Mathematics Commons^™

Tme Volume 8, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

Editorial: Opening 2011’S Journal Treasure Chest, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Vignette Of Doing Mathematics: A Meta-Cognitive Tour Of The Production Of Some Elementary Mathematics, Hyman Bass

The Mathematics Enthusiast

Mathematics educators, including some mathematicians, have, in various ways, urged that the school curriculum provide opportunities for learners to have some authentic experience of doing mathematics, opportunities to experience and develop the practices, dispositions, sensibilities, habits of mind characteristic of the generation of new mathematical knowledge and understanding – questioning, exploring, representing, conjecturing, consulting the literature, making connections, seeking proofs, proving, making aesthetic judgments, etc. (Polya 1954, Cuoco et al 2005, NCTM 2000 - Standard on Reasoning and Proof). While this inclination in curricular design has a certain appeal and merit, its curricular and instructional expressions are often contrived, or …

Transcriptions, Mathematical Cognition, And Epistemology, Wolff-Michael Roth, Alfredo Bautista

The Mathematics Enthusiast

The epistemologies researchers bring to their studies mediate not only their theories but also their methods, including what they select from their data sources to present the findings on which claims are based. Most articles reduce mathematical knowing to linguistic/mathematical structures, which, in the case of embodiment/enactivist theories, undermines the very argument about the special nature of mathematical knowing. The purpose of this study is to illustrate how different transcriptions of mathematics lessons are generally used to support different epistemologies of mathematical knowing/competence. As part of our third illustration, we provide embodiment/enactivist researchers with an innovative means of representing classroom …

Revisiting Tatjana Ehrenfest-Afanassjewa’S (1931) “Uebungensammlung Zu Einer Geometrischen Propädeuse”: A Translation And Interpretation, Klaus Hoechsmann

The Mathematics Enthusiast

No abstract provided.

New Perspectives On Identification And Fostering Mathematically Gifted Students: Matching Research And Practice, Viktor Freiman, Ali Rejali

The Mathematics Enthusiast

This special section of vol8,nos1&2 of The Montana Mathematics Enthusiast is a result of tremendous enthusiastic team work of many outstanding mathematics educators worldwide who are concerned with the issues related to mathematical giftedness and devoted to share with the international community their ideas, research results and best practices. The idea of the special issue on mathematical giftedness arose during the Topic Study Group 6 (TSG6) meeting at the 11th International Congress on Mathematics Education (ICME-11) in Monterrey, Mexico, in 2009 led by Viktor Freiman and Ali Rejali in collaboration with Mark Applebaum, Pablo Dartnell, and Arne Mogensen. More than …

Problem-Based Learning In Mathematics, Thomas C. O'Brien, Chris Wallach, Carla Mash-Duncan

The Mathematics Enthusiast

A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations, he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge and helps them to solve their problems with stimulating questions, he may give them a taste for, and some independent means of, independent thinking.

The Proficiency Challenge: An Action Research Program On Teaching Of Gifted Math Students In Grades 1-9, Arne Mogensen

The Mathematics Enthusiast

The paper describes design and outcome of a 3-year action research program on the teaching mathematics to gifted students in grades 1-9 in mixed ability classes in Denmark 2003- 2006. The intention was to combine ideas and experience of many teachers with theories and suggestions of researchers to test and develop useful recommendations for future teaching.

Modular And Graceful Edge Colorings Of Graphs, Ryan Jones

Dissertations

Abstract attached as separate file.

Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski

Dissertations

Abstract attached as separate file.

Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.

Normal And Δ-Normal Configurations In Toric Algebra, Liam Solus

Honors Papers

Toric algebra is a field of study that lies at the intersection of algebra, geometry, and combinatorics. Thus, the algebraic properties of the toric ideal IA defined by the vector configuration A are often characterizable via the geometric and combinatorial properties of its corresponding toric variety and A, respectively. Here, we focus on the property of normality of A. A normal vector configuration defines the toric ideal of a normal toric variety. However, the definition of normality of A is based entirely on the algebraic structures associated with A without regard to any of its combinatorial properties. In this paper, …

Optimal Summer Camp Layout, Anthony Bonifonte

Honors Papers

Convex optimization is an important branch of operations research. It generalizes linear programming and offers powerful tools for modelling problems and discovering optimal solutions to real world problems. Mathematically it is an interesting topic because it ties together many branches: linear algebra, multivariable calculus, and numerical analysis, to name a few. Modelling a problem as a convex optimization problem can be challenging but offers many benefits. Algorithm design is critically important to ensure precision of solutions that solve with minimal computation power. From an engineering perspective it is also incredibly useful, since many more situations can be modeled than with …

Equality Of P-Partition Generating Functions, Ryan Ward

Honors Theses

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko

Department of Math & Statistics Faculty Publications

Springer varieties are studied because their cohomology carries a natural action of the symmetric group S_n and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties X_n as subvarieties of the product of spheres (S²)ⁿ. We show that if X_n is embedded antipodally in (S²)ⁿ then the natural S_n-action on (S²)ⁿ induces an Sn-representation on the image of H_*(X_n). This representation is the Springer representation. Our construction admits an elementary (and geometrically …

Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …

Products Of Multiplication, Composition And Differentiation Between Weighted Bergman-Nevanlinna And Bloch-Type Spaces, Ajay K. Sharma

Turkish Journal of Mathematics

Let \varphi and \psi be holomorphic maps on D such that \varphi ( D ) \subset D . Let C_{\varphi} , M_{\psi} and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces A^{\beta}_N to Bloch-type spaces. In fact, we prove that these operators map A^{\beta}_N compactly into Bloch-type spaces if and only if they map A^{\beta}_N boundedly into these spaces.

