scholarly journals The role of computer in the process of solving of mathematical problems (results of research)

2007 ◽  
Vol 5 (1) ◽  
pp. 67-80
Author(s):  
Henryk Kakol ◽  
Tadeusz Ratusinski
1986 ◽  
Vol 29 (2) ◽  
pp. 129-139 ◽  
Author(s):  
Cathleen Synge Morawetz

AbstractWe present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial airlines. The problem is simplified and the important role of modifying the equations with physics terms is examined.


2019 ◽  
Vol 27 (3) ◽  
pp. 381-439
Author(s):  
Walter Dean

Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.


Author(s):  
Aline Dorimana ◽  
Alphonse Uworwabayeho ◽  
Gabriel Nizeyimana

This study explored teachers' beliefs about mathematical problem-solving. It involved 36 identified teachers of Kayonza District in Rwanda via an explanatory mixed-method approach. The findings indicate that most teachers show a positive attitude towards advancing problem-solving in the mathematics classroom. However, they expose different views on its implementation. Role of problem-solving, Mathematical problems, and Problem-solving in Mathematics were identified as main themes. Problem-solving was highlighted as an approach that helps teachers use time adequately and helps students develop critical thinking and reasoning that enable them to face challenges in real life. The study recommends teacher professional development initiatives with their capacity to bring problem-solving to standard.


Pythagoras ◽  
2010 ◽  
Vol 0 (72) ◽  
Author(s):  
Inderasan Naidoo ◽  
Belinda Huntley

This paper explores and promotes the notion of ‘procept’ in an undergraduate mathematics course in Linear Algebra for first year pure and engineering students. On the basis of students’ preference for procedural to conceptual solutions to mathematical problems, this paper augments the role of certain concepts in pure and applied mathematics, particularly in the problem‐solving approaches at the undergraduate level by providing novel solutions to problems solved in the usual traditional manner. The development of the concept of ‘procept’ and its applicability to mathematics teaching and learning is important to mathematics education research and tertiary pure and applied mathematics didactics in South Africa, welcoming the amalgamation of the theories developed at pre‐tertiary level mathematics with theorems and proof at the undergraduate level.


2019 ◽  
Vol 62 (7) ◽  
pp. 37-53 ◽  
Author(s):  
Igor F. Mikhailov

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: (a) thinking is based on the inherent rules of rationality, (b) logic is an extract of rationality, and (c) types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality (if not falsity) of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated.


Respuestas ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 56
Author(s):  
Oscar Abel Cardona-Hurtado

Antecedentes: En la notación tradicional para los conectivos proposicionales binarios son tenidos en cuenta solamente algunos de estos. A lo largo del siglo XX fueron propuestas varias notaciones que subsanan esa falencia, dando lugar al planteamiento de interesantes problemas matemáticos. Objetivo: En este escrito se presenta la notación creada por el norteamericano Charles Peirce, se muestran algunas propiedades de las cuales goza esta simbología, y se evidencian sus ventajas con respecto a la tradicional. Método: Se describe la notación propuesta por Peirce, y se verifican algunas propiedades de carácter lógico geométrico y algebraico entre sus conectivos; también se analiza la posible actuación de estas propiedades en la notación usual. Resultados: Además de varias propiedades individuales y de múltiples relaciones entre los conectivos, las simetrías del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Peirce. Conclusión: Diversas bondades de las cuales goza la notación propuesta por Peirce, permiten afirmar que la notación usual es superada de manera clara por la simbología diseñada por el científico norteamericano.Abstract Background: In traditional binary notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the notation proposed by Peirce, support the conclusion that the usual notation is clearly surpassed by the symbolism designed by the American scientist.Palabras clave: Conectivo proposicional, Charles S. Peirce, operación, simetría, tabla de verdad.


2021 ◽  
Vol 14 (5) ◽  
pp. 109
Author(s):  
Rania H. Friehat ◽  
Anoud Al-Khresha

This study aimed to identify the RAMP initiative’s role (read comprehensively, answer with understanding) in raising the level of literacy skills and numeracy from the point of view of teachers. It also aimed to identify its effectiveness in improving the reading and writing level of the basic minimum stage, as an initiative that reduces the delay in reading and helps in the development of skills to help students solve mathematical problems with understanding and accommodating. Closed questionnaires were distributed to the Central Badia region; the questionnaire consisted of (35) paragraphs divided into three areas of reading, writing, and arithmetic, where 88 teachers answered the questionnaire. Statistical analysis was adopted (Statistical Package of Social Sciences (SPSS) was adopted to show the study results. The results showed a role for the RAMP initiative in raising the level of reading and numeracy skill to a reasonable degree, where the skill of reading got a good degree, was the highest skill of voice awareness to an extraordinary degree and other standards are good. Writing skill got a good degree; it was the highest, the skill of writing words and the least skill of creative writing, and also obtained the skill of calculating a good degree above (counting units) and the lowest domain (participation and composition of groups). The results showed no statistically significant differences due to variable years of experience, while the results showed statistically significant differences in favor of a bachelor’s degree.


2021 ◽  
Vol 35 (1) ◽  
pp. 42-47
Author(s):  
Maria E. Chekulaeva ◽  
◽  
Angela S. Kotova ◽  

Based on the analysis of the current level of mathematical training of students, the importance of finding ways to develop students ‘ cognitive interest in the subject is justified. The purpose of this work is to identify the influence of the proposed methods of solving and composing applied mathematical problems by students on the development of students ‘ cognitive interest. The research objectives included the theoretical substantiation of the role of applied problems in increasing the level of knowledge and interest of students in studying mathematics; as well as the development of methods for the use of applied tasks in the classroom and the management of students ‘ activities in the preparation of applied tasks. The method of presentation of educational material in the conditions of distance learning is proposed. In the course of distance learning, students learn theoretical material through solving applied problems.


2010 ◽  
Vol 94 (529) ◽  
pp. 84-93
Author(s):  
R.W. Smyth

I often recommend to my students that they follow their noses when solving mathematical problems. The role of intuition in creative mathematical work is difficult to explain. Still its value should never be underestimated and its development may be fostered by experience, including even unsuccessful trips down dead ends and meandering forays into thickets of apparently untameable complexity. In this article I invite you to corne with me and explore a simple calculus problem using any tools and ideas that seem to offer some promise of moving us along in the right direction. The scenic route embraces Taylor's formula, geometric series expansions, relations in Pascal's triangle, and matrix diagonalisation. Don't forget to bring along a pencil and some scrap paper… and a computer algebra system too, if you like.


Author(s):  
Giuseppe Amoruso

Interior design is taught to be an essential tool for envisioning and modeling the environments we live in. Representing interior spaces through drawings and physical models requires a continuous process of imagination. The chapter exploits the projective tools for illusory design describing the processes of representation to design and build interiors but also their perception as a space. Crucial is the role of perspective in designing and building interiors; techniques of perspective, distancing itself from the mathematical problems, become a projective tool to add illusory qualities and creating the perfect tuning among spaces that remind us that designing methods aim to add dimensions to the human sphere, not only in the physical one but also in the creation of material images and allegories. The research highlights the principles of projective-geometric design of illusory spaces. Descriptive geometry and disciplines of representation provide, in the many phases of design, scientific and artistic tools for practical resolutions of geometric and constructive problems.


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