Developing Critical Thinking Military Officers, 2022 Naval Postgraduate School

#### Developing Critical Thinking Military Officers, Thor Martinsen

*Mathematica Militaris*

Critical thinking is frequently identified as an important trait for military officers. This paper examines critical thinking from a historical, pedagogical, and warfighting perspective. The author uses his experience teaching mathematical reasoning at the Naval Postgraduate School to provide helpful advice for educators charged with teaching deductive and inductive reasoning. The paper argues that critical thinking should be taught early in an officer's career. It emphasizes a systematic and Socratic instructional approach along with the importance of equipping students with the necessary tools to evaluate problem-solving techniques and critique their associated solutions. Finally, the paper discusses Augmented Intelligence and ...

How To Guard An Art Gallery: A Simple Mathematical Problem, 2022 St. John Fisher College

#### How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

*The Review: A Journal of Undergraduate Student Research*

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊*n*/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with *n* walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph ...

Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, 2022 Belmont University

#### Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy

*Honors Theses*

This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be ...

Gödel's Incompleteness Theorems, 2022 Liberty University

#### Gödel's Incompleteness Theorems, Derick Swarey

*Senior Honors Theses*

The Incompleteness Theorems of Kurt Godel are very famous both within and outside of mathematics. They focus on independence and consistency within mathematics and hence a more thorough understanding of these is beneficial to their study. The proofs of the theorems involve many ideas which may be unfamiliar to many, including those of formal systems, Godel numbering, and recursive functions and relations. The arguments themselves mirror the Liar’s Paradox in that Godel constructs a statement asserting its own unprovability and then shows that such a statement and its negation must both be independent of the system, otherwise the system ...

(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, 2021 University of M’sila

#### (R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, Lemnaouar Zedam, Soheyb Milles, Abdelhamid Bennoui

*Applications and Applied Mathematics: An International Journal (AAM)*

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations ...

Introduction To Discrete Mathematics: An Oer For Ma-471, 2021 CUNY Queensborough Community College

#### Introduction To Discrete Mathematics: An Oer For Ma-471, Mathieu Sassolas

*Open Educational Resources*

The first objective of this book is to define and discuss the meaning of truth in mathematics. We explore **logics**, both propositional and first-order , and the construction of **proofs**, both formally and human-targeted. Using the proof tools, this book then explores some very fundamental definitions of mathematics through **set theory**. This theory is then put in practice in several applications. The particular (but quite widespread) case of **equivalence and order relations** is studied with detail. Then we introduces **sequences and proofs by induction**, followed by **number theory**. Finally, a small introduction to **combinatorics** is given.

Contributions To The Teaching And Learning Of Fluid Mechanics, 2021 Montclair State University

#### Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

*Department of Mathematics Facuty Scholarship and Creative Works*

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science and engineering ...

Negative Representability Degree Structures Of Linear Orders With Endomorphisms, 2021 National University of Uzbekistan

#### Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

The structure of partially ordered sets of degrees of negative representability of linear orders with endomorphisms is studied. For these structures, the existence of incomparable, maximum and minimum degrees, infinite chains and antichains is established,and also considered connections with the concepts of reducibility of enumerations, splittable degrees and positive representetions.

On The Generalization Of Interval Valued Fuzzy Generalized Bi-Ideals In Ordered Semigroups, 2021 Hazara University

#### On The Generalization Of Interval Valued Fuzzy Generalized Bi-Ideals In Ordered Semigroups, Muhammad S. Ali Khan, Saleem Abdullah, Kostaq Hila

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, a new general form than interval valued fuzzy generalized bi-ideals in ordered semigroups is introduced. The concept of interval valued fuzzy generalized bi-ideals is initiated and several properties and characterizations are provided. A condition for an interval valued fuzzy generalized bi-ideal to be an interval valued fuzzy generalized bi-ideal is obtained. Using implication operators and the notion of implication-based an interval valued fuzzy generalized bi-ideal, characterizations of an interval valued fuzzy generalized bi-ideal and an interval valued fuzzy generalized bi-ideal are considered.

