Physical Sciences and Mathematics Commons^™

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 …

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.

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, …

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 …

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 …

Tme Volume 6, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

Shadowing Chaos Via Optimization, Henrik Haakonsen

Mathematics, Statistics, and Computer Science Honors Projects

A prominent idea in the theory of chaos is that of shadowing, which says that, in many cases, the numerical results one sees after accuracy is lost are not total nonsense, but are in fact very close to the exact trajectory for an initial value that is near the one used. Using high-precision computation, I have researched the use of optimization as a way of finding exact shadows for several chaotic systems, such as the quadratic map r x (1 - x) and a billiard problem from the SIAM 100-Digit Challenge.

The Hidden Injuries Of Overloading 'Adt, Duane Buck, David J. Stucki

Mathematics Faculty Scholarship

The most commonly stated definition of abstract data type (ADT) is that it is a domain of values and the operations over that domain. So, for example, a language's built-in types, like int are seen to be ADTs. It is our opinion that a pure interpretation of this definition yields a semantics in which using an ADT is the same as using built-in types: the operations are side effect free and there is no concern over alias, shallow copy or synchronization problems. Unfortunately, the term abstract data type has over time been associated with at least three distinct meanings, and …

Reliability Goodness Of Fit For Oil Spills In The Gulf Of Mexico, William V. Harper, Thomas R. James, Ted G. Eschenbach

Mathematics Faculty Scholarship

Eschenbach and Harper (2006) analyzed offshore oil spills in the Gulf of Mexico with extensions to the northern seas of Alaska. This involved multiple methods including assessing what statistical distribution adequately fits the data. Empirical distribution function (EDF) statistical procedures are powerful goodness of fit tests and also provide for good visual assessments. The most powerful of the current EDF methods is the Anderson-Darling test. This paper focuses on the Anderson-Darling EDF goodness of fit procedure for both the two and three parameter Weibull distribution that is often used in reliability analysis. Excel VBA code has been developed to compute …

Multiplicative Riesz Decomposition On The Ring Of Matrices Over A Totally Ordered Field, Julio Cesar Urenda

Open Access Theses & Dissertations

The Riesz Decomposition Theorem for lattice ordered groups asserts that when G is an l-group and when a nonnegative element a is bounded by a product of nonnegative elements b1,...,bn, then a can be decomposed into a product of nonnegative elements b'1,...,b'n, i.e., a = b'1·...·b' n, with the property that b'i ≤ bi for any i = 1,...,n. In this work we characterize all nonnegative matrices for which this decomposition is possible with respect to matrix multiplication. In addition, we show that this result can be applied to ordered semigroups.

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.

The Maximum Of The Maximum Rectilinear Crossing Numbers Of D-Regular Graphs Of Order N, Matthew Alpert, Elie Feder, Heiko Harborth

Publications and Research

We extend known results regarding the maximum rectilinear crossing number of the cycle graph (Cn) and the complete graph (Kn ) to the class of general d-regular graphs Rn,d. We present the generalized star drawings of the d-regular graphs Sn,d of order n where n + d ≡ 1 (mod 2) and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of Sn,d for n ≡ d ≡ 0 (mod 2) is introduced and we conjecture that this drawing maximizes the maximum rectilinear crossing numbers, too. We offer a simpler proof of two results initially proved by …

The Orchard Crossing Number Of An Abstract Graph, Elie Feder, David Garber

Publications and Research

.We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple families of graphs. We also prove some properties of this crossing number.

Moreover, we define a variant of this crossing number which is tightly connected to the rectilinear crossing number, and compute it for some simple families of graphs.

Proceedings Of The Third Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 3rd Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents
• Letter from President

