Digital Commons Network^™

An Analysis Of The Academic Success Achieved By Five Freshman Cohorts Through A Community College Developmental Education Program., Nancy K. Gray-Barnett

Electronic Theses and Dissertations

The challenge of underprepared students' entering America's colleges and universities is not new. Because of their "open door" policies, community colleges are more likely to enroll students who are not college prepared. This retrospective study focused on the performance of students who had completed required developmental education courses compared to the performance of students without developmental requirements. The study examined developmental education success measures for five cohorts of first-time degree-seeking freshmen each tracked for a six-year period enrolled at Walters State Community College located in Tennessee.

The success measures compared included grade point averages earned in college-level mathematics and English …

Chords Of Longest Circuits Of Graphs, Xuechao Li

Graduate Theses, Dissertations, and Problem Reports

This thesis is on a long standing open conjecture proposed by one of the most prominent mathematicians, Dr. C. Thomassen: Every longest circuit of 3-connected graph has a chord. In 1987, C. Q. Zhang proved that every longest circuit of a 3-connected planar graph G has a chord if G is cubic or if the minimum degree is at least 4. In 1997, Carsten Thomassen proved that every longest circuit of 3-connected cubic graph has a chord.;In this dissertation, we prove the following three independent partial results: (1) Every longest circuit of a 3-connected graph embedded in a projective plane …

Dynamic Coloring Of Graphs, Bruce Montgomery

Graduate Theses, Dissertations, and Problem Reports

In this dissertation, we introduce and study the idea of a dynamic coloring of a graph, a coloring in which any multiple-degree vertex of the graph must be adjacent to at least two color classes.;As parts of the overall research, we study (for some interesting subjects of colorings) the corresponding subjects of dynamic colorings, we compare the chromatic number and dynamic chromatic number, and we study some problems unique to dynamic colorings. Also, we introduce and briefly study a generalization of dynamic coloring.;The interesting subjects of colorings we consider are the chromatic number of important graphs, upper bounds of the …

Set-Theoretic And Algebraic Properties Of Certain Families Of Real Functions, Krzysztof Plotka

Graduate Theses, Dissertations, and Problem Reports

Given two families of real functions F1 and F2 we consider the following question: can every real function f be represented as f = f 1 + f2, where f1 and f2 belong to F1 and F2 , respectively? This question leads to the definition of the cardinal function Add: Add( F1,F2 ) is the smallest cardinality of a family F of functions for which there is no function g in F1 such that g + F is contained in F2 . This work is devoted entirely to the study of the function Add for different pairs of families of …

How Many Blocks To The Empire State Building? : An Original Story, Enakshi Bose

Graduate Student Independent Studies

Presents a children's story for eight and nine year old children that poses several mathematical questions, including the central one of how many blocks it is from the 215th Street subway station in Inwood to the Empire State Building. Photographs and maps enhance the mathematical concepts involved. Discusses the developmental appropriateness of the book's content and how the material meets various standards in mathematics.

Approximating Eigenvalues For Double Well Potentials., Chad Fulk

Student Work

One dimensional double well potentials usually refer to those potentials which have two equivalent or non-equivalent minima. They have been used to model diverse systems ranging from the electronic structure of diatomic molecules to electron-lattice coupling in high temperature superconductors [1][2]. However, one difficulty to the utility of these models is that exact analytical solutions for almost all double well potentials have not been found, in spite of the fact that this type of potential is constantly utilized as an illustra­tive example in the literature. Despite intensive research into this problem, only a few types of double wells have been …

Mathematics Achievement In Tennessee Schools In The Context Of Opportunity To Learn., Richard Lee Kitzmiller

Electronic Theses and Dissertations

This study examines the relationship of student achievement in mathematics and factors purported to influence such achievement. The factors utilized in the study were selected from those contained in accountability reports issued by the state of Tennessee in 1995-96. The student achievement measures were based on four high school end-of-course mathematics tests. Student performance on these tests is examined both in terms of actual scores and value-added measures. This study organizes the available accountability measures in an Opportunity-to-Learn (OTL) framework for the purpose of determining relationships that can inform practice and give policy guidance.

