Mathematics Commons^™

Intelligent Algorithm For Trapezoidal Interval Valued Neutrosophic Network Analysis, Florentin Smarandache, Said Broumi, Deivanayagampillai Nagarajan, Malayalan Lathamaheswari, Mohamed Talea, Assia Bakali

Branch Mathematics and Statistics Faculty and Staff Publications

The shortest path problem has been one of the most fundamental practical problems in network analysis. One of the good algorithms is Bellman-Ford, which has been applied in network, for the last some years. Due to complexity in the decision-making process, the decision makers face complications to express their view and judgment with an exact number for single valued membership degrees under neutrosophic environment. Though the interval number is a special situation of the neutrosophic, it did not solve the shortest path problems in an absolute manner. Hence, in this work, the authors have introduced the score function and accuracy …

A Collocation Method Via The Quasi-Affine Biorthogonal Systems For Solving Weakly Singular Type Of Volterra-Fredholm Integral Equations, Mutaz Mohammad, Carlo Cattani

All Works

© 2020 Faculty of Engineering, Alexandria University Tight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many more. In this manuscript we provide a numerical solution of important weakly singular type of Volterra - Fredholm integral equations WSVFIEs using the collocation type quasi-affine biorthogonal method. We present a new computational method based on special B-spline tight framelets and use it to introduce our numerical scheme. The method provides …

Transitioning From The Abstract To The Concrete: Reasoning Algebraically, Andrea Lynn Martin

Graduate Theses/Dissertations

Why are students not making a smooth transition from arithmetic to algebra? The purpose of this study was to understand the nature of students’ algebraic reasoning through tasks involving generalizing. After students’ algebraic reasoning had been analyzed, the challenges they encountered while reasoning were analyzed. The data was collected through semi-structured interviews with six eighth grade students and analyzed by watching recorded interviews while tracking algebraic reasoning. Through data analysis of students’ algebraic reasoning, three themes emerged: 1) it was possible for students to reach stage two (informal abstraction) and have an abstract understanding of the mathematical pattern even if …

Embedding Parallelohedra Into Primitive Cubic Networks And Structural Automata Description, Mikhail M. Bouniaev, Sergey V. Krivovichev

School of Mathematical & Statistical Sciences Faculty Publications

The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists. The question of how many ways the embedding of a parallelohedron can …

Analyzing The Von Neumann Entropy Of Contact Networks, Thomas J. Brower

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

When modeling the spread of disease, ecologists use ecological or contact networks to model how species interact with their environment and one another. The structure of these networks can vary widely depending on the study, where the nodes of a network can be defined as individuals, groups, or locations among other things. With this wide range of definition and with the difficulty of collecting samples, it is difficult to capture every factor of every population. Thus ecologists are limited to creating smaller networks that both fit their budget as well as what is reasonable within the population of interest. With …

Methods In Modeling Wildlife Disease From Model Selection To Parameterization With Multi-Scale Data, Ian Mcgahan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The effects of emerging wildlife diseases are global and profound, resulting in loss of human life, economic and agricultural impacts, declines in wildlife populations, and ecological disturbance. The spread of wildlife diseases can be viewed as the result of two simultaneous processes: spatial spread of wildlife populations and disease spread through a population. For many diseases these processes happen at different timescales, which is reflected in available data. These data come in two flavors: high-frequency, high-resolution telemetry data (e.g. GPS collar) and low-frequency, low-resolution presence-absence disease data. The multi-scale nature of these data makes analysis of such systems challenging. Mathematical …

Universal Localizations Of Certain Noncommutative Rings, Tyler B. Bowles

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common theme throughout algebra is the extension of arithmetic systems to ones over which new equations can be solved. For instance, someone who knows only positive numbers might think that there is no solution to x + 3 = 0, yet later learns x = -3 to be a feasible solution. Likewise, when faced with the equation 2x = 3, someone familiar only with integers may declare that there is no solution, but may later learn that x = 3/2 is a reasonable answer. Many eventually learn that the extension of real numbers to complex numbers unlocks solutions …

Social Justice Mathematical Modeling For Teacher Preparation, Patrick L. Seegmiller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today's math teachers face significant social and political challenges for which they receive little preparation. Mathematics content courses can potentially provide additional preparation in this regard by providing future teachers with experiences to mathematically explore social justice issues. This provides them with opportunities to increase their awareness and sensitivity to social justice issues, develop greater empathy for their future students, and serve as examples for high quality instruction that they can emulate in their future careers. This dissertation recounts the development and revision of three social justice mathematical modeling projects, and shares evidence from student work samples of the ways …

The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond

Journal of Humanistic Mathematics

You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.

