Exploring Mathematical Strategies For Finding Hidden Features In MultiDimensional Big Datasets, 2016 University of Houston
Exploring Mathematical Strategies For Finding Hidden Features In MultiDimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta
STAR (STEM Teacher and Researcher) Presentations
With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches ...
Mathematical Practice And Human Cognition, 2016 Indiana University  Purdue University Fort Wayne
Mathematical Practice And Human Cognition, Bernd Buldt
Philosophy Faculty Presentations
Frank Quinn (of JaffeQuinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following threepronged approach:

(i) sever as many ties to ordinary language as possible and limit ordinary language explanations ...
On Fixed Points, Diagonalization, And SelfReference, 2016 Indiana University  Purdue University Fort Wayne
On Fixed Points, Diagonalization, And SelfReference, Bernd Buldt
Philosophy Faculty Presentations
We clarify the respective role fixed points, diagonalization, and self reference play in proofs of G ̈odel’s first incompleteness theorem. We first show that the usual fixedpoint construction can be reduced to a double diagonalization; this is done to address widely held views such as that fixedpoint are “paradoxical” (Priest), or work by “black magic” (Soare), or that their construction is “intuitively unclear” (Kotlarski). We then discuss three notions of selfreference; this can be seen an extension of a recent study by Halbach and Visser and is meant to show that we do not (yet?) have a robust theory ...
Mathematical Practice And Human Cognition, 2016 Indiana University  Purdue University Fort Wayne
Mathematical Practice And Human Cognition, Bernd Buldt
Philosophy Faculty Presentations
Frank Quinn (of JaffeQuinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following threepronged approach:

(i) sever as many ties to ordinary language as possible and limit ordinary language explanations ...
Sentential Logic, 2016 CSU, San Bernardino
Sentential Logic, Tony Roy
Excerpted from the longer Roy, Symbolic Logic, including chapter 1 and just the first parts of chapters 2  7.
From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The ...
Symbolic Logic, 2016 CSU, San Bernardino
Symbolic Logic, Tony Roy
From the preface: There is, I think, a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. While courses in mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first course may also leave these untreated, and fail explicitly to lay down the definitions upon which the second course is based. The aim of this text is to integrate material from these courses and, in particular, to make serious mathematical logic ...
On Fixed Points, Diagonalization, And SelfReference, 2016 Indiana University  Purdue University Fort Wayne
On Fixed Points, Diagonalization, And SelfReference, Bernd Buldt
Philosophy Faculty Publications
We clarify the respective roles fixed points, diagonalization, and self reference play in proofs of Gödel’s first incompleteness theorem.
The Logic Of Uncertain Justifications, 2016 Kenyon College
The Logic Of Uncertain Justifications, Robert Milnikel
Robert Milnikel
No abstract provided.
The Logic Of Uncertain Justifications, 2016 Kenyon College
The Logic Of Uncertain Justifications, Robert Milnikel
Robert Milnikel
No abstract provided.
Conservativity For Logics Of Justified Belief: Two Approaches, 2016 Kenyon College
Conservativity For Logics Of Justified Belief: Two Approaches, Robert Milnikel
Robert Milnikel
No abstract provided.
Exploring Argumentation, Objectivity, And Bias: The Case Of Mathematical Infinity, 2016 University of Ontario Institute of Technology
Exploring Argumentation, Objectivity, And Bias: The Case Of Mathematical Infinity, Ami Mamolo
OSSA Conference Archive
This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece (e.g., Dubinsky et al., 2005). Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise (e.g., Brown et al., 2010; Fischbein et al., 1979, Tsamir, 1999). This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation as ...
On The Conjugacy Problem For Automorphisms Of Trees, 2016 Boise State University
On The Conjugacy Problem For Automorphisms Of Trees, Kyle Douglas Beserra
Boise State University Theses and Dissertations
In this thesis we identify the complexity of the conjugacy problem of automorphisms of regular trees. We expand on the results of Kechris, Louveau, and Friedman on the complexities of the isomorphism problem of classes of countable trees. We see in nearly all cases that the complexity of isomorphism of subtrees of a given regular countable tree is the same as the complexity of conjugacy of automorphisms of the same tree, though we present an example for which this does not hold.
