Physical Sciences and Mathematics Commons^™

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 …

Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright

John B. Geddes

We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.

On The Utility Of I = √-1, Adam J. Hammett

Science and Mathematics Faculty Presentations

No abstract provided.

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. …

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. …

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.

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 …

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 …

An Examination Of The Yang-Baxter Equation, Alexandru Cibotarica

Master's Theses

The Yang-Baxter equation has been extensively studied due to its application in numerous fields of mathematics and physics. This thesis sets out to analyze the equation from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of characterizing the solutions of the Yang-Baxter equation.

We begin by examining the simple case of 22 matrices where it is possible to fully characterize the solutions. We connect the Yang-Baxter equation to the Cecioni-Frobenius Theorem and focus on obtaining solutions to the Yang-Baxter equation for special matrices where solutions are more easily found. Finally, …

Ball Remotality In Banach Spaces And Related Topics, Tanmoy Paul Dr.

Doctoral Theses

In this work we aim to study Ball Remotality and densely Ball Remotality of subspaces in Banach spaces. We study this property in many classical spaces of type c0, c,\\â„“p and C(K) where K is a compact Hausdorff space. The said problem also discussed for Banach spaces when considered as a subspace in its bidual. It is observed M-ideals in C(K) are densely ball remotal. It is shown that a particular type of M-ideal in A(K) where K is a Choquet simplex is densely ball remotal.

Parts Of The Whole: An Algebra Lesson, Dorothy Wallace

Numeracy

This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.

Reducing Math Anxiety: Findings From Incorporating Service Learning Into A Quantitative Reasoning Course At Seattle University, Allison Henrich, Kristi Lee

Numeracy

How might one teach mathematics to math-anxious students and at the same time reduce their math anxiety? This paper describes what we found when we incorporated a service learning component into a quantitative reasoning course at Seattle University in Fall 2010 (20 students) and Spring 2011 (28 students). The course is taken primarily by humanities majors, many of whom would not take a course in math if they didn’t need to satisfy the university’s core requirement. For the service learning component, each student met with and tutored children at local schools for 1-2 hours per week (total about 15 service …

Quantitative Literacy At Michigan State University, 2: Connection To Financial Literacy, Dennis Gilliland, Vince Melfi, Alla Sikorskii, Edward Corcoran, Eleanor Melfi

Numeracy

The lack of capability of making financial decisions has been recently described for the adult United States population. A concerted effort to increase awareness of this crisis, to improve education in quantitative and financial literacy, and to simplify financial decision-making processes is critical to the solution. This paper describes a study that was undertaken to explore the relationship between quantitative literacy and financial literacy for entering college freshmen. In summer 2010, incoming freshmen to Michigan State University were assessed. Well-tested financial literacy items and validated quantitative literacy assessment instruments were administered to 531 subjects. Logistic regression models were used to …

Quantitative Literacy At Michigan State University, 1: Development And Initial Evaluation Of The Assessment, Alla Sikorskii, Vince Melfi, Dennis Gilliland, Jennifer Kaplan, Suzie Ahn

Numeracy

Development, psychometric testing, and the results of the administration of a quantitative literacy (QL) assessment to undergraduate students are described. Three forms were developed covering a wide range of skills, contexts, and quantitative information presentation formats. Following item generation and revision based on preliminary testing and cognitive interviewing, a total of 3,701 consented undergraduate students at Michigan State University completed one of the three forms. Two of the forms contained 14 multiple-choice items, and one form contained 17 multiple-choice items. All forms were completed by students in less than 30 minutes. Evidence of validity and reliability were obtained for the …

A Leap Forward For Quantitative Literacy, H. L. Vacher

Numeracy

The Association of American College and Universities’ Learning Education and America’s Promise (LEAP) initiative has identified quantitative literacy (QL) as one of its Essential Learning Outcomes and classified it amongst five other Intellectual and Practical Skills such as inquiry and analysis, critical and creative thinking, and written and oral communication. This brings to mind a spreadsheet in which these transdisciplinary intellectual and practical skills are rows and academic disciplines are columns. With the view that the learning outcome QL is a row crossing mathematics and other disciplinary columns, this editorial considers how the papers in this and previous issues of …

Careers In Mathematics, Adam J. Hammett

Science and Mathematics Faculty Presentations

No abstract provided.