Hamacher Operations Of Fermatean Fuzzy Matrices, 2021 Annamalai University

#### Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan

*Applications and Applied Mathematics: An International Journal (AAM)*

The purpose of this study is to extend the Fermatean fuzzy matrices to the theory of Hamacher operations. In this paper, the concept of Hamacher operations of Fermatean fuzzy matrices are introduced and some desirable properties of these operations, such as commutativity, idempotency, and monotonicity are discussed. Further, we prove DeMorgan’s laws over complement for these operations. Furthermore, the scalar multiplication and exponentiation operations of Fermatean fuzzy matrices are constructed and their algebraic properties are investigated. Finally, some properties of necessity and possibility operators of Fermatean fuzzy matrices are proved.

Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, 2021 Annamalai University

#### Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, Veerappan Chinnadurai, Albert Bobin

*Applications and Applied Mathematics: An International Journal (AAM)*

The primary focus of this manuscript comprises three sections. Initially, we introduce the concept of a simplified intuitionistic neutrosophic soft set. We impose an intuitionistic condition between the membership values of truth and falsity such that their sum does not exceed unity. Similarly, for indeterminacy, the membership value is a real number from the closed interval [0, 1]. Hence, the sum of membership values of truth, indeterminacy, and falsity does not exceed two. We present the notion of necessity, possibility, concentration, and dilation operators and establish some of its properties. Second, we define the similarity measure between two simplified intuitionistic ...

Applications Of Nonstandard Analysis In Probability And Measure Theory, 2021 Louisiana State University and Agricultural and Mechanical College

#### Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam

*LSU Doctoral Dissertations*

This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.

In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinite-dimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is ...

Zariski Geometries And Quantum Mechanics, 2021 Boise State University

#### Zariski Geometries And Quantum Mechanics, Milan Zanussi

*Boise State University Theses and Dissertations*

Model theory is the study of mathematical structures in terms of the logical relationships they define between their constituent objects. The logical relationships defined by these structures can be used to define topologies on the underlying sets. These topological structures will serve as a generalization of the notion of the Zariski topology from classical algebraic geometry. We will adapt properties and theorems from classical algebraic geometry to our topological structure setting. We will isolate a specific class of structures, called Zariski geometries, and demonstrate the main classification theorem of such structures. We will construct some Zariski structures where the classification ...

Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, 2021 King Abdullah University of Science and Technology

#### Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, David Keyes

*Mathematical Sciences Spring Lecture Series*

As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the ...

Lecture 00: Opening Remarks: 46th Spring Lecture Series, 2021 University of Arkansas, Fayetteville

#### Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman

*Mathematical Sciences Spring Lecture Series*

Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.

The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), 2021 University of New Mexico

#### The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez

*Mathematics and Statistics Faculty and Staff Publications*

Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión ...

Some Model Theory Of Free Groups, 2021 The Graduate Center, City University of New York

#### Some Model Theory Of Free Groups, Christopher James Natoli

*Dissertations, Theses, and Capstone Projects*

There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form A-Fraisse classes and that the class of non-abelian limit groups fails to form a strong A-Fraisse class.

The second main result is that if a countable group is elementarily ...

Mathematical Zendo: A Game Of Patterns And Logic, 2021 Westfield State University

#### Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

*Journal of Math Circles*

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce ...

Occam Manual, 2021 Portland State University

#### Occam Manual, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Occam is a Discrete Multivariate Modeling (DMM) tool based on the methodology of Reconstructability Analysis (RA). Its typical usage is for analysis of problems involving large numbers of discrete variables. *Models* are developed which consist of one or more *components*, which are then evaluated for their fit and statistical significance. Occam can search the lattice of all possible models, or can do detailed analysis on a specific model.

In *Variable-Based Modeling (VBM)*, model components are collections of variables. In *State-Based Modeling (SBM)*, components identify one or more specific states or substates.

Occam provides a web-based interface, which allows uploading a ...

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, 2021 Ateneo de Manila University

#### Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

*Mathematics Faculty Publications*

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the ...