scholarly journals L’infini entre deux bouts. Dualités, univers algébriques, esquisses, diagrammes

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
René Guitart
Keyword(s):  
Set Theory ◽  
Mathematical Theory ◽  
Mathematical Thinking ◽  
Mathematical Work ◽  
Mathematical Activity ◽  
Actual Infinity ◽  
Zeno's Paradoxes ◽  
Mathematical Problems ◽  
Technical Details ◽  
The One

The article affixes a resolutely structuralist view to Alain Badiou’s proposals on the infinite, around the theory of sets. Structuralism is not what is often criticized, to administer mathematical theories, imitating rather more or less philosophical problems. It is rather an attitude in mathematical thinking proper, consisting in solving mathematical problems by structuring data, despite the questions as to foundation. It is the mathematical theory of categories that supports this attitude, thus focusing on the functioning of mathematical work. From this perspective, the thought of infinity will be grasped as that of mathematical work itself, which consists in the deployment of dualities, where it begins the question of the discrete and the continuous, Zeno’s paradoxes. It is, in our opinion, in the interval of each duality ― “between two ends”, as our title states ― that infinity is at work. This is confronted with the idea that mathematics produces theories of infinity, infinitesimal calculus or set theory, which is also true. But these theories only give us a grasp of the question of infinity if we put ourselves into them, if we practice them; then it is indeed mathematical activity itself that represents infinity, which presents it to thought. We show that tools such as algebraic universes, sketches, and diagrams, allow, on the one hand, to dispense with the “calculations” together with cardinals and ordinals, and on the other hand, to describe at leisure the structures and their manipulations thereof, the indefinite work of pasting or glueing data, work that constitutes an object the actual infinity of which the theory of structures is a calculation. Through these technical details it is therefore proposed that Badiou envisages ontology by returning to the phenomenology of his “logic of worlds”, by shifting the question of Being towards the worlds where truths are produced, and hence where the subsequent question of infinity arises.

The Theory and Prevention of Undamped Aeroplane Nosewheel Shimmy

1956 ◽  
Vol 7 (3) ◽  
pp. 193-220
Author(s):  
D. Williams
Keyword(s):  
Mathematical Theory ◽  
The Other ◽  
Linkage Mechanism ◽  
Model Experiments ◽  
Good Feature ◽  
The One ◽  
Value Model ◽  
Elastic Constraint

SummaryThe mathematical theory of nosewheel shimmy is given, with particular reference to twin nosewheel assemblies. It is shown that a sovereign remedy for shimmy is to make the castor length greater than what is here called the “ creep distance,” which in practice is found to be approximately equal to the tyre radius. Lateral flexibility of the oleo leg is disadvantageous but elastic constraint at the pivot is a good feature. The one necessitates an increased castor for stability while the other allows a smaller castor. It is also shown how, by the use of a compact linkage mechanism, the effective castor length can be made independent of the wheel-leg offset and can have any desired value. Model experiments that confirm the theoretical conclusions are described.

scholarly journals The World Is Not a Theorem

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1467
Author(s):  
Stuart Kauffman ◽  
Andrea Roli
Keyword(s):  
Set Theory ◽  
Mathematical Theory ◽  
Generative Process ◽  
Behavioral Adaptations ◽  
The World

The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, for organisms can exploit them for new morphological and behavioral adaptations achieved by heritable variations and selection. This way, the opportunities offered by affordances are then actualized as ever novel adaptations. In this paper, we maintain that affordances elude a formalization that relies on set theory: we argue that it is not possible to apply set theory to affordances; therefore, we cannot devise a set-based mathematical theory to deduce the diachronic evolution of the biosphere.

scholarly journals KEMAMPUAN BERPIKIR KRITIS MELALUI PEMBELAJARAN MATEMATIKA DENGAN PROBLEM BASED LEARNING

Eksponen ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 55-66
Author(s):  
Berta Apriza
Keyword(s):  
Critical Thinking ◽  
Mathematics Learning ◽  
Problem Based Learning ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Learning Needs ◽  
The Social ◽  
Learning Programs ◽  
Mathematical Problems ◽  
The One

