Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Mathematics (3)
- Neutrosophic logic (3)
- Book review (2)
- Cardinal Number (2)
- Consciousness (2)
-
- Epistemic Access (2)
- Euclid (2)
- Geometry (2)
- Hilbert space (2)
- Mathematical Object (2)
- Mathematical platonism (2)
- Philosophy (2)
- Philosophy of Mathematical Practice (2)
- Proof (2)
- Qualia (2)
- 1889-1951 (1)
- 18th-Century Algebraic Analysis (1)
- Adjoint (1)
- Algebra (1)
- Algebraic Version (1)
- Altruism (1)
- Analysis/ synthesis (1)
- Analytical Mechanic (1)
- And AntiStructure (1)
- Anthology (1)
- Archimedean Spiral (1)
- Arithmetic Progression (1)
- Aryabhata (1)
- Attractive Force (1)
- Begriffsschrift (1)
- Publication Year
Articles 31 - 48 of 48
Full-Text Articles in Other Mathematics
Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza
Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza
MPP Published Research
We follow two of the many paths leading from Newton’s to Euler’s scientific productions, and give an account of Euler’s role in the reception of some of Newton’s ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton’s conceptions within a new conceptual frame also influenced by Descartes’s views sand Leibniz’s formalism.
From Velocities To Fluxions, Marco Panza
From Velocities To Fluxions, Marco Panza
MPP Published Research
"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."
Oyun: A New, Free Program For Iterated Prisoner’S Dilemma Tournaments In The Classroom, Charles H. Pence, Lara Buchak
Oyun: A New, Free Program For Iterated Prisoner’S Dilemma Tournaments In The Classroom, Charles H. Pence, Lara Buchak
Faculty Publications
Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (oy-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner's dilemma tournaments, competitions between prisoner's dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, …
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza
MPP Published Research
We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …
Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives
Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives
MSS Finding Aids
Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.
Rethinking Geometrical Exactness, Marco Panza
Rethinking Geometrical Exactness, Marco Panza
MPP Published Research
A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in …
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
MPP Published Research
A review of Paolo Mancosu (ed.): The Philosophy of Mathematical Practice.
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
MPP Published Research
In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
MPP Published Research
"Both historians and philosophers of mathematics frequently speak of mathematical objects. Are they speaking of the same or of similar things? Better: are they appealing to the same notion or to similar notions?"
The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza
The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza
MPP Published Research
Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …
Techno-Art Of Selariu Supermathematics Functions, Florentin Smarandache
Techno-Art Of Selariu Supermathematics Functions, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this album we include the so called Super-Mathematics functions (SMF), which constitute the base for, most often, generating, technical, neo-geometrical objects, therefore less artistic. These functions are the results of 38 years of research, which began at University of Stuttgart in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in the References. The name was given by the regretted mathematician Professor Emeritus Doctor Engineer Gheorghe Silas who, at the presentation of the very first work in this domain, during the First National Conference of Vibrations in Machine Constructions, Timişoara, Romania, 1978, …
Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman
Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman
Branch Mathematics and Statistics Faculty and Staff Publications
Is there an absolute reality? Yes, “God” is the only absolute reality. The three main religions: Judaism, Christianity and Islam have all claimed that God is a supreme reality, and that all other creatures are finite beings. Since they relatively continue and also relatively change, so they can not be absolute. The world is full of paradoxes, there is no absolute persistence, and also there is no change at a stretch. There is no absolute truth and there is no continuous falsehood. What exist are many faces or aspects between the two terms. Those faces are reduced to a neutral …
François Viète, Between Analysis And Cryptanalysis, Marco Panza
François Viète, Between Analysis And Cryptanalysis, Marco Panza
MPP Published Research
François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same …
Some Sober Conceptions Of Mathematical Truth, Marco Panza
Some Sober Conceptions Of Mathematical Truth, Marco Panza
MPP Published Research
It is not sufficient to supply an instance of Tarski’s schema, ⌈“p” is true if and only if p⌉ for a certain statement in order to get a definition of truth for this statement and thus fix a truth-condition for it. A definition of the truth of a statement x of a language L is a bi-conditional whose two members are two statements of a meta-language L’. Tarski’s schema simply suggests that a definition of truth for a certain segment x of a language L consists in a statement of the form: ⌈v(x) is true if and only if τ(x)⌉, …
Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza
Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza
MPP Published Research
In this paper we investigate two problems concerning the theory of power series in 18th-century mathematics: the development of a given function into a power series and the inverse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular on the conception of a series as the result of a formal transformation of a function. After describing the procedures considered acceptable by 18th-century mathematicians, we examine in detail the different strategies—both direct and …
Mathematisation Of The Science Of Motion And The Birth Of Analytical Mechanics : A Historiographical Note, Marco Panza
Mathematisation Of The Science Of Motion And The Birth Of Analytical Mechanics : A Historiographical Note, Marco Panza
MPP Published Research
Usually, one speaks of mathematization of a natural or social science to mean that mathematics comes to be a tool of such a science: the language of mathematics is used to formulate its results, and/or some mathematical techniques is employed to obtain these results.
Dialectics And The Dao: On Both, A And Non-A In Neutrosophy And Chinese Philosophy, Feng Liu, Florentin Smarandache
Dialectics And The Dao: On Both, A And Non-A In Neutrosophy And Chinese Philosophy, Feng Liu, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper introduces readers to a new approach to dialectical logic: neutrosophy. Specifically it proposes a multi-valued logic in which the statement “both A and Non-A,” historically rejected as logically incoherent, is treated as meaningful. This unity of opposites constitutes both the objective world and the subjective world –a view with deep roots in Buddhism and Daoism, including the I-Ching. This leads in turn to the presentation of a framework for the development of a contradiction oriented learning philosophy inspired by the Later Trigrams of King Wen in the I-Ching. We show that although A and Non-A are logically inconsistent, …
La Révolution Scientifique, Les Révolutions, Et L'Histoire Des Sciences. Comment Ernest Coumet Nous A Libérés De L'Héritage D'Alexandre Koyré, Marco Panza
MPP Published Research
Dans son intervention au colloque Koyré (Paris, 1986), Ernest Coumet a suggéré que le terme «révolution scientifique» ne désigne pas chez Koyré un événement historique, mais un idéaltype, au sens de Max Weber. L'auteur discute d'abord cette thèse de Coumet et expose les arguments que ce dermier apporte pour la soutenir. Dans la deuxième partie de l'article, il critique l'usage de la notion de révolution en histoire des sciences, en s'opposant en particulier à la possibilité de distinguer dans les productions des savants une «pensée scientifique» qui serait influencée par la «pensée philosophique» et dont les bouleversements marqueraient l'avènement d'une …