Mathematics Commons^™

An A1 Function That Is Not In Lipα For Any Positive Α, Ryan Mullen

Mathematics Faculty Publications

Let A1 be the Banach algebra of all continuous functions on the torus whose Fourier coefficients are in 1, and let Lipα be the Banach algebra of all continuous function f on the torus such that ...

Adaptive Nonparametric Distribution-Free Procedures In Factorial Data Analysis, Richard Nzagong Ferim

Mathematics Dissertations - Archive

Many statisticians have questioned the basic assumptions about underlying models which might dominate the analysis of the data in many cases. The assumption of normality without much thought is of concern to a growing group of statisticians. If wrongly assumed, the assumption of normality can lead in serious flaws in the analysis of data. It therefore becomes important to consider distribution-free procedures that don't have to rely on the normality assumption. This is where the adaptive procedures come into play. When data is skewed or light tailed, these adaptive methods produce better results than the regular Wilcoxon and parametric methods. …

Toric Surface Codes And Minkowski Length Of Polygons, Ivan Soprunov, Jenya Soprunova

Mathematics and Statistics Faculty Publications

In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.

Algebraic Entropy For Abelian Groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, Paolo Zanardo

Articles

The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. Here we study the algebraic entropy of the endomorphisms of Abelian groups, introduced in 1965 by Adler, Konheim and McAndrew. The so-called Addition Theorem is proved; this expresses the algebraic entropy of an endomorphism $ \phi$ of a torsion group as the sum of the algebraic entropies of the restriction to a $ \phi$-invariant subgroup and of the endomorphism induced on the quotient group. Particular attention is paid to endomorphisms with zero algebraic entropy …

Daemon Decay And Inflation, Emil Prodanov

Articles

In 1971, Hawking suggested [1] that there may be a very large number of gravitationally collapsed charged objects of very low masses, formed as a result of fluctuations in the early Universe. A mass of of these objects could be accumulated at the centre of a star like the Sun. The masses of these collapsed objects are from and above and their charges are up to ±30 electron units [1].

The Wright Message, 2009, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2009 - 2010 Tenure-Stream Faculty
-- Mathematics Education Program
-- Project and Grants
-- Summer Research for UNI Math Students
-- Student Competitions
-- The Iowa Collegiate Mathematics Competition
-- TEAM News
-- Alliance Program
-- Two Endowment Funds
-- Mathematics Contribution Form
-- Mathematics Scholarship Funds
-- Applause and Congratulations!
-- Math Walk Challenge

To Publish Or Not To Publish?- That Is The (Editorial) Question, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

What Makes A “Good” Statistics Student And A “Good” Statistics Teacher In Service Courses?, Sue Gordon, Peter Petocz, Anna Reid

The Mathematics Enthusiast

Statistics is taught within a diverse array of disciplines and degree programs at university. In recent research we investigated international educators’ ideas about teaching and learning ‘service’ statistics. This paper investigates what these educators think are important attributes, knowledge and skills for learners and teachers of statistics. Results show that educators are in agreement about qualities of ‘good’ statistics students, such as curiosity and critical thinking. An emerging issue was the role mathematics plays in learning statistics as a service subject with some academics postulating mathematics as the basis of statistical learning, others proposing it has limited or little importance …

Students’ Conceptions About Probability And Accuracy, Ignacio Nemirovsky, Mónica Giuliano, Silvia Pérez, Sonia Concari, Aldo Sacerdoti, Marcelo Alvarez

The Mathematics Enthusiast

College students’ conceptions about probability and accuracy were explored. Both qualitative and quantitative analyses were done by means of two tests applied at two different moments. We show the results referring to the beliefs and conceptions about probability, margin for error, accuracy, certainty, truth and validity. Previous misconceptions about science may cause difficulties in the interpretation of scientific models. So, to find out students’ beliefs about science and technology, a Likert scale type test was made and presented to part of the sample. Although most of the people who answered the survey accredited the incidence of probability in the results …

Undergraduate Student Difficulties With Independent And Mutually Exclusive Events Concepts, Adriana D'Amelio

The Mathematics Enthusiast

The concepts of disjunctive events and independent events are didactical ideas that are used widely in the classroom. Previous observations of attitudes in assessments given to students at university level who attended the introductory Statistics course helped to detect the confusion between disjunctive and independent events, and indicate the spontaneous ideas that students tend to elaborate about both concepts in different situations in which these appear. However the didactical relation between these ideas and their formal definitions is not known in detail. In this work, we analyze students’ misconceptions, their persistence, and the process by which the student confronts his …

For The Rest Of Your Life, Mike Fletcher

The Mathematics Enthusiast

‘For the Rest of Your Life’ is a new TV game show. Contestants play to win money every month. This can be for as little as one month or, if every one of their guesses is correct, for the rest of their lives.