Education functions to upgrading, forming, character and develop civilization nation. Having the ability to think and actions to effective and creative in the realm of abstract and concrete can be used as self development independently. Students need to armed with critical thinking skills, systematic, logical, creative, and cooperate effectively to obtain, choose, and manage an information. Mathematics learning is directed to develop critical thinking skills and discussed open and objective because mathematics having strong and structure clear and links between the concept of the one with another concept. By analyzing learning needs of mathematics, formulate and designed a learning programs, choose a strategies and evaliated them correctly to get good results. The ability critical thinking is very important in studying new matter and that known way, and learn to ask effectively and reach a conclusion consistent with the facts. Mathematic learning with problem based learning is the concept of better used activity of the student during learning. In accordance with statements from Westwood (2008: 31) stated that PBL: 1) propel oneself directly in learning, 2) prepared students to critical thinking and analytical, 3) give opportunity to students to identify, find and use numerous this approuch in should think, 4) is the learning is very closely related to the real world and motivate students, 5) involving activeness in integrating information and skills of various the discipline, and 6) knowledge and strategy by the possibility of will be maintained and tranferred to the learning situation other, improve the ability to communicate and the social skills needed to cooperation and teamwork. By chance the learning process as an alternative in solving mathematical problems with using the ability critical think an to cultivate the scientific attitude of student.

scholarly journals Bilingualism and numerical cognition

2020 ◽  
Vol 24 (1) ◽  
pp. 340-360
Author(s):  
Carina da Silva Santos ◽  
Ingrid Finger
Keyword(s):  
Task Performance ◽  
Numerical Cognition ◽  
Language Background ◽  
Language History ◽  
Mathematical Problems ◽  
The One ◽  
The Relationship ◽  
The Way

The present study aimed to investigate the relationship between bilingualism and numerical cognition, more specifically, the way English-Portuguese bilinguals solve simple mathematical problems when these are presented in different formats (digits, English, and Portuguese) and whether their language history background has any effect on such behavior. The main results suggest that bilinguals are faster and more accurate in solving mathematical problems presented in digit format and in solving those problems presented in the written format when the language of the stimuli was the one in which they learned basic arithmetic. Also, the participants’ language background experience did not have any significance in their task performance.

scholarly journals Applications of Fuzzy Technology in Business Intelligence

2011 ◽  
Vol 6 (3) ◽  
pp. 428 ◽  
Author(s):  
Andreas Meyer ◽  
Hans-Jürgen Zimmermann
Keyword(s):  
Set Theory ◽  
Fuzzy Clustering ◽  
Fuzzy Set ◽  
Business Intelligence ◽  
Fuzzy Set Theory ◽  
Mathematical Theory ◽  
Business Management ◽  
Knowledge Based Systems ◽  
Knowledge Based ◽  
Single Method

Fuzzy Set Theory has been developed during the last decades to a demanding mathematical theory. There exist more than 50,000 publications in this area by now. Unluckily the number of reports on applications of fuzzy technology has become very scarce. The reasons for that are manifold: Real applications are normally not single-method-applications but rather complex combinations of different techniques, which are not suited for a publication in a journal. Sometimes considerations of competition my play a role, and sometimes the theoretical core of an application is not suited for publication. In this paper we shall focus on applications of fuzzy technology on real problems in business management. Two versions of fuzzy technology will be used: Fuzzy Knowledge based systems and fuzzy clustering. It is assumed that the reader is familiar with basic fuzzy set theory and the goal of the paper is, to show that the potential of applying fuzzy technology in management is still very large and hardly exploited so far.

scholarly journals Piloting a problem solving module for undergraduate mathematics students

2019 ◽  
Vol 17 (2) ◽  
pp. 46
Author(s):  
David McConnell
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Mathematical Work ◽  
Assessment Practices ◽  
Traditional Teaching ◽  
Mathematics Students ◽  
Undergraduate Mathematics ◽  
Students First ◽  
Academic Year

We report on a new problem solving module for second-year undergraduate mathematics students first piloted during the 2016-17 academic year at Cardiff University.  This module was introduced in response to the concern that for many students, traditional teaching and assessment practices do not offer sufficient opportunities for developing problem-solving and mathematical thinking skills, and more generally, to address the recognised need to incorporate transferrable skills into our undergraduate programmes.  We discuss the pedagogic and practical considerations involved in the design and delivery of this module, and in particular, the question of how to construct open-ended problems and assessment activities that promote mathematical thinking, and reward genuinely original and independent mathematical work.  

