Mathematics Commons^™

The Effects Of The Use Of Dynamic Geometry Software On Student Achievement And Interest, Heidi B. Hansen

Mathematics Graduate Theses

This study examines the current research that exists on the effects that the use of dynamic geometry software has on student achievement and interest level in mathematics. Additional questions examined are whether using dynamic geometry software has a greater impact on high or low achievers, and what current methods of implementation are suggested by the research. A review of the relevant literature indicates that the use of dynamic geometry software does have a positive effect on student achievement, particularly achievement in areas of high-level thinking. Insufficient research has been done on the effect that the use of dynamic geometry software …

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 …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Intersection Properties Of Balls In Banach Spaces And Related Topics., Sudipta Dutta Dr.

Doctoral Theses

In the first part of this chapter, we explain in general terms the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. In the second part, we introduce some notations and preliminaries that will be used in the subsequent chapters.As a prototype of the properties we will study in this thesis, let us call a closed linear subspace Y of a Banach space X a (P)-subspace of X if Y has a certain property P as a subspace of X. If a Banach space X, in its canonical embedding, is a (P)-subspace …

The Use Of Filters In Topology, Abdellatif Dasser

Electronic Theses and Dissertations

Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).

Mathematical Magic, Arthur T. Benjamin

All HMC Faculty Publications and Research

In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.

Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford

Publications

The article focuses on the use of standards-based teaching and learning that has been gaining significant attention in the education world. State and national associations now base their specific subject area or discipline solely on standards, i.e., International Technology Education Association (ITEA), National Council of Teachers of Mathematics (NCTM), National Science Education Association (NSEA). Moreover, at the public school level, state boards of education are holding school districts accountable for teaching standards-based curricula. It is with the latter definition in mind that the authors created a standards-based, integrated technology and mathematics lesson using the design and construction of stair systems.

Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.

Objectivity, Information, And Maxwell's Demon, Steven Weinstein

Dartmouth Scholarship

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Combinatorial Techniques For Digital Image Charecterization And Retrieval:Algorithms,Architectures,And Applications., Arijit Bishnu Dr.

Doctoral Theses

Interest in digital images stems mostly from its application to various areas of computer vision [33, 57] and pattern recognition [145). Problems include robotic vision and con- trol, geographic and topographic map matching, target recognition, space applications, character recognition, scene analysis, fingerprint and face recognition, etc. Lately, with the advent of content-based image retrieval (CBIR) and proliferation of the Internet, digital imaging applications are in vogue now than ever before. In almost all the cases, the data size is enormously large, and at the same time, fast on-line as well as real- time computation is needed. For example, in fingerprint …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

On The Approximability Of Linear Ordering And Related Np-Optimization Problems., Sounaka Mishra Dr.

Doctoral Theses

We investigate approximability of both maximum and minimum linear ordering problems (MAX-LOP and MIN-LOP) and several related problems such as the well known feedback set problems, acyclie subdigraph problem and several others and their variants.We show that both MAX-LOP and MIN-LOP are strongly NP-complete, and MIN- LOP, MIN-QAP(S) (a special case of minimum quadratic assignment problem) and MIN-W-FAS are equivalent with respect to strict-reduction. The strict-equivalence is also established among these problems as well as MIN-W-FVS, with weights on arcs/vertices bounded by a polynomial, and the unweighted versions of the feedback set. problems. We also show that MAX-LOP is strict-equivalent …

Deformation Theory Of Dialgebras., Anita Majumdar Dr.

Doctoral Theses

The main objective of this thesis is to develop an algebraic deformation theury for associative dialgebras, which are binary quadratic algebras discovered by J.-L. Loday in (16). (17), and subisequently, to derive a G-algebra siructure ou the dialgebra colhomology with cocfticients in itself.Deformation theory dates back at Ieast to Riemann's 1837 memoir on alelian fianetions in which he studied IHanifolds of complex dimension one and calculated the mumber of parameters (called moduli) upon which a deformation depends. The modern theory of deformations of structures on manifolds was developed extensively ly Frolicher-Kodaira-Nijenhnis-Nirenberg-Spencer (13], [14], [15). [25|, [26).The study of deformations of …

Essays In Financial Intermediation., Bappaditya Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

Spectral Triples And Metric Aspects Of Geometry On Some Noncommutative Spaces., Partha Sarathi Chakraborty Dr.

