Physical Sciences and Mathematics Commons^™

Versal Deformations Of Leibniz Algebra., Ashis Mandal Dr.

Doctoral Theses

No abstract provided.

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

Review Of Calculation Vs. Context: Quantitative Literacy And Its Implications For Teacher Education By Bernard L. Madison And Lynn Arthur Steen (Editors), Maura B. Mast

Numeracy

Madison, Bernard L. and Steen, Lynn Arthur (Eds.). Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education. (Washington, DC: Mathematical Association of America, 2009). 197 pp. Softcover. ISBN 978-0-88385-908-7. Available free on the MAA website at http://www.maa.org/ql/calcvscontext.html

The papers in Calculation vs. Context discuss the role of quantitative literacy in the K-12 curriculum and in teacher education. The papers present a varied set of perspectives and address three themes: the changing environment of education in American society; the challenges, and the necessity, of preparing teachers to teach quantitative literacy and of including quantitative literacy in the K-12 education; …

Engaging Math-Avoidant College Students, M. Paul Latiolais, Wendi Laurence

Numeracy

This paper is an informal, personal account of how we, as two college teachers, became interested in math anxiety, decided to explore it amongst students at our institution in order to inform our teaching, and became convinced that the massive problem is math avoidance. We tried discussion groups, but few students attended, although those that did made useful suggestions. Thus informed, we designed an innovative course, Confronting College Mathematics as a Humanities course with the possibility of credit toward the math requirement, but it was undersubscribed in its first offering and had to be canceled. How can we get college …

Measuring Resource Inequality: The Gini Coefficient, Michael T. Catalano, Tanya L. Leise, Thomas J. Pfaff

Numeracy

This paper stems from work done by the authors at the Mathematics for Social Justice Workshop held in June of 2007 at Middlebury College. We provide a description of the Gini coefficient and some discussion of how it can be used to promote quantitative literacy skills in mathematics courses. The Gini Coefficient was introduced in 1921 by Italian statistician Corrado Gini as a measure of inequality. It is defined as twice the area between two curves. One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function …

A Space Topologized By Functions From Omega To Omega, Akira Iwasa

Faculty Publications

No abstract provided.

6th Annual Student Scholars’ Expo Of The School Of Mathematics, Engineering, And Business, Messiah College

School of Science, Engineering & Health (SEH) Symposium

Celebrating the scholarly work our students have been engaged in throughout the year.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Certain Pattern Recognition Tasks Using Genetic Programming., Durga Muni Dr.

Doctoral Theses

No abstract provided.

2009 Sonia Kovalevsky Math For Girls Day Flyer, Association For Women In Mathematics, Lincoln University Of Missouri

Math for Girls Day Documents

4th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 24, 2009.

Distance To The Sagittarius Dwarf Galaxy Using Macho Project Rr Lyrae Stars, Andrea Kunder, Brian Chaboyer

Dartmouth Scholarship

We derive the distance to the northern extension of the Sagittarius (Sgr) dwarf spheroidal galaxy from 203 Sgr RR0 Lyrae stars found in the MACHO database. Their distances are determined differentially with respect to 288 Galactic bulge RR0 Lyrae stars also found in the MACHO data. We find a distance modulus difference of 2.41 mag at l = 5^◦ and b =− 8^◦ and that the extension of the Sgr galaxy toward the galactic plane is inclined toward us. Assuming R GC = 8 kpc, this implies the distance to these stars is (m − M) 0 = …

Math Island At Brewer Elementary School: A Learner-Centered Model For Education, Vikki K. Collins, H. Marguerite Yates

Georgia Educational Researcher

This paper examines a learner-centered model for the teaching of elementary mathematics established at an urban Georgia school that serves a highly mobile, diverse population of approximately 475 students. The school was on its state’s list of schools needing improvement because students continued to perform poorly on standardized tests. Math Island, a support center for students designed to facilitate the conceptual understanding of mathematics, was created, and professional development programs were implemented to assist teachers in developing their pedagogical and content expertise in the teaching of mathematics. The school made substantial progress after these initiatives were employed and was removed …

The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers

FIU Electronic Theses and Dissertations

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …

New Neighbors: Parallaxes Of 18 Nearby Stars Selected From The Lspm-North Catalog, Sébastien Lépine, John R. Thorstensen, Michael M. Shara, R. Michael Rich

Dartmouth Scholarship

We present astrometric parallaxes for 18 suspected nearby stars selected from the LSPM-north proper motion catalog. 16 objects are confirmed to be main-sequence M dwarfs within 16 pc of the Sun, including three stars (LSPM J0011+5908, LSPM J0330+5413, and LSPM J0510+2714) which lie just within the 10 pc horizon. Two other targets (LSPM J1817+1328, LSPM J2325+1403) are confirmed to be nearby white dwarfs at distances of 14 and 22 pc, respectively. One of our targets, the common proper motion pair LSPM J0405+7116E + LSPM J0405+7116W, is revealed to be a triple system, with the western component resolved into a pair …

Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.

Doctoral Theses

In everyday life, there arise many situations where two parties, sender and receiver, need to communicate. The channel through which they communicate is assumed to be binary symmetric, that is, it changes 0 to 1 and vice versa with equal probability. At the receiver’s end, the sent message has to be recovered from the corrupted received word using some reasonable mechanism. This real life problem has attracted a lot of research in the past few decades. A solution to this problem is obtained by adding redundancy in a systematic manner to the message to construct a codeword. The collection of …

Spectral Analysis And Synthesis For Radial Sections Of Homogenous Vector Bundles On Certain Noncompath Riemannian Symmetric Spaces., Sanjoy Pusti Dr.

