Education Commons^™

The Convergence Of Two Algorithms For Compressed Sensing Based Tomography, Xiezhang Li, Jiehua Zhu

Department of Mathematical Sciences Faculty Publications

The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

Mathematics Educators And The “Math Wars”: Who Controls The Discourse?, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this editorial, the author expresses support of a colleague, Professor Jo Boaler of Stanford University, in her actions of going public with the harassment that she has experienced through professional and personal attacks by James Milgram of Stanford University and Wayne Bishop of California State University, Los Angeles.

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

Assessing The Structure Of Binghamton University's Emerging Leaders Program, Tyler D. Lenga

MPA Capstone Projects 2006 - 2015

The Emerging leaders Program (ELP) is a multi-faced student leadership program coordinated through Binghamton University's Office of New Student Programs and sponsored by the Division of Student Affairs. This capstone project was designed to assess the effectiveness of the 'leadership team" component of the ELP, as well as identify areas of improvement. The leadership team component of the ELP plays a large role in the program achieving its desired outcomes. Therefore, the program has identified this component as an area needing further performance evaluation.

Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang

Department of Mathematical Sciences Faculty Publications

The degree distance of a graph G is D'(G)=(1/2)∑ⁿ_i=1∑ⁿ_j=1(d_i+d_j)L_{i ,j}, where d_i and d_j are the degrees of vertices v_i, v_j ∈ V (G), and L_i,j is the distance between them. The Wiener index is defined as W(G)=(1/2)∑ⁿi₌₁ ∑ⁿ_j-1L_{i, j}. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that D'(T)=4W(T)-n(n-1)for a tree T with n vertices. In …

The Awards Project: Promoting Good Practices In Award Selection, Betty Mayfield, Francis Su

All HMC Faculty Publications and Research

Every year the MAA honors many members of our community with a wide variety of prizes, awards, and certificates for excellence in teaching, writing, scholarship, and service (see maa.org/awards). The winners exemplify our ideals as an association; consequently, they are often viewed as role models and leaders. So it is important to ask: Do these awards, as a whole, reflect the outstanding contributions of the breadth of association membership?

Commutative Rings Graded By Abelian Groups, Brian P. Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

Rings graded by Z and Z^d play a central role in algebraic geometry and commutative algebra, and the purpose of this thesis is to consider rings graded by any abelian group. A commutative ring is graded by an abelian group if the ring has a direct sum decomposition by additive subgroups of the ring indexed over the group, with the additional condition that multiplication in the ring is compatible with the group operation. In this thesis, we develop a theory of graded rings by defining analogues of familiar properties---such as chain conditions, dimension, and Cohen-Macaulayness. We then study the …

An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich

Department of Mathematics: Dissertations, Theses, and Student Research

In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson

Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis concerns three topics in commutative algebra:

1) The projective line over the integers (Chapter 2),

2) Prime ideals in two-dimensional quotients of mixed power series-polynomial rings (Chapter 3),

3) Fiber products and connected sums of local rings (Chapter 4),

In the first chapter we introduce basic terminology used in this thesis for all three topics.

In the second chapter we consider the partially ordered set (poset) of prime ideals of the projective line Proj(Z[h,k]) over the integers Z, and we interpret this poset as Spec(Z[x]) U Spec(Z[1/x]) with an appropriate identification. …

On The Brilliance Of Black Children: A Response To A Clarion Call, Erika Bullock, Maisie Gholson, Nathan Alexander

Middle-Secondary Education and Instructional Technology Faculty Publications

In this editorial, three dotoral students in Mathematics Education reflect on their experiences as conference organizers and co-editors of the Proceedings of the 2010 Philadelphia and 2011 Atlanta Bejamin Banneker Associaton Conferences.

Beyond The Numbers: A Benjamin Banneker Association Conference Series, Jacqueline Leonard, Erica R. Davila, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

The authors discuss how the "white male math myth" can be effectively debunked by conferences such as the Benjamin Banneker Association Beyond the Numbers conference series, which focus on urban mathematical education and highlight the achievements of black children.

The Weak Discrepancy And Linear Extension Diameter Of Grids And Other Posets, Katherine Victoria Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

A linear extension of a partially ordered set is simply a total ordering of the poset that is consistent with the original ordering. The linear extension diameter is a measure of how different two linear extensions could be, that is, the number of pairs of elements that are ordered differently by the two extensions. In this dissertation, we calculate the linear extension diameter of grids. This also gives us a nice characterization of the linear extensions that are the farthest from each other, and allows us to conclude that grids are diametrally reversing.

A linear extension of a poset might …

Generalized Diamond-Alpha Dynamic Opial Inequalities, Nuriye Atasever, Billûr Kaymakçalan, Goran Lesaja, Kenan Taş

Department of Mathematical Sciences Faculty Publications

We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob

Department of Mathematical Sciences Faculty Publications

Given a double complex X there are spectral sequences with the E₂ terms being either H_I (H_II(X)) or H_II(H_I(X)). But if H_I(X)=H_II(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with X. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we …

Formulæ For The Number Of Partitions Of N Into At Most M Parts (Using The Quazi-Polynomial Ansatz), Andrew Sills, Doron Zeilberger

Department of Mathematical Sciences Faculty Publications

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for p_m(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.