Learning, Participation And Local School Mathematics Practice, Cristina Frade, Konstantinos Tatsis

The Mathematics Enthusiast

This paper reports on a study whose aim was to examine students’ learning in terms of participation in collective mathematical discussions. Our basic theoretical assumptions are based on a combination of situated learning perspectives and a framework that links social and psychological approaches of mathematical activity and learning. The research was carried out in a Year-8 classroom (students were aged 12 to 13), and the mathematical subject under investigation was area measurement. Data are presented to illustrate possible correspondences between ‘signs’ of learning and ‘local’ changes of participation. We conclude by discussing some pedagogical implications resulting from the study.

If A.B = 0 Then A = 0 Or B = 0?, Cristina Ochoviet, Asuman Oktaç

The Mathematics Enthusiast

We present a study carried out in Uruguay, with secondary school students and tertiary level mathematics students, concerning the zero-product property. In our research we observed that when early secondary and late secondary school students have to solve equations of the form (ax + b)(cx + d) = 0, they do not always apply the property, even when it is the only available tool and have received specific instruction on its application to the resolution of equations of this type. We also detected an error that students make when they have to verify the solutions of this type of equations. …

The Origins Of The Genus Concept In Quadratic Forms, Mark Beintema, Azar Khosravani

The Mathematics Enthusiast

We present an elementary exposition of genus theory for integral binary quadratic forms, placed in a historical context.

The Impact Of Undergraduate Mathematics Courses On College Student’S Geometric Reasoning Stages, Nuh Aydin, Erdogan Halat

The Mathematics Enthusiast

The purpose of this study is to investigate possible effects of different college level mathematics courses on college students’ van Hiele levels of geometric understanding. Particularly, since logical reasoning is an important aspect of geometric understanding, it would be interesting to see whether there are differences in van Hiele levels of students who have taken non-geometry courses that emphasize or focus on logic and proofs (Category I) and those that don’t (Category II). We compared geometric reasoning stages of students from the two categories. One hundred and forty nine college students taking various courses from the two categories have been …

Elementary School Pre-Service Teachers’ Understandings Of Algebraic Generalizations, Jean E. Hallagan, Audrey C. Rule, Lynn F. Carlson

The Mathematics Enthusiast

It is critical for all students to learn algebra, including the ability to generalize, to function in our increasingly complex world. This pretest/intervention/posttest study of preservice elementary teachers (N = 63) in their math methods course assessed their knowledge of writing and applying algebraic generalizations using instructor-made rubrics along with analysis of work samples and reported insights. Initially, although most subjects could solve a specific case, they had considerable difficulty determining an algebraic rule. After a problemsolving- based teaching intervention, students improved in their ability to generalize, however, they encountered more difficulty with determining the algebraic generalization for items arranged …

A Longitudinal Study Of Student’S Representations For Division Of Fractions, Sylvia Bulgar

The Mathematics Enthusiast

The representations that students use as part of their mathematical problem solving can provide us with a window into their grasp of the concepts they are exploring and developing. In this paper, the author indicates how these representations can evolve over time and enrich the understanding of division of fractions, often thought to be the most difficult of elementary school mathematical topics. The results of this research suggest that when appropriate problems are provided for students, in a meaningful context, they can demonstrate understanding of division of fractions that is durable over time, and that they are able to flexibly …

Catch Me If You Can!, Steve Humble

The Mathematics Enthusiast

Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individuals understanding of the subject.