Doctoral Theses

Quantization of mathematical theories is now more than half a century old idea in mathe- matics. It goes back to Gelfand-Naimarks seminal paper [37] in 1943. As the name suggests noncommutative geometry is the quantization" of differential geometry. It is the study of noncommutative algebras as if they were algebras of functions on spaces like the commuta- tive algebras associated to affine algebraic varieties, smooth manifolds, topological spaces. One can trace its roots in the Gelfand-Naimark theorems (1943, 37]). In modern terminol- ogy their theorem says there is an antiequivalence between the category of (locally) compact Hausdorff spaces and (proper, …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …

Resources Related To Mathematics, Art And Nature, Vicki Beitler

Sabbaticals

The purpose of my sabbatical work was to learn about resources related to mathematics and art, nature, music and architecture. These subjects appeal to a wide audience, yet their mathematical connections are often on the periphery of a mathematics student's studies. In this way I planned to increase my knowledge of mathematics but at the same time broaden my understanding of cross-disciplinary subjects.

Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti

Dartmouth Scholarship

No abstract provided.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

An Extension Of Elton's L(1)(N) Theorem To Complex Banach Spaces, S J. Dilworth, Joseph P. Patterson

Faculty Publications

No abstract provided.

Writing Mathematics-A Nut And A Bolt Of Style, Frank A. Farris

Mathematics and Computer Science

As editor of Mathematics Magazine, I see a lot of manuscripts. Some of them are written with a charming sense of style, but many of them leave me thinking that the author's only concern was to set out the mathematics clearly. This is a fine place to start, but the tradition of the Magazine is to offer things that people will enjoy reading, and this requires more than clarity. Let me explain an important step authors can take in order to make their work more attractive.

Limits Highlights From Over 2000 Years Of Developments In Calculus Limits, Lauri A. Nevalainen

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Nsu Innovative Teaching In Math 2002, Nova Southeastern University

Abraham S. Fischler College of Education and School of Criminal Justice College Archive

No abstract provided.

Zero-Cycles And K-Theory On Normal Surfaces., Amalendu Krishna Dr.

Doctoral Theses

The main theme of this thesis is to study the theory of algebraic cycles on singular varieties over a field. This has been studied before extensively by Collins, Barbieri-Viale, Levine, Srinivas among several others. Our interest in this thesis is to address some well known problems in the theory of zero-cycles over nominal varieties. The use of K- theoretic techniques in our proofs illustrate the interplay between the study of algebraic cycles and algebraic K-theory.For a quasi-projective surface X over a field k, we define FA,(X) to be the subgroup of the Grothendieck group Ko(X) of vector bundies generated by …

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

High-Stakes Tests Require High-Stakes Pedagogy, Randy Lattimore

Trotter Review

High-stakes mathematics tests continue to gain popularity in the United States, with an increasing number of states setting the passing of such tests as a high school graduation requirement. Consequently, instruction and instructional content have changed, with teachers emphasizing materials on the test while neglecting other important aspects of learning. The tests have become all-consuming, taking over many students' lives. Yet students are often ill prepared for these tests. This is even more true for African-American students whose cultural and social circumstances make their preparation for high-stakes tests inadequate and ineffective. The author examines six such students - their hopes …

Why Makik Can "Do" Math: Race And Status In Integrated Classrooms, Jacqueline Leonard, Scott Jackson Dantley

Trotter Review

This case study reports on the small group interactions and achievements of Malik, an African American sixth grader, who attended a Maryland elementary school in 1997. Student achievement was measured by the Maryland Functional Mathematics Test (MFMT-I), which was given on a pre/post basis. Students' scores on the MFMT-I were analyzed using the ANOVA. The analysis revealed a significant difference (F = 3-330, p < .05) between the scores of Caucasian (M = 342.12) and African American students (M = 323-56). However, Malik's MFMT-I score rose from 293 to 353. A passing score is 340. This study examines Malik's interactions to ascertain what factors influenced his achievement. The findings are that Malik had a positive attitude about mathematics and a strong command of mathematical and scientific language. Recommendations are that teachers become cultural brokers to help all children learn the "language" of mathematics and encourage all students to become self-advocates to overcome negative social dynamics in small groups.