Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), 2023 Dordt University

#### Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

*Faculty Work Comprehensive List*

Reviewed Title: *Generations of Reason: A Family's Search for Meaning in Post-Newtonian England *by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Richard Whately's Revitalization Of Syllogistic Logic, 2023 Dordt University

#### Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma

*Faculty Work Comprehensive List*

This is an expanded version of the first chapter *Richard Whately’s Revitalization of Syllogistic Logic *in **Aristotle’s Syllogism and the Creation of Modern Logic** edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.

Self-Reference And Diagonalisation, 2023 Technische Universität Darmstadt

#### Self-Reference And Diagonalisation, Joël A. Doat

*Journal of Humanistic Mathematics*

This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox.

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, 2023 Benedictine University

#### Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

*Journal of Humanistic Mathematics*

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

Completeness Of Nominal Props, 2023 Runtime Verication Inc.

#### Completeness Of Nominal Props, Samuel Balco, Alexander Kurz

*Engineering Faculty Articles and Research*

We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.

(R1958) On Deferred Statistical Convergence Of Fuzzy Variables, 2022 Bartin University

#### (R1958) On Deferred Statistical Convergence Of Fuzzy Variables, Ömer Kişi, Mehmet Gürdal, Ekrem Savaş

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

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated.

(R1509) Topsis And Vikor Methods For Spherical Fuzzy Soft Set Aggregating Operator Framework, 2022 Saveetha Institute of Medical and Technical Sciences

#### (R1509) Topsis And Vikor Methods For Spherical Fuzzy Soft Set Aggregating Operator Framework, M. Palanikumar, K. Arulmozhi, Lejo J. Manavalan

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

The Spherical Fuzzy Soft (SFS) set is a generalization of the Pythagorean fuzzy soft set and the intuitionistic fuzzy soft set. We introduce the concept of aggregating SFS decision matrices based on aggregated operations. The techniques for order of preference by similarity to ideal solution (TOPSIS) and viekriterijumsko kompromisno rangiranje (VIKOR) for the SFS approaches are the strong points of multi criteria group decision making (MCGDM), which is various extensions of fuzzy soft sets. We define a score function based on aggregating TOPSIS and VIKOR methods to the SFS-positive and SFS-negative ideal solutions. The TOPSIS and VIKOR methods provide decision-making …

(R1500) Type-I Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, 2022 Annamalai University

#### (R1500) Type-I Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, M. Palanikumar, K. Arulmozhi

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

In the present communication, we introduce the concept of Type-I generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a Type-I generalized soft set model. We introduce a similarity measure based on the Type-I …

(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, 2022 PSG College of Technology

#### (Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan

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

In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.

Asymptotic Classes, Pseudofinite Cardinality And Dimension, 2022 The Graduate Center, City University of New York

#### Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel

*Dissertations, Theses, and Capstone Projects*

We explore the consequences of various model-theoretic tameness conditions upon the behavior of pseudofinite cardinality and dimension. We show that for pseudofinite theories which are either Morley Rank 1 or uncountably categorical, pseudofinite cardinality in ultraproducts satisfying such theories is highly well-behaved. On the other hand, it has been shown that pseudofinite dimension is not necessarily well-behaved in all ultraproducts of theories which are simple or supersimple; we extend such an observation by constructing simple and supersimple theories in which pseudofinite dimension is necessarily ill-behaved in all such ultraproducts. Additionally, we have novel results connecting various forms of asymptotic classes …

Unomaha Problem Of The Week (2021-2022 Edition), 2022 University of Nebraska at Omaha

#### Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

*UNO Student Research and Creative Activity Fair*

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

(R1956) Neutrosophic Soft E-Compact Spaces And Application Using Entropy Measure, 2022 Government Polytechnic College for Women, Annamalai University

#### (R1956) Neutrosophic Soft E-Compact Spaces And Application Using Entropy Measure, P. Revathi, K. Chitirakala, A. Vadivel

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

In this paper, the concept of neutrosophic soft e-compactness is presented on neutrosophic soft topological spaces using the definition of e-open cover and its types. In addition, neutrosophic soft e-compactness and neutrosophic soft e-separation axioms are associated. Also, the concept of neutrosophic soft locally e-compactness is introduced in neutrosophic soft topological spaces and some of its properties are discussed. Added to that, an application in decision making problem is given using entropy.

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 the …

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

#### 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 Scholars Collaborative Projects*

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 discussed as …

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 is …

The Algebra Of Type Unification, 2022 Bard College

#### The Algebra Of Type Unification, Verity James Scheel

*Senior Projects Spring 2022*

Type unification takes type inference a step further by allowing non-local flow of information. By exposing the algebraic structure of type unification, we obtain even more flexibility as well as clarity in the implementation. In particular, the main contribution is an explicit description of the arithmetic of universe levels and consistency of constraints of universe levels, with hints at how row types and general unification/subsumption can fit into the same framework of constraints. The compositional nature of the algebras involved ensure correctness and reduce arbitrariness: properties such as associativity mean that implementation details of type inference do not leak in …

(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 …

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 …