Doctoral Theses

We consider two classical theorems of real analysis which deals with translation invariant subspaces of integrable and smooth functions on R respectively. The first one is a theorem of Norbert Wiener [63] which states that if the Fourier transform of a function f ∈ L 1 (R) has no real zeros then the finite linear combinations of translations f(x − a) of f with complex coefficients form a dense subspace in L 1 (R), equivalently, span{g ∗ f | g ∈ L 1 (R)} is dense in L 1 (R). This theorem is well known as the Wiener-Tauberian Theorem (WTT). …

Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.

Doctoral Theses

Although, we have used techniques developed in the paper of Cowen-Douglas [18, 20], a systematic account of Hilbert space operators using a variety of tools from several different areas of mathematics is given in the book [26]. This book provides, what the authors call, a sheaf model for a large class of commuting Hilbert space operators. It is likely that these ideas will play a significant role in the future development of the topics discussed here.

Web Surfer Models: Preprocessing, Page Ranking, And Quantitative Evaluation., Narayan L. Bhamidipati Dr.

Doctoral Theses

The World Wide Web [12] (usually referred to as the Web, WWW or W3) is an enormous collection of data available over the Internet, which is a vast network of computers. It was created in the year 1990 by Tim Berners-Lee, while he worked at CERN, Switzerland, and was made available over the Internet in 1991. The World Wide Web Consortium [136] authoritatively defines the Web as the universe of network-accessible information, the embodiment of human knowledge. The Web consists of objects, also called documents or pages in a generic sense, that are identified using a Uniform Resource Identifier (URI), …

Quantitative Literacy On The Web Of Science, 2 – Mining The Health Numeracy Literature For Assessment Items, H L. Vacher, Todd Chavez

Numeracy

A topic search of the Web of Science (WoS) database using the term “numeracy” produced a bibliography of 293 articles, reviews and editorial commentaries (Oct 2008). The citation graph of the bibliography clearly identifies five benchmark papers (1995-2001), four of which developed numeracy assessment instruments. Starting with the 80 papers that cite these benchmarks, we identified a set of 25 papers (1995-2008) in which the medical research community reports the development and/or application of health-numeracy assessments. In all we found 10 assessment instruments from which we have compiled a total of 48 assessment items. There are both general and context-specific …

Establishing The Quantitative Thinking Program At Macalester, David Bressoud

Numeracy

In November 2005, the faculty of Macalester College voted to institute a graduation requirement in Quantitative Thinking (QT) that is truly interdisciplinary. It currently draws on courses from thirteen departments including Anthropology, Economics, Geography, Political Science, Theater, Mathematics, Environmental Science, and Geology. This article describes the process that led to the creation of this program. It explains how we were able to get broad buy-in at the beginning and the long process of trial and error—informed by formative assessment—that was needed to refine the initial vision and shape it into a viable program that would be accepted by most of …

Confronting Challenges, Overcoming Obstacles: A Conversation About Quantitative Literacy, Bernard L. Madison, Lynn A. Steen

Numeracy

An edited transcript of the opening session of a workshop on quantitative literacy held Oct. 10-12, 2008 at Carleton College, Northfield, Minnesota. The workshop, which brought together interdisciplinary teams from two dozen colleges and universities, was sponsored by the Quantitative Inquiry, Reasoning, and Knowledge (QuIRK) Initiative at Carleton and the Washington-based Project Kaleidoscope. Two mathematicians in the forefront of quantitative literacy initiatives over the period 1997-2008, Lynn Arthur Steen and Bernard L. Madison, converse about attitudes, obstacles, changes and accomplishments. The conversation, structured as an interview, begins with the relationship between mathematics and quantitative literacy and moves through issues central …

All The More Reason For Qr Across The Curriculum, Bernard L. Madison

Numeracy

No abstract provided.

Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney

Educational Leadership & Workforce Development Faculty Publications

The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.

Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison

Articles

The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism group of the labeled graph is trivial. The fixing number can be thought of as a variation of the distinguishing number in which every label …

Creating A Warmer Environment For Women In The Mathematical Sciences And In Philosophy, Samantha Brennan, Rob Corless

Samantha Brennan

No abstract provided.

Predictability In The Indian Stock Market: A Study From An Econometric Perspective., Debabrata Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

Greedy Signal Recovery Review, Deanna Needell, Joel A. Tropp, Roman Vershynin

CMC Faculty Publications and Research

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.

Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This …

Contributions To Random Energy Models., Nabin Kumar Jana Dr.

Doctoral Theses

In this introductory chapter, we begin with a brief description of spin glasses in section 1. We are not physicists. The purpose of this section is to trace the history of the models. Section 2 gives a brief summary of the thesis and section 3 recalls certain known facts which will be used later in the thesis.Origin of the problem The models considered in this thesis have their origin in spin glass theory. Roughly, spin glass is a glassy state in a spin system or a disordered material exhibiting high magnetic frustration. The origin of this behavior can be either …

Biggers, Covella (Houchens), 1921-2022 (Sc 1610), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 1610. Three handwritten sermons by Episcopalian clergyman John Wesley Venable, and one early nineteenth-century ciphering book (unbound) executed by Burrell Adams.