Mathematical ontology the question of the mathematical source of objectivity

Dorrikhteh, Omid
This thesis traces the source of mathematical objectivity, as an approach to justify mathematical properties to be real, through how our mind and language were evolved. In the mirror of the indispensability argument, and the unreasonable effectiveness of mathematics, it will be argued that the reason why the world and the mind exhibit ontologically similar structures (and properties) is because they have the same ontological origin. Accordingly, it will be shown that (1) why/how that “the world and the mind have the same ontological origin” explains “the world and the mind exhibit ontologically similar structures (and properties)” And (2) to bring out the self-evidence of the sameness of the ontological origin.


Geometric invariant theory and Einstein-Weyl geometry
Kalafat, Mustafa (Elsevier BV, 2011-01-01)
In this article, we give a survey of geometric invariant theory for Toric Varieties, and present an application to the Einstein-Weyl geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP(1,1,2). We also find and classify all possible quotients. (C) 2011 Published by Elsevier GmbH.
Isomorphism classes of elliptic curves over finite fields of characteristic two
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Mathematics (2005)
In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphi...
Strictly singular operators and isomorphisms of Cartesian products of power series spaces
Djakov, PB; Onal, S; Terzioglu, T; Yurdakul, Murat Hayrettin (1998-01-02)
V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E-0(p)(a) x E-infinity(q) (b) where 1 less than or equal to p, q < infinity, p not equal q, a = (a(n))(n=1)(infinity) and b = (b(n))(n=1)(infinity) are sequences of positive numbers and E-0(p)(a), E(infinity)q(b) are respectively l(p)-finite and l(q)-infinite type...
Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes
Hatisaru, Vesife; Erbaş, Ayhan Kürşat (Springer Science and Business Media LLC, 2017-04-01)
The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers and students, follow-up interviews with teachers, and classroom observations. Findings indicated that teachers' MKT and students' learning outcomes were related to...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Citation Formats
O. Dorrikhteh, “Mathematical ontology the question of the mathematical source of objectivity,” Thesis (M.S.) -- Graduate School of Social Sciences. Philosophy., Middle East Technical University, 2019.