K-8 Preservice Teachers’ Inductive Reasoning In The Problem-Solving Contexts, Marta Magiera

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed.

The Mathematics Portfolio: An Alternative Tool To Evaluate Students’ Progress, Marla A. Sole

Publications and Research

This article describes the need for more thorough and varied forms of assessment to evaluate students’ level of understanding in mathematics. Portfolios are one type of assessment tool that, when added to a teacher’s repertoire can improve students’ comprehension and retention and enable students to monitor their own progress and to take more responsibility for their own learning. Portfolio assignments can also help students and teachers to detect and remedy weaknesses and misunderstandings and can increase students’ self-confidence in mathematics. This article discusses what a portfolio is, gives an example of a unit portfolio used in an undergraduate Finite Mathematics …

Generalized Borcea-Voisin Construction, Jimmy Dillies

Department of Mathematical Sciences Faculty Publications

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …

Combinatorics Using Computational Methods, Derrick Stolee

Department of Mathematics: Dissertations, Theses, and Student Research

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.

Lecture Hall Sequences, Q-Series, And Asymmetric Partition Identities, Sylvie Corteel, Carla D. Savage, Andrew Sills

Department of Mathematical Sciences Faculty Publications

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.

Undergraduate Students' Self-Reported Use Of Mathematics Textbooks, Aaron Weinberg, Emilie Wiesner, Bret Benesh, Timothy Boester

Mathematics Faculty Publications

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the …

What Mathematics Do Elementary Education Teachers Need To Know?, Bret Benesh

Forum Lectures

Almost no one is happy with the state of America's mathematics education. I examine the mathematics textbooks elementary education majors commonly use in college to determine what effect this might be having on their future elementary school students. In this Thursday Forum, I report on what I found in these textbooks---and why I do not like them. I then supply an alternative vision that would better serve our elementary school students.

Mathematical Competitions In Hungary: Promoting A Tradition Of Excellence & Creativity, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary has long been known for its outstanding production of mathematical talent. Extracurricular programs such as camps and competitions form a strong foundation within the Hungarian tradition. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. This study explores some of the recent developments in Hungarian mathematics competitions and the potential implications these changes have for the very competition-driven system that currently exists. The founding of so many new competitions reflects a possible shift in the focus and purpose of competitions away from …

Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

We investigate the length-biased inverse Weibull (LBIW) distribution, deriving its density function, hazard and reverse hazard functions, and reliability function. The moments, moment-generating function, Fisher information and Shannon entropy are also given. We discuss parameter estimation via the method of moments and maximum likelihood, and hypothesis testing for the LBIW and parent distributions.

Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai

Department of Mathematical Sciences Faculty Publications

This paper applies the class of weighted generalized beta distribution of the second kind (WGB2) as descriptive models for size distribution of income. The properties of WGB2 including mean, variance, coefficient of variation (CV), coefficient of skewness (CS), coefficient of kurtosis (CK) are presented. Other properties including top-sensitive index, bottom-sensitive index, mean logarithmic deviation (MLD) index and Theil index obtained from generalized entropy (GE) are applied in this paper. WGB2 proved to be in the generalized beta-F family of distributions, and maximum likelihood estimation (MLE) is used to obtain the parameter estimates. WGB2 is fitted to U.S. family income (2001-2009) …

Critical Pedagogy And Teaching Mathematics For Social Justice, David W. Stinson, Carla R. Bidwell, Ginny C. Powell

Middle-Secondary Education and Instructional Technology Faculty Publications

In this article, the authors explore critical pedagogy within the context of mathematics classrooms. The exploration demonstrates the evolving pedagogical practices of mathematics teachers when teaching mathematics is explicitly connected to issues of social justice. To frame the exploration, the authors provide brief overviews of the theoretical tenets of critical pedagogy and of teaching mathematics for social justice. Through using narrative and textual data, the authors illustrate how a graduate-level, critical theory and teaching mathematics for social justice course assisted, in part, in providing not only a new language but also a legitimization in teachers becoming critical mathematics pedagogues.

Transitioning Into Contemporary Theory: Critical Postmodern Theory In Mathematics Education Research, David W. Stinson, Erika Bullock

Middle-Secondary Education and Instructional Technology Faculty Publications

In this theoretical paper, the authors provide an overview of mathematics education as a research domain, identifying and briefly discussing four transitions or historical moments in mathematics education research. Using the Instructional Triangle as a point of reference for the dynamics of mathematics instruction, they illustrate how mathematics education researchers working in different moments explore different questions and use different theoretical perspectives. The authors then provide brief summaries of critical theory and postmodern theory, and suggest critical postmodern theory (CPT) as a hybrid theory that offers new possibilities for conceptualizing and conducting mathematics education research.

2011 Benjamin Banneker Association National Science Foundation Conference Program - Beyond The Numbers: The Brilliance Of Black Children In Mathematics, Benjamin Banneker Association

Middle-Secondary Education and Instructional Technology Faculty Publications

No abstract provided.

Ua94/6/9 Student / Alumni Personal Papers Wku Lena Annis, Wku Archives

WKU Archives Collection Inventories

Records created by and about Lena Annis. Series includes term papers and subject notebooks for English, Mathematics, Geography and Education. Also included are Class of 1931 reunion materials.