The study examined 65 (of 139) …

Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

National studies indicate major deficiencies in students' understanding of mathematics. Research suggests that students tend to view mathematics as a set of computational rules rather than a process of discovery and a tool for problem-solving. Most students fail to grasp the concepts behind the computations.

Technology provides a partial solution to this problem. Over the past decade, computers have emerged as a powerful tool in education. Computers place the control of action in the learning process with the student. They allow students to experiment with, explore, and discover mathematics at their own pace. With computers, students can consider more examples …

Some Problem In Homogenization., M. Rajesh Dr.

Doctoral Theses

No abstract provided.

Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.

Doctoral Theses

The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than the median of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to compare the variability of X with that of Y based only on numerical measures of variability. Besides, these characteristics of distributions might not exist in some cases. In most …

Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.

Doctoral Theses

Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of …

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …

Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr.

Doctoral Theses

In recent years random iterations of maps on Polish spaces has gained prominence. They are. nice examples of Markov processes whose invariant measures can be used in Computer imaging (see Berger ( 1). They also arise as random perturabations of deterministic dynamical systems.Let S be a Polish space with its Borel a-field. Let r be a collection of Borel maps from S to S. Let P be a probability on r. Then starting with a point z in S, we choose a map yn er according to the law P and move to ya(x). Then we choose 2 € r …

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …

Orientations Of Graphs Which Have Small Directed Graph Minors., Glenn Randolph Berman

LSU Historical Dissertations and Theses

Graphs are characterized by whether or not they have orientations to avoid one or more of the digraphs K&ar;3 , S&ar;3 , and P&ar;3 . K&ar;3 , S&ar;3 and P&ar;3 are created by starting with a triangle, a three point star, or a path of length three respectively, and replacing each edge with a pair of arcs in opposite directions. Conditions are described when all orientations of 3-connected and 4-connected graphs must have one or more of the above digraphs as a minor. It is shown that double wheels, and double wheels without an axle, are the only 4-connected graphs …

Densities Of 4-Ranks Of K(2) Of Rings Of Integers., Robert Burke Osburn

LSU Historical Dissertations and Theses

Conner and Hurrelbrink established a method of determining the structure of the 2-Sylow subgroup of the tame kernel K2( O ) for certain quadratic number fields. Specifically, the 4-rank for these fields was characterized in terms of positive definite binary quadratic forms. Numerical calculations led to questions concerning possible density results of the 4-rank of tame kernels. In this thesis, we succeed in giving affirmative answers to these questions.

On K-Conjugacy Classes Of Maximal Tori In Semi-Simple Algebraic Groups., Uroyoan Ramon-Emeterio Walker

LSU Historical Dissertations and Theses

An attempt was made to make this a self-contained reading. The first three chapters are intended to provide the necessary background. Chapter one develops the tools needed from Galois Cohomology. Chapter two is a brief description of involutions, and in chapter three we define the notion of (linear) algebraic group, we give some examples and discuss some of their properties. In chapter four, we discuss some variants of the classical Skolem-Noether theorem, requiring only that the subalgebra have a unique faithful representation of full degree over a separable closure. We verify that we can extend every isomorphism to the whole …

The Level Of Teacher Involvement In The Vermont Mathematics Portfolio Assessment Process And Instructional Practices In Grade 4 Classrooms, Carol Anne Fritz

Doctoral Dissertations

The comprehensive assessment system in Vermont includes student mathematics portfolios that are submitted to the state Department of Education for scoring. A student portfolio should include 5--7 pieces of best work selected by the student that can be scored. This alternative assessment process has been in place for ten years, but limited information has been available from classroom teachers about the instructional practices they use when teaching mathematics, or whether or not those practices have been influenced by the portfolio process.

The study was developed to answer questions about the instructional practices used by teachers. Teachers' responses were compared to …

Making Connections: Compartmentalization In Pre -Calculus Students' Understanding Of Functions, Hope H. Gerson

Doctoral Dissertations

Students develop knowledge constructs that they build into concepts through their experiences. Students demonstrate compartmentalization when they understand a construct or concept within one representation, but not another, or when they do not connect mathematically related ideas. For instance, a student may understand f(x) to mean plug x into the function within a symbolic representation, but the same student may understand f(x) to mean f times x within a tabular representation. A student with these understandings has a compartmentalized understanding of function notation.