On A MultipleChoice Guessing Game, 2016 Bethel College  Mishawaka
On A MultipleChoice Guessing Game, Ryan Cushman, Adam J. Hammett
The Research and Scholarship Symposium
We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a koption multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every mquestion algorithm which maximizes the probability ...
Constructing A Categorical Framework Of Metamathematical Comparison Between Deductive Systems Of Logic, 2016 Bard College
Constructing A Categorical Framework Of Metamathematical Comparison Between Deductive Systems Of Logic, Alex Gabriel Goodlad
Senior Projects Spring 2016
The topic of this paper in a broad phrase is “proof theory". It tries to theorize the general
notion of “proving" something using rigorous definitions, inspired by previous less general
theories. The purpose for being this general is to eventually establish a rigorous framework
that can bridge the gap when interrelating different logical systems, particularly ones
that have not been as well defined rigorously, such as sequent calculus. Even as far as
semantics go on more formally defined logic such as classic propositional logic, concepts
like “completeness" and “soundness" between the “semantic" and the “deductive system"
is too arbitrarily defined ...
A Generalization Of The Difference Of Slopes Test To Poisson Regression With ThreeWay Interaction, 2016 Marshall University
A Generalization Of The Difference Of Slopes Test To Poisson Regression With ThreeWay Interaction, Melinda Bierhals
Theses, Dissertations and Capstones
Linear regression models involving interaction can use the difference of slopes test to compare slopes for various situations. We will be generalizing this process to develop a procedure to compare rates in a Poisson regression model, allowing us to consider unbounded count data as opposed to continuous data. We will apply this process to an educational data set from a sample of students located in two different Los Angeles high schools. Our model will include a threeway interaction and address the following questions:
• Does language ability impact the relationship between math ability and attendance in the same way for males ...
Approximate Method For Solving The Linear Fuzzy Delay Differential Equations, 2015 Bharathiar University
Approximate Method For Solving The Linear Fuzzy Delay Differential Equations, Yookesh Lakshmanasamy
Yookesh Lakshmanasamy
The Strict Higher Grothendieck Integral, 2015 University of NebraskaLincoln
The Strict Higher Grothendieck Integral, Scott W. Dyer
Dissertations, Theses, and Student Research Papers in Mathematics
This thesis generalizes A. Grothendieck’s construction, denoted by an integral, of a fibered category from a contravariant pseudofunctor, to a construction for n and even ∞categories. Only strict higher categories are considered, the more difficult theory of weak higher categories being neglected. Using his axioms for a fibered category, Grothendieck produces a contravariant pseudofunctor from which the original fibered category can be reconstituted by integration. In applications, the integral is often most efficient, constructing the fibered category with its structure laid bare. The situation generalizes the external and internal definitions of the semidirect product in group theory: fibration is ...
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, 2015 Northern Michigan University
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar
Conference Presentations
Collaboration, if to occur successfully at all, needs to be based on careful representation and communication of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that a complete representation is not possible. This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We ...
Paratodo X: Una Introducción A La Lógica Formal, 2015 University at Albany, State University of New York
Paratodo X: Una Introducción A La Lógica Formal, P.D. Magnus
Philosophy Faculty Books
A translation of the logic textbook forall x (v 1.30) into Spanish. Translation by José Ángel Gascón.
Gödel’S Second Incompleteness Theorem, 2015 Indiana University  Purdue University Fort Wayne
Gödel’S Second Incompleteness Theorem, Bernd Buldt
Philosophy Faculty Presentations
Slides for the third tutorial on Gödel's incompleteness theorems, held at UniLog 5 Summer School, Istanbul, June 24, 2015