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What Is A Number?, Nicholas Radley
What Is A Number?, Nicholas Radley
HON499 projects
This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.
Categories Of Residuated Lattices, Daniel Wesley Fussner
Categories Of Residuated Lattices, Daniel Wesley Fussner
Electronic Theses and Dissertations
We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on …
Logic -> Proof -> Rest, Maxwell Taylor
Logic -> Proof -> Rest, Maxwell Taylor
Senior Independent Study Theses
REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.
The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes
The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes
Electronic Theses and Dissertations
Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus FL. We denote by 𝖱𝖫𝑛 � the varieties of knotted residuated lattices. Examples of these knotted rules include integrality and contraction. The extension of �� by the rules corresponding to these two equations is …
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Williams Honors College, Honors Research Projects
In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.
A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan
A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan
Honors College Theses
Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.
Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks, John Douglas Butler
Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks, John Douglas Butler
Master's Theses, Dissertations, Graduate Research and Major Papers Overview
Describes students' attempts to solve nonroutine math problems and explores possible correlates of their performance, focusing on inattended (i.e., intentionally avoided) dimensions underrepresented in the literature, including attitudes, interests, values, aesthetics, metacognition, and representation. Analyzes objective and subjective data gathered from a sample of 9th-grade students at a high school in Rhode Island. Finds strong evidence of students' math-aesthetics in problem solving.