A two-month study was conducted with a class of pre-calculus students enrolled in a parochial high school. …

A Study Of Mathematics Course Sequence And Student Performance In Mathematics In A Block Scheduled High School, John Harvell Moody

Doctoral Dissertations

The 1983 study of the condition of American Education, A Nation at Risk, brought a significant amount of attention to the way in which schools provided students with the skills necessary to be productive citizens. Many of the recommendations contained in A Nation at Risk focused on the perceived poor performance of American students when compared to their counterparts worldwide. The year after publication of A Nation at Risk, the National Commission on Time and Learning published Prisoners of Time, a report that called for the establishment of high academic standards for students and a major restructuring of the school …

Reflexivity, Elementary Operators And Cohomology, Jiankui Li

Doctoral Dissertations

Let H be a separable complex Hilbert space and let B(H) be the set of all bounded operators on H. In this dissertation, we show that if S is a n-dimensional subspace of B( H), then S is [ 2n ]-reflexive, where [t] denotes the largest integer that is less than or equal to t.

We obtain some lattice-theoretic conditions on a subspace lattice L which imply alg L , is strongly rank decomposable. Let S be either a reflexive subspace or a bimodule of a reflexive algebra. We find some conditions such that T has a rank one summand …

Physics Experiences And Calculus: How Students Use Physics To Construct Meaningful Conceptualizations Of Calculus Concepts In An Interdisciplinary Calculus /Physics Course, Karen Ann Marrongelle

Doctoral Dissertations

The purpose of this study was to investigate the manner by which students enrolled in an integrated Calculus/Physics course use their understanding of physics to inform their conceptualizations of calculus concepts. This study utilized a multiple case study design with analysis by and across cases. The cases represent eight first year students in the College of Engineering and Physical Sciences at the University of New Hampshire who enrolled in an integrated calculus/physics program. Data was gathered in a three-part process: (1) Semi-structured task-based interviews, (2) Participant-observation in the calculus/physics course, and (3) Obtaining copies of students' in-class notes, in-class activities, …

Learning And Understanding In Abstract Algebra, Bradford Reed Findell

Doctoral Dissertations

Students' learning and understanding in an undergraduate abstract algebra class were described using Tall and Vinner's notion of a concept image, which is the entire cognitive structure associated with a concept, including examples, nonexamples, definitions, representations, and results. Prominent features and components of students' concept images were identified for concepts of elementary group theory, including group, subgroup, isomorphism, coset, and quotient group.

Analysis of interviews and written work from five students provided insight into their concept images, revealing ways they understood the concepts. Because many issues were related to students' uses of language and notation, the analysis was essentially semiotic, …

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Depth-First Search Embedded Wavelet Algorithm For Hardware Implementation, Li-Minn Ang

Theses: Doctorates and Masters

The emerging technology of image communication over wireless transmission channels requires several new challenges to be simultaneously met at the algorithm and architecture levels. At the algorithm level, desirable features include high coding performance, bit stream scalability, robustness to transmission errors and suitability for content-based coding schemes. At the architecture level, we require efficient architectures for construction of portable devices with small size and low power consumption. An important question is to ask if a single coding algorithm can be designed to meet the diverse requirements. Recently, researchers working on improving different features have converged on a set of coding …

Vlsi Implementation Of A Massively Parallel Wavelet Based Zerotree Coder For The Intelligent Pixel Array, Geoffrey N. Alagoda

Theses: Doctorates and Masters

In the span of a few years, mobile multimedia communication has rapidly become a significant area of research and development constantly challenging boundaries on a variety of technologic fronts. Mobile video communications in particular encompasses a number of technical hurdles that generally steer technological advancements towards devices that are low in complexity, low in power usage yet perform the given task efficiently. Devices of this nature have been made available through the use of massively parallel processing arrays such as the Intelligent Pixel Processing Array. The Intelligent Pixel Processing array is a novel concept that integrates a parallel image capture …