The three activities described in this article can all be used outside the classroom in a maths lesson. Teaching mathematical concepts in this way engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can occur in the classroom. By taking maths beyond the classroom, we can more clearly illustrate the connections between the real world and what they are studying …

Fostering Connections Between The Verbal, Algebraic, And Geometric Representations Of Basic Planar Curves For Student’S Success In The Study Of Mathematics, Margo F. Kondratieva, Oana G. Radu

The Mathematics Enthusiast

We discuss the significance of making connections between the verbal, algebraic, and geometric representations of basic mathematical objects for students’ understanding of mathematical instructions. Our survey of 499 students enrolled in a precalculus university course reveals that such connections are not always present, even if the objects themselves are familiar to the students. We stress that the ability of making these connections needs to be specifically addressed in teaching mathematics at various levels. A proper attention to the matter contributes to the formation of students’ mathematical background, which makes a difference for their success in study of calculus, in particular.

How To Increase Mathematical Creativity- An Experiment, Kai Brunkalla

The Mathematics Enthusiast

Creativity is an integral part of mathematics. In this article I examine the increase in awareness of creativity in mathematics using Fröbel’s blocks in a college classroom. A majority of students found the introduction of the “gifts” of the founder of Kindergarten to a college geometry classroom enhancing their interest in mathematics. They judged the wooden blocks helpful in their understanding of geometry. The students showed increased awareness of creativity in mathematics.

Korean Teachers’ Perceptions Of Student Success In Mathematics: Concept Versus Procedure, Insook Chung

The Mathematics Enthusiast

This article examines the Korean classroom teachers’ beliefs about mathematics education in elementary schools. Their perceptions about contributing factors to Korean students’ high achievement scores in international comparative studies in the area of mathematics are explored. Elementary classroom teachers were surveyed using the researchermade questionnaire (Teacher Perception about Mathematics Curriculum) and 141 teachers completed the questionnaire. The data collected was analyzed by a descriptive analysis. The results reveal that the majority of classroom teachers agreed that real life applications, processing skills, using concrete instructional manipulatives, and conceptual knowledge are very important in teaching children mathematics. Most of teachers participating in …

Book X Of The Elements: Ordering Irrationals, Jade Roskam

The Mathematics Enthusiast

Book X from The Elements contains more than three times the number of propositions in any of the other Books of Euclid. With length as a factor, anyone attempting to understand Euclidean geometry may be hoping for a manageable subject matter, something comparable to Book VII’s investigation of number theory. They are instead faced with a dizzying array of new terminology aimed at the understanding of irrational magnitudes without a numerical analogue to aid understanding. The true beauty of Book X is seen in its systematic examination and labeling of irrational lines. This paper investigates the early theory of irrationals, …

Tme Volume 6, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

A Note On The Application Of Ec2sls And Ec3sls Estimators In Panel Data Models, Badi H. Baltagi, Long Liu

Center for Policy Research

Baltagi and Li (1992) showed that for estimating a single equation in a simultaneous panel data model, EC2SLS has more instruments than G2SLS. Although these extra instruments are redundant in White (1986) terminology, they may yield different estimates and standard errors in empirical studies with finite N and T. We illustrate this using the crime data of Cornwell and Trumbull (1994). We show that the standard errors of EC2SLS are smaller than those of G2SLS for this example. In general, we prove that the asymptotic variance of G2SLS differs from that of EC2SLS by a positive semi-definite matrix. Although this …

Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk.

Topology And Infinite Graphs, Nicholas Blackburn Lowery

Honors Papers

The main focus of this paper will be on two very different areas in which topology is relevant to the study of infinite graphs. The first is the mechanics of compactness proofs, which use a particular group of lemmas to extend results about finite subgraphs to apply to an entire infinite graph. We will explore these results by using them to prove a result of de Bruijn and Erdos, that an infinite graph is k-colorable if its finite subgraphs are k-colorable, in several different ways.

The second area is a relatively new area of study pioneered by Diestel which redefines …

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …

Rook Polynomials In Higher Dimensions, Nicholas Krzywonos, Feryal Alayont

Student Summer Scholars Manuscripts

A rook polynomial counts the number of placements of non-attacking rooks on a board. In this paper we describe generalizations of the definition and properties of rook polynomials to "boards" in three and higher dimensions. We also defefine generalizations of special two dimensional boards to three dimensions, including the triangle board and the board representing the probleme des rencontres. The number of rook placements on these three dimensional families of rook boards are shown to be related to famous number sequences, such as central factorial numbers, the number of Latin rectangles and the Genocchi numbers.

Gas-Kinetic Schemes For Direct Numerical Simulations Of Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Reλ =72.0 and the turbulence Mach number Ma_t between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K (t), the dissipation rate ε (t), …