Development And Implementation Of High-Throughput Snp Genotyping In Barley, Timothy J. Close, Prasanna R. Bhat, Stefano Lonardi, Yonghui Wu, Nils Rostoks, Luke Ramsay, Arnis Druka, Nils Stein, Jan T. Svensson, Steve Wanamaker, Serdar Bozdag, Mikeal L. Roose, Matthew J. Moscou, Shiaoman Chao, Rajeev K. Varshney, Peter Szucs, Kazuhiro Sato, Patrick M. Hayes, David E. Matthews, Andris Kleinhofs, Gary J. Muehlbauer, Joseph Deyoung, David F. Marshall, Kavitha Madishetty, Raymond D. Fenton, Pascal Condamine, Andreas Graner, Robbie Waugh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High density genetic maps of plants have, nearly without exception, made use of marker datasets containing missing or questionable genotype calls derived from a variety of genic and non-genic or anonymous markers, and been presented as a single linear order of genetic loci for each linkage group. The consequences of missing or erroneous data include falsely separated markers, expansion of cM distances and incorrect marker order. These imperfections are amplified in consensus maps and problematic when fine resolution is critical including comparative genome analyses and map-based cloning. Here we provide a new paradigm, a high-density consensus genetic map of …

Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills

Department of Mathematical Sciences Faculty Publications

We provide the missing member of a family of four q-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in Identities of the Ramanujan-Slater type related to the moduli 18 and 24.

Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers. In this book the authors introduce the new notion of superbimatrices and generalize it to super trimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerized world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case …

Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich

Scholarship and Professional Work - LAS

We have noticed a certain kind of n-gon dissection into triangles that has a wonderful property of interest to most puzzlists. Namely that any two triangles have at least one edge in common yet no two triangles need be congruent. In an informal poll of specialists at a recent convention, none of them saw immediately how this could be accomplished. But in fact it is very straightforward.

Employing The Spectral Collocation Method In The Modeling Of Laminar Tube Flow Dynamics, Corey Michael Thibeault

All Graduate Theses, Dissertations, and Other Capstone Projects

The spectral collocation method is a numerical approximation technique that seeks the solution of a differential equation using a finite series of infinitely differentiable basis functions. This inherently global technique enjoys an exponential rate of convergence and has proven to be extremely effective in computational fluid dynamics. This paper presents a basic review of the spectral collocation method. The derivation is driven with an example of the approximation to the solution of a 1D Helmholtz equation. A Matlab code modeling two fluid dynamics problems is then given. First, the classic two-dimensional Graetz problem is simulated and compared to an analytical …

Teaching Statistics Must Be Adapted To Changing Circumstances: A Case Study From Hungarian Higher Education, Andras Komaromi

The Mathematics Enthusiast

Teaching statistics can bring up difficulties of various types for the teacher. Some of these are independent of the environment, i.e. they could occur at any place and time; some are specifically conditional on the surrounding circumstances. This paper presents an example for both of these kinds from the practice of two Hungarian teachers.

Superposition Formulas For Darboux Integrable Exterior Differential Sys-Tems, Ian M. Anderson, Mark E. Fels, Peter J. Vassiliou

Mathematics and Statistics Faculty Publications

In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original. The fact that a system can be written as a quotient can be used to find the general solution to these equations. Some examples are given to demonstrate the theory.

On C2 -Smooth Surfaces Of Constant Width, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

A number of results for C2 -smooth surfaces of constant width in Euclidean 3-space E 3 are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along its normal lines. We also give a characterization of surfaces of constant width that have rational support function. Our techniques, which are complex differential geometric in nature, allow us to construct explicit smooth surfaces of constant width in E 3 , and their focal sets. They also …

On Some Differential Equations, Mekki Terbeche, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

This paper investigates Cauchy and Goursat problems for partial differential operators. Successive approximation techniques for partial differential equations and the estimated results are employed to obtain the existence and the uniqueness of the solutions of such problems. An extended Darboux-Goursat-Beudon problem is studied.

Common Cyclic Vectors For Unitary Operators, William T. Ross, Warren R. Wogen

Department of Math & Statistics Faculty Publications

In this paper, we determine whether or not certain natural classes of unitary multiplication operators on L²(dƟ) have common cyclic vectors. For some classes which have common cyclic vectors, we obtain a classification of these vectors.

An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …

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 …

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 …

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.

Calculating Dependent Probabilities, Mike Fletcher

The Mathematics Enthusiast

In the 2004 European soccer competition France were one of the favourites to win the World Cup and Thierry Henry, their star forward, was one of the favourites to be top goal scorer. Bookkeepers were offering odds of 4 :1 on France winning the competition and odds of 8: 1 on Thierry Henry being the top scorer. A large number of punters went into betting shops in the United Kingdom and made a single bet that France would win the competition and that Thierry Henry would be top scorer. The counter clerks in the betting shops accepted the bets and …

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.