The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.

Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …

Numberlines: The Evil Triplets, Egan J. Chernoff, Nat Banting, Jay Wilson

Journal of Humanistic Mathematics

The purpose of this article is to further the recent introduction of numberlines. Number lines, still, yes, are a pictorial abstraction of the real numbers; numberlines, however, are hockey line nicknames based on jersey numbers. A discussion of numberlines, the recent playoff woes of the Tampa Bay Lightning, and the binary expansions of the jersey numbers worn by “The Triplets” (who play for The Bolts) culminates with a new nickname more befitting such a transcendent trio.

How To Measure A Coastline, Nora E. Culik

Journal of Humanistic Mathematics

The infinite shoreline of Lake Superior is embedded in the mathematical imagination, the memory of its stony beaches, and in the unifying consciousness that holds them all, just as the lake itself lies cradled in the land. The narrator of these paradoxes finds the lake, its border, and the calculi strewn along its shore a place a space between worlds where we rediscover that we can’t measure what we can’t locate, and can’t locate what we can’t measure, even the versions of ourselves.

Changes And Deltas, Jim Wolper

Journal of Humanistic Mathematics

Lecturing about Mathematics is like playing Jazz.

Hexagons, Barbara Quick

Journal of Humanistic Mathematics

No abstract provided.

Dear Arithmetic, Mary Soon Lee

Journal of Humanistic Mathematics

A short poem anthropomorphizing Arithmetic.

Four Seasons (Haikus), Stephen Luecking

Journal of Humanistic Mathematics

No abstract provided.

Natural By Design, Craig Steele

Journal of Humanistic Mathematics

I’m a professor in the Department of Biology and Health Sciences at Edinboro University, in Edinboro, Pennsylvania, a small, comprehensive liberal arts institution within the Pennsylvania State System of Higher Education. My major teaching duties involve environmental biology, zoology, and ichthyology. I emphasize to my students how mathematics underlies the natural world of plants and animals, pointing out to them how many of “our” most amazing engineering and constructional achievements are copied from nature (from geodesic domes to the fusiform bows of modern commercial ships), as well as how plant and animal physiology and animal behavior (of individuals and of …

Mental Logic: Two Poems, Ashley Delvento

Journal of Humanistic Mathematics

My submission is comprised of two poems that aim to intertwine mathematical themes with that of creative struggle, a working title for this pairing being “Mental Logic”. The first poem, ‘-ematics’ is a literary work created in the midst of mathematical problem solving. Being an avid writer and a mathematics enthusiast, the theme of this poem struck me while completing the University of Rochester Mathematics Olympiad. There seems to be a belief that literary creativity and mathematics cannot compliment one another, but throughout solving a probability problem on this Olympiad proved to be the ultimate moment of inspiration. This poem …

The Human Face Of Mathematics: Reuben Hersh (1927-2020) In Memoriam, Elena Anne Corie Marchisotto

Journal of Humanistic Mathematics

Reuben Hersh (1927-2020) celebrated mathematics as a human endeavor, historically evolved and intelligible only in a social context. It is therefore appropriate to remember him in the Journal of Humanistic Mathematics. There have been many tributes to Reuben, which commemorate his life and impressive mathematical and philosophical achievements. This memoriam to Reuben instead focuses on showing how his humanistic philosophy was so indicative of the person he was.

“All Of These Political Questions”: Anticommunism, Racism, And The Origin Of The Notices Of The American Mathematical Society, Michael J. Barany

Journal of Humanistic Mathematics

A recent controversy involving the Notices of the American Mathematical Society and questions of politics, racism, and the appropriate role of a professional mathematical organization began with a comparison to events the American Mathematical Society confronted in 1950. A close look at the AMS’s own archives for that period shows that the controversies that vexed the society around 1950 do indeed resonate strongly with those of today, but not in the ways recently suggested. Then, as now, the AMS confronted allegations of political and viewpoint discrimination in universities, the challenges of structural racism in American education and society, and the …

Pattern Blocks Art, Gunhan Caglayan

Journal of Humanistic Mathematics

Pattern blocks are versatile manipulatives facilitating connections that can be made among various strands of mathematics such as number sense, algebra, geometry and measurement, spatial reasoning, probability and trigonometry. This note focuses on an artistic interpretation of the pattern blocks with primary focus on convex polygons made with pattern blocks, and describes five mathematically rich activities using them.