The Onset Of Oscillations In Microvascular Blood Flow, John B. Geddes, Russell T. Carr, Nathaniel J. Karst, Fan Wu

John B. Geddes

We explore the stability of equilibrium solution(s) of a simple model of microvascular blood flow in a two-node network. The model takes the form of convection equations for red blood cell concentration, and contains two important rheological effects—the Fåhræus–Lindqvist effect, which governs viscosity of blood flow in a single vessel, and the plasma skimming effect, which describes the separation of red blood cells at diverging nodes. We show that stability is governed by a linear system of integral equations, and we study the roots of the associated characteristic equation in detail. We demonstrate using a combination of analytical and numerical …

Pulse Dynamics In An Actively Mode-Locked Laser, John Geddes, Willie Firth, Kelly Black

John B. Geddes

We consider pulse formation dynamics in an actively mode-locked laser. We show that an amplitude-modulated laser is subject to large transient growth and we demonstrate that at threshold the transient growth is precisely the Petermann excess noise factor for a laser governed by a nonnormal operator. We also demonstrate an exact reduction from the governing PDEs to a low-dimensional system of ODEs for the parameters of an evolving pulse. A linearized version of these equations allows us to find analytical expressions for the transient growth below threshold. We also show that the nonlinear system collapses onto an appropriate fixed point, …

On The Sum Of Reciprocals Of Amicable Numbers, Jonathan Bayless, Dominic Klyve

Mathematics Faculty Scholarship

Two numbers m and n are considered amicable if the sum of their proper divisors,
s(n) and s(m), satisfy s(n) = m and s(m) = n. In 1981, Pomerance showed that
the sum of the reciprocals of all such numbers, P, is a constant. We obtain both a
lower and an upper bound on the value of P.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Geometric Invariants For A Class Of Semi-Fredholm Hilbert Modules., Shibananda Biswas Dr.

Doctoral Theses

One of the basic problem in the study of a Hilbert module H over the ring of polynomials C[z] := C[z1, . . . , zm] is to find unitary invariants (cf. [15,7]) for H. It is not always possible to find invariants that are complete and yet easy to compute. There are very few instances where a set of complete invariants have been identified. Examples are Hilbert modules over continuous functions (spectral theory of normal operator), contractive modules over the disc algebra (model theory for contractive operator) and Hilbert modules in the class Bn for a bounded domain C …

A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, Matthew Ciaffone

Honors Projects in Mathematics

Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through regression …

Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame

Honors Projects in Mathematics

This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon …

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

2011 Sonia Kovalevsky Math For Girls Day Flyer, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

2011 Sonia Kovalevsky Math For Girls Day Evaluation Forms, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Presenter, student and teacher evaluation forms for the 6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

A Census Of Vertices By Generations In Regular Tessellations Of The Plane, Alice Paul '12, Nicholas Pippenger

All HMC Faculty Publications and Research

We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q < 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation.

Teaching Statistics To Elementary Children: Using A Problem-Solving Approach To Enhance Learning, Kayla Lee Botelho

Honors Projects

When teaching statistics (or data analysis) to elementary children, it is beneficial to use a problem-solving approach that incorporates meaningful tasks to enhance the students' learning. This was determined through a careful review of literature, observations of elementary teachers, and the creation and instruction of data analysis unit. The unit required the students to collect data on heights, organize the data in charts, and display the data in line plots. In addition, the students analyzed the data to recalculate the average and other measures of central tendency and to answer questions that arose through the implementation of the lessons. In …

Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr.

Doctoral Theses

Motivated by the major role played by probabilistic models in many areas of science, several quantum (i.e. non-commutative) generalizations of classical probability have been attempted by a number of mathematicians. The pioneering works of K.R. Parthasarathy, L. Accardi, R.L. Hudson, P.A. Meyer and others led to the development of one such non-commutative model called ‘quantum probability’ which has a very rich theory of quantum stochastic calculus a la Hudson and Parthasarathy. Within the framework of quantum stochastic calculus, the ‘grand design’ that engages us is the canonical construction and study of ∗-homomorphic flows (jt)t≥0 on a given C ∗ or …

King, John (Sc 594), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.