE, the follow-up component of SMART, is a Saturday program for students who are concurrently enrolled in Algebra I. Archival data from achievement tests, surveys, and records of students who completed Algebra I during the 2008-2009 school year were collected and analyzed to answer the research questions. The researcher also collected results from two …

Effect Of Geometer’S Sketchpad On Student Knowledge And Attitude, David J. Dekker

Master of Education Program Theses

This study examines the effects of Geometer’s Sketchpad on student achievement and attitudes in algebra classrooms. It has a quasi-experimental design. The sample included 93 students enrolled in Advanced Algebra courses at Calvin Christian High School in Grandville, MI. Four classes participated in a five-day unit that explored graphs of equalities and inequalities. Two classes used traditional graphing calculators and two classes used Geometer’s Sketchpad. One class of each type took a pretest to measure prior knowledge. All classes took a posttest and attitude survey at the end of the study. A t-test was used to compare class averages. There …

Quantitative Characterization Of Microstructure Features For 1st Generation Advanced High Strength Steels, Margarita Vidrio, Ellen Liu, Donsheng Li, Kyoo Sil Choi, Xin Sun

STAR Program Research Presentations

The role of Advanced High Strength Steels (AHSS) in the automotive industry is important because of its affordability and excellent mechanical properties. The 1st generation of AHSS achieves its preferred combination of strength and ductility by embedding harder martensite grains into softer ferritic matrix. Ductility and strength of these steels are important to safety, formability, application, and life. However, a noticeable degree of inconsistent forming behaviors has been observed in the 1st generation AHSS in production, which seems to be related to the microstructure-level inhomogeneity. The objective of this project is to grain fundamental understandings on how different microstructure level …

Shapes, Beth Morrow, Anne Peppers

Understanding by Design: Complete Collection

This unit addresses the Texas Pre-Kindergarten Guidelines “Child recognizes/describes common shapes” (MVC1) and “Child slides, flips, turns shapes to demonstrate they remain the same” (MVC4), as well as the math standard “Child covers an area with shapes.” At the conclusion of this unit, students will know:

- names and features (number of sides/angles) of common shapes: rectangle, square, triangle, circle, oval, and rhombus; and

- shapes remain the same regardless of their position;

and will be able to:

- identify and describe common shapes: rectangle, square, triangle, circle, oval, and rhombus

- cover an area with shapes and explain how …