Some Products Involving The Fourth Greek Letter Family Element \Tilde{\Delta}_S In The Adams Spectral Sequence, Xiu-Gui Liu, He Wang

Turkish Journal of Mathematics

Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E_2-term of the Adams spectral sequence, Ext_A^{\ast,\ast} (Z_p,Z_p). In this paper we prove that in the cohomology of A, the product k_0 h_n \tilde \delta _{s + 4} \in Ext_A^{s + 7, t(s,n) + s} (Z_p, Z_p), is nontrivial for n \geq 5, and trivial for n=3, 4, where \tilde\delta_{s + 4} is actually \tilde\alpha_{s + 4}^{(4)} described by Wang and Zheng, p \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p + (s + 3)p^2 + (s + 4)p^3 + p^n].

Pseudo Pq-Injective Modules, Zhanmin Zhu

Turkish Journal of Mathematics

A module M_R is called Pseudo PQ-injective (or PPQ-injective for short) if every monomorphism from a principal submodule of M to M extends to an endomorphism of M. Some characterizations and properties of this class of modules are investigated, PPQ-injective modules with some additional conditions are studied, semisimple artinian rings are characterized by PPQ-injective modules.

B. Y. Chen Inequalities For Submanifolds Of A Riemannian Manifold Of Quasi-Constant Curvature, Ci̇han Özgür

Turkish Journal of Mathematics

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

Top Generalized Local Cohomology Modules, Amir Mafi

Turkish Journal of Mathematics

Let (R,m) be a commutative Noetherian local ring and M, N two non-zero finitely generated R-modules with d(M)=n

Minimal And Symmetric Global Partition Polynomials For Reproducing Kernel Elements, Mario Jesus Juha

USF Tampa Graduate Theses and Dissertations

The Reproducing Kernel Element Method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker-δ property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This dissertation shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use in previous formulations of incomplete polynomials that are subsequently non-affine invariant. This dissertation lays out …

Problems In Classical Potential Theory With Applications To Mathematical Physics, Erik Lundberg

USF Tampa Graduate Theses and Dissertations

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.

Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).

Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is …

Parametric And Bayesian Modeling Of Reliability And Survival Analysis, Carlos A. Molinares

USF Tampa Graduate Theses and Dissertations

The objective of this study is to compare Bayesian and parametric approaches to determine the best for estimating reliability in complex systems. Determining reliability is particularly important in business and medical contexts. As expected, the Bayesian method showed the best results in assessing the reliability of systems.

In the first study, the Bayesian reliability function under the Higgins-Tsokos loss function using Jeffreys as its prior performs similarly as when the Bayesian reliability function is based on the squared-error loss. In addition, the Higgins-Tsokos loss function was found to be as robust as the squared-error loss function and slightly more efficient. …

Enumeration Of Inequivalent Cycle Decompositions, William J. Laffin

Dissertations, Master's Theses and Master's Reports - Open

A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n.

Parallel Algorithm For Solving Integer Linear Programs, David O. Torrey Jr.

Dissertations, Master's Theses and Master's Reports - Open

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for …

Neutrosophic Interpretation Of The Analects Of Confucius, Florentin Smarandache, Fu Yuhua

Branch Mathematics and Statistics Faculty and Staff Publications

This book is the companion volume of "Neutrosophic Interpretation of Tao Te Ching,” its purpose is to extend the foundation and application range of “The Analects of Confucius.” The reasons for this are as follows. Firstly, we are willing to point out that The Analects of Confucius already has some limitations, because many questions we are interested in cannot be answered within “The Analects of Confucius.” For example, The Analects of Confucius basically discussed the matters in China, however considering all possible situations it should matter in foreign countries as well, i.e. the “global village.” This was impossible in Confucian …

Covering Systems Of Polynomial Rings Over Finite Fields, Michael Wayne Azlin

Electronic Theses and Dissertations

In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n + k?” Examples of covering systems of the integers are presented along with some brief history and a sketch of the disproof by Erd?s. Open conjectures concerning covering systems and best known results of attempts to prove these conjectures are given. Analogies are drawn between the integers and Fq[x], and …

Asymptotics Of Carleman Polynomials For Level Curves Of The Inverse Of A Shifted Joukowsky Transformation, Michael Carr Northington

Electronic Theses and Dissertations

Let L be a level curve of the inverse of the shifted Joukowsky transformation w [special characters omitted] w − 1 + (w − 1) –1, that is, [special characters omitted]In this thesis we investigate the asymptotic properties of the sequence of polynomials that are orthonormal over the interior domain of L with respect to the area measure. We establish strong asymptotic formulas describing the behavior of these polynomials (as their degree increases) at every point of the complex plane.

Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden

Mathematics Faculty Publications

In this work we present some analytic and semi-analytic traveling wave solutions of a generalized Burgers' equation for unidirectional flow of power-law non-Newtonian fluids. The solutions include the corresponding well-known traveling wave solution of the Burgers' equation for Newtonian flows. We also derive estimates of shock thickness for the power-law flows.