Mathematics Commons^™

Numeracy, Financial Literacy, And Financial Decision-Making, Annamaria Lusardi

Numeracy

Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for …

The Joy Of Quantitative Reasoning, Caren Diefenderfer

Numeracy

One of the advantages of focusing on quantitative reasoning is that it spans a wide variety of topics. As incoming president of the National Numeracy Network, I would like to take the opportunity of this editorial to tell my story of intellectual reward from finding common purpose in quantitative reasoning with colleagues from disciplines outside of mathematics. The story starts with an NSF-funded faculty development project (DUE-9952807) to further a QR across-the-curriculum program and the finding from that program that merging authentic context with mathematics brings interaction and collaboration. That joy in learning from and working with colleagues in other …

What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan

Pomona Faculty Publications and Research

Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …

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.

In Defense Of Frivolous Questions, Gizem Karaali

Pomona Faculty Publications and Research

Is there any reason for today's academic institutions to encourage the pursuit of answers to seemingly frivolous questions? The opinionated business leader who does not give a darn about your typical liberal arts classes "because they do not prepare today’s students for tomorrow's work force" might snicker knowingly here: Have you seen some of the ridiculous titles of the courses offered by the English / literature / history / (fill in the blank) studies department in the University of So-And-So? Why should any student take "Basketweaving in the Andes during the Peloponnesian Wars"? Just what would anyone gain from …

Humanistic Mathematics: An Oxymoron?, Gizem Karaali

Pomona Faculty Publications and Research

Mathematics faculty are trained as mathematicians, first and foremost. If we did not experience the soul-expanding possibilities of liberal education during our own undergraduate years, we may hesitate to bridge disciplinary divides when pursuing our core human need to inquire and understand. Although most mathematicians I know are amazing teachers, communicators, and mentors, many still teach the same material that their professors and their professors’ professors taught. This time-tested approach can be powerful, fascinating, and even quite entertaining. But it can also seem far removed from the world we inhabit. Yes, we teach “real world applications” of mathematical concepts. Yet …

"Our Research Was Centered On Whether Or Not The Following Changes Made To The Pre-Calculus Algebra Class Positively Affected Student Performance…", Andrea Winchester

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Math Department Newsletter, 2011-2012 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

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 …

Cotorsion Pairs In C(R-Mod), Diego Bravo, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada

Mathematical Sciences: Faculty Publications

In [8] Salce introduced the notion of a co-torsion pair (A, B) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C, D)in the category C(R-Mod) of complexes of left R-modules over some ring R.If(C, D) is such a pair, and if C is closed un-der taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(R-Mod), then the embedding functors K(C) → K(R-Mod) and …

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

Mathematical Sciences: Faculty Publications

In this paper, a new class of weighted generalized beta distribution of the second kind (WGB2) is presented. The construction makes use of the "conservability approach" which includes the size or length-biased distribution as a special case. The class of WGB2 is used as descriptive models for the distribution of income. The results that are presented generalizes the generalized beta distribution of second kind (GB2). The properties of these distributions including behavior of hazard functions, moments, variance, coefficients of variation, skewness and kurtosis are obtained. The moments of other weighted distributions that are related to WGB2 are obtained. Other important …

Supporting Implementation Of The Common Core State Standards For Mathematics: Recommendations For Professional Development, Paola Sztajn, Karen A. Marrongelle, Peg Smith, Bonnie L. Melton

Mathematics and Statistics Faculty Publications and Presentations

In 2010, the National Governor’s Association and the Council of Chief State School Officers published the Common Core State Standards for Mathematics (CCSSM) and to date, 44 states, the District of Columbia, and the U.S. Virgin Islands have adopted the document. These content and practice standards, which specify what students are expected to understand and be able to do in K-12 mathematics, represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable …

The Wright Message, 2012-2013, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Department Head
-- Around Wright Hall
-- 2012 - 2013 Tenure-Stream Faculty
-- New Faculty
-- Retiring Faculty: Larry Leutzinger
-- In Memory of Bonnie Litwiller
-- John & Marla Peterson: Making an Impact
-- The 2012 Hari Shankar Lecture
-- Internal UNI Awards
-- Projects and Grants
-- Student Spotlight: Melinda McDowell & Duncan Wright
-- Recent winners of the Purple and Old Gold Award
-- Alumni Spotlight: Karla Digmann, Kamilla Svajgl, & Suzanne Shontz
-- Math Day 2012
-- Squigonometry
-- Student Organizations
-- News from KME
-- …

Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions, Xueheng Shi, Broderick O. Oluyede, Marvis Pararai

Mathematical Sciences: Faculty Publications

In this paper, a new class of weighted generalization of the Rayleigh distribution is constructed and studied. The statistical properties of these distributions including the behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coecient of variation, coecient of skewness, coecient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions are also presented.