Platonism and Mathematical Explanations

2021 ◽  
Vol 13 (2) ◽  
pp. 113-122
Author(s):  
Fabrice Pataut ◽  
Keyword(s):  
Mathematical Theory ◽  
Causal Explanation ◽  
Applied Mathematics ◽  
Propositional Attitude ◽  
Abstract Objects ◽  
Mathematical Explanations ◽  
Parsimony Principle ◽  
The Face ◽  
Numerical Formulation ◽  
The One

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a non numerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (Rizza), the parsimony principle has been respected. Since derivations resorting to conservative mathematics and proofs involved in non numerical best explanations also require abstract objects, concepts, and principles under the usual reading of “abstract,” one might complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. One might then urge that ontological parsimony is also required of these nominalistic accounts. It might, however, prove more fruitful to leave this particular worry to the side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism. Two aspects are worthy of our attention: epistemic cost and debunking claims. Our knowledge that applied mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a genuine theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do indeed play their respective theoretical role involves some question-begging assumptions regarding the nature and validity of proofs. As for debunking, even if the face value content of either non numerical claims, or conservative mathematical claims, or platonistic mathematical claims didn’t figure in our causal explanation of why we hold the mathematical beliefs that we do, construed or understood as beliefs about such contents, or as beliefs held in either of these three ways, we could still be justified in holding them, so that the distinction between nominalistic deductions or non numerical explanations on the one hand and platonistic ones on the other turns out to be spurious with respect to the relevant propositional attitude, i.e., with respect to belief.

Mathematical Mysteries in Byzantium

2013 ◽  
Author(s):  
Judith Herrin
Keyword(s):  
Seventeenth Century ◽  
Third Century ◽  
Greek Text ◽  
Nontrivial Solutions ◽  
Fermat's Last Theorem ◽  
The Third ◽  
Fermat’S Last Theorem ◽  
Mathematical Problems ◽  
The One

This chapter examines how the mathematical mysteries of Diophantus were preserved, embellished, developed, and enjoyed in Byzantium by many generations of amateur mathematicians like Pierre de Fermat, who formulated what became known as Fermat's last theorem. Fermat was a seventeenth-century scholar and an amateur mathematician who developed several original concepts in addition to the famous “last theorem.” One of his sources was the Arithmetika, a collection of number problems written by Diophantus, a mathematician who appears to have flurished in Alexandria in the third century AD. It was through the Greek text translated into Latin that Fermat became familiar with Diophantus's mathematical problems, and in particular the one at book II, 8, which encouraged the formulation of his own last theorem. Fermat's last theorem claims that “the equation xn + yn = zn has no nontrivial solutions when n is greater than 2”.

scholarly journals A Proposed Model to Improve the Skills of Mathematical Thinking (C.A.S.M.E) and Its Impact on The Achievement of Students in the Fifth Grade in Solving the Mathematical Problems

2018 ◽  
Vol 7 (4.36) ◽  
pp. 696
Author(s):  
Ahmed HamzahAbed AL-Ubodi ◽  
. .
Keyword(s):  
Mathematical Thinking ◽  
Thinking Skills ◽  
T Test ◽  
Fifth Grade ◽  
Teaching Model ◽  
Mathematical Education ◽  
Proposed Model ◽  
Post Test ◽  
Mathematical Problems ◽  
Experimental Group

The current research aims to design a proposed teaching model to improve the thinking skills of the students in the fifth grade of the primary and to know its effect on their achievement solving mathematical problems. The proposed model was used CASME, which means accelerating mental growth through scientific and mathematical education. Acronym to Cognitive Acceleration Through Science and Mathematics Education.This model combines two models: the CASE model and the CAME model, as well as the modification of some steps and procedures that help in the process of improving thinking and be compatible at the same time to the process of accelerating thinking.The sample was selected randomly  (62) students from the university mixed primary school, and the sample was divided into two, the first experimental group (31) students and the second group control (31) students, and the search tools were three, the first questionnaire for thinking, Second Pre- test and third Post-test, dimension It was sure to have psychometric properties, has been used Cooder Richardson equation 20,(t)test  for two independent samples and(t)  test for statistical samples interconnecting means, and the results showed .There were statistically significant differences between the pre and post test of the experimental group, as well as the existence of statistically significant differences between the post-test of the two research groups, both in favor of the proposed teaching model. In the end of the results, a set of recommendations were written.  

Tips for Beginners: Exploiting the quadratic function

1962 ◽  
Vol 55 (4) ◽  
pp. 299-301
Author(s):  
Lowell Leake
Keyword(s):  
Set Theory ◽  
Subject Matter ◽  
Mathematical Theory ◽  
Quadratic Function ◽  
Analytic Geometry ◽  
Mathematics Class

The quadratic function offers some unusual opportunities to assemble several segments of mathematical theory chosen from algebra, analytic geometry, and set theory. The exploitation of these opportunities invariably arouses the interest of students in any mathematics class having the proper background, and gives them an elegant vignette of the unity of subject matter in mathematics.

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