Mathematics Commons^™

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.

Practical Need For Algebraic (Equality-Type) Solutions Of Interval Equations And For Extended-Zero Solutions, Ludmila Dymova, Pavel Sevastjanov, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems in interval computations is solving systems of equations under interval uncertainty. Usually, interval computation packages consider united, tolerance, and control solutions. In this paper, we explain the practical need for algebraic (equality-type) solutions, when we look for solutions for which both sides are equal. In situations when such a solution is not possible, we provide a justification for extended-zero solutions, in which we ignore intervals of the type [−a, a].

Granular Approach To Data Processing Under Probabilistic Uncertainty, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, uncertainty can be naturally described as a combination of several components, components which are described by probabilistic, fuzzy, interval, etc. granules. In such situations, to process this uncertainty, it is often beneficial to take this granularity into account by processing these granules separately and then combining the results.

In this paper, we show that granular computing can help even in situations when there is no such natural decomposition into granules: namely, we can often speed up processing of uncertainty if we first (artificially) decompose the original uncertainty into appropriate granules.

International Baccalaureate Mathematics, Advanced Placement Mathematics, And Dual Credit Mathematics Courses – An In Depth Look, Lawrence Benjamin Jaskunas

All Capstone Projects

Every year in the United States, many students who believe they are fully prepared for college find out that they have to take remedial math courses before they can take any credit bearing math courses toward their degree. A student can avoid this situation by taking an early college program in high school and potentially earning a college math credit. The purpose of this research project was to take an in depth look at three such programs. The names of these programs are the International Baccalaureate program, the Advanced Placement program, and Dual Credit programs. This research project looked into …

Apex Calculus: Und Edition, Gregory Hartman, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free. …

Blow-Up Algebras, Determinantal Ideals, And Dedekind-Mertens-Like Formulas, Alberto Corso, Uwe Nagel, Sonja Petrović, Cornelia Yuen

Mathematics Faculty Publications

We investigate Rees algebras and special fiber rings obtained by blowing up specialized Ferrers ideals. This class of monomial ideals includes strongly stable monomial ideals generated in degree two and edge ideals of prominent classes of graphs. We identify the equations of these blow-up algebras. They generate determinantal ideals associated to subregions of a generic symmetric matrix, which may have holes. Exhibiting Gröbner bases for these ideals and using methods from Gorenstein liaison theory, we show that these determinantal rings are normal Cohen–Macaulay domains that are Koszul, that the initial ideals correspond to vertex decomposable simplicial complexes, and we determine …

Quantitative Skills And Reasoning (Armstrong), Patricia Brown, Joshua Lambert

Mathematics Grants Collections

This Grants Collection for Quantitative Skills and Reasoning was created under a Round Five ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

A Privacy Preserving Framework For Rfid Based Healthcare Systems, Farzana Rahman, Anwarul A. Bhuiyan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID (Radio Frequency IDentification) is anticipated to be a core technology that will be used in many practical applications of our life in near future. It has received considerable attention within the healthcare for almost a decade now. The technology’s promise to efficiently track hospital supplies, medical equipment, medications and patients is an attractive proposition to the healthcare industry. However, the prospect of wide spread use of RFID tags in the healthcare area has also triggered discussions regarding privacy, particularly because RFID data in transit may easily be intercepted and can be send to track its user (owner). In a …

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.

Complex Neutrosophic Graphs Of Type 1, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduced a new neutrosophic graphs called complex neutrosophic graphs of type1 (CNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of CNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1) and generalized single valued neutrosophic graphs of type 1 (GSVNG1).

Shortest Path Problem Under Trapezoidal Neutrosophic Information, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali

Branch Mathematics and Statistics Faculty and Staff Publications

In this research paper, a new approach is proposed for computing the shortest path length from source node to destination node in a neutrosophic environment. The edges of the network are assigned by trapezoidal fuzzy neutrosophic numbers. A numerical example is provided to show the performance of the proposed approach.

A Critical Path Problem Using Triangular Neutrosophic Number, Florentin Smarandache, Mai Mohamed, Yongquan Zhou, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision makers are only approximate, which gives rise of neutrosophic critical path problem. In this paper, the proposed method has been made to find the critical path in network diagram, whose activity time uncertain. The vague parameters in the network are represented by triangular neutrosophic numbers, instead of crisp numbers. At the end of paper, two illustrative examples are provided to validate the proposed approach.

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen

Mathematics Grants Collections

This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Foundations For College Algebra, Da'mon Andrews, Antre' Drummer

Mathematics Grants Collections

This Grants Collection for Biochemistry was created under a Round Seven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Ready, Set, Learn, Michael G. Wright

Masters Essays

No abstract provided.

Spaces Of Weakly Holomorphic Modular Forms In Level 52, Daniel Meade Adams

Theses and Dissertations

Let M^#_k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S^#_k(52) the subspace of forms which vanish at all cusps other than infinity. For these spaces we construct canonical bases, indexed by the order of vanishing at infinity. We prove that the coefficients of the canonical basis elements satisfy a duality property. Further, we give closed forms for the generating functions of these basis elements.

Weakly Holomorphic Modular Forms In Level 64, Christopher William Vander Wilt

Theses and Dissertations

Let M^#_k(64) be the space of weakly holomorphic modular forms in level 64 and weight k which can have poles only at infinity, and let S^#_k(64) be the subspace of M^#_k(64) consisting of forms which vanish at all cusps other than infinity. We explicitly construct canonical bases for these spaces and show that the coefficients of these basis elements satisfy Zagier duality. We also compute the generating function for the canonical basis.

Busemann G-Spaces, Cat(K) Curvature, And The Disjoint (0, N)-Cells Property, Clarke Alexander Safsten

Theses and Dissertations

A review of geodesics and Busemann G-spaces is given. Aleksandrov curvature and the disjoint (0, n)-cells property are defined. We show how these properties are applied to and strengthened in Busemann G-spaces. We examine the relationship between manifolds and Busemann G-spaces and prove that all Riemannian manifolds are Busemann G-spaces, though not all metric manifolds are Busemann G-spaces. We show how Busemann G-spaces that also have bounded Aleksandrov curvature admit local closest-point projections to geodesic segments. Finally, we expound local properties of Busemann G-spaces and define a new property which we call the symmetric property. We show that Busemann …

Discovering Calculus With The Ti-Nspire Cas Calculator, Meghan A. Nielsen

Masters Essays

No abstract provided.