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

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.

On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies

Mathematical Sciences: Faculty Publications

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.

Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić

Mathematical Sciences: Faculty Publications

In this paper we consider an Infeasible Full Newton-step Interior-Point Method (IFNS-IPM) for monotone Linear Complementarity Problems (LCP). The method does not require a strictly feasible starting point. In addition, the method avoids calculation of the step size and instead takes full Newton-steps at each iteration. Iterates are kept close to the central path by suitable choice of parameters. The algorithm is globally convergent and the iteration bound matches the best known iteration bound for these types of methods.

Structure Of Colored Complete Graphs Free Of Proper Cycles, Vincent E. Coll, Colton Magnant, Kathleen Ryan

Mathematical Sciences: Faculty Publications

For a fixed integer m, we consider edge colorings of complete graphs which contain no properly edge colored cycle Cm as a subgraph. Within colorings free of these subgraphs, we establish global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of smaller cycles, namely C4,C5, and C6, we show that our bounds are sharp.

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

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) …

Estimating Population Exposure To Fine Particulate Matter In The Conterminous U.S. Using Shape Function-Based Spatiotemporal Interpolation Method: A County Level Analysis, Lixin Li, Xingyou Zhang, James B. Holt, Jie Tian, Reinhard Piltner

Mathematical Sciences: Faculty Publications

This paper investigates spatiotemporal interpolation methods for the application of air pollution assessment. The air pollutant of interest in this paper is fine particulate matter PM_2.5. The choice of the time scale is investigated when applying the shape function-based method. It is found that the measurement scale of the time dimension has an impact on the quality of interpolation results. Based upon the result of 10-fold cross validation, the most effective time scale out of four experimental ones was selected for the PM_2.5 interpolation. The paper also estimates the population exposure to the ambient air pollution of …

The New Publishing Scene And The Tenure Case: An Administrator’S View, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

No abstract provided.

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 …

Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee

Publications & Research

This presentation discusses the need to develop high quality performance based assessments of the Common Core Mathematical Standards and Mathematical Practices. Several examples of performance assessments from high achieving countries as well as from the 2009 PISA test are included.

Compositions, Partitions, And Fibonacci Numbers, Andrew Sills

Mathematical Sciences: Faculty Publications

A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n+ 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.

Multiplicative Noise For Masking Numerical Microdata Data With Constraints, Anna Oganian

Mathematical Sciences: Faculty Publications

Before releasing databases which contain sensitive information about individuals, statistical agencies have to apply Statistical Disclosure Limitation (SDL) methods to such data. The goal of these methods is to minimize the risk of disclosure of the confidential information and at the same time provide legitimate data users with accurate information about the population of interest. SDL methods applicable to the microdata (i. e. collection of individual records) are often called masking methods. In this paper, several multiplicative noise masking schemes are presented. These schemes are designed to preserve positivity and inequality constraints in the data together with the vector of …

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

On Doing Mathematics, Sue Vanhattum

Journal of Humanistic Mathematics

Who is a mathematician? What does it mean to do mathematics? I discuss my process in solving a math problem, and what it meant to me.

Covariant Representations Of C*-Dynamical Systems Involving Compact Groups, Firuz Kamalov

Department of Mathematics: Dissertations, Theses, and Student Research

Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A x _σG encodes the action of G on A. By the universal property of A x _σG there exists a one to one correspondence between the set all covariant representations of the system (A, G, σ) and the set of all *-representations of A x _σG. Therefore, the study of representations of A x _σG is equivalent to that of covariant representations of (A, G, σ).

We study induced covariant representations of systems involving compact groups. We prove that every irreducible (resp. factor) covariant …

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 …