Top Research Papers on Mathematics

In the AustMS Gazette 32 (2005), 146–147, the question above was included in a letter to the Editor. Readers were asked for their responses in one or two sentences. Below is the set of responses, pseudo-randomly ordered and without comment. Respondents sometimes included extra information about themselves or their perspectives and some of these have been included. The respondents were readers of the Gazette who identified themselves as mathematicians or users of mathematics, and a group of people involved in the mathematics education of teachers.

After investigating definitions of mathematics, this paper deals with the sort of mathematics, interpretation of mathematics and uses of mathematics. Mathematics as an universal method for scienctific research is very important. The evolution of its definition shows us that mathematics is being perfected.

Mathematics is the manipulation of abstract symbols according to specific rules. As such, mathematics is a language, but it differs from other languages in its universal nature and its applicability to human endeavors. The symbols that are manipulated usually represent quantities or geometric objects. The quantities can be as specific as numbers, or they can be abstract and variable. The quantities manipulated often are the rules of manipulation themselves. A mathematician is a linguist who constructs symbols and words from their conceptual roots. These symbols represent an ever increasingly i...

Colleagues, in our profession it is meaningless to wish someone to be wealthy; however, to be healthy is most appropriate, particularly, after sixty when every additional year is a bonus from God. To a scientist even a small recognition works as a catalyst for him to continue in his research at least for some more time. Thus, I am really grateful to the administration of the University of Babes–Bolyai, Cluj–Napoca, and specially Professors Adrian Petrusel and Radu Precup for awarding me the title Professor Honoris Causa.

In the AustMS Gazette 32 (2005), 146–147, the question above was included in a letter to the Editor. Readers were asked for their responses in one or two sentences. Below is the set of responses, pseudo-randomly ordered and without comment. Respondents sometimes included extra information about themselves or their perspectives and some of these have been included. The respondents were readers of the Gazette who identified themselves as mathematicians or users of mathematics, and a group of people involved in the mathematics education of teachers.

Mathematics plays a central role in modern science. However, it is very common an instrumental and utilitarian view of math leading to the underestimation of its scientific nature. We propose some consideration to emphasize a different idea on the fundamental role of math in modern science.

This is an exciting and challenging time to be a math teacher. Technology has opened the door to teaching and doing mathematics in new and different ways. Because of computers and graphing calculators, mathematics educators are in a continuous process of revising curriculum to take full advantage of available technology. The opportunity to create new curriculum carries with it the necessity to learn new methods and techniques as well as the responsibility to make correct choices. Implied in this process of reworking mathematics curriculum is a basic question: what above all else do we want to ...

Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in detail, for the core of modern mathematics, how modern mathematical formalism encapsulates deep realities about extension into a system of symbols and axiomatic rules. In particular, we proceed from the foundations in our senses to the natural numbers through integers, rational numbers, and real numbers, including introducing the concept of a field. An appendix...

historically evolved, and intelligible only in a social context.” Hersh describes some of the standard issues of philosophy of mathematics, such as existence of finite and infinite mathematical entities, intuition, proof, and truth, and tries to show that his philosophy deals with these issues better than do the philosophies he rejects. Although I found the book very interesting and informative in many ways, I am not sure Hersh succeeds in making his case for his humanist philosophy. Part One The opening gambit of the book is presented as both “a worked exercise in Pólya’s heuristic” and “an i...

ion and Generality Abstraction is the generalization of myriad particularities. It is the identification of the essence of the subject, together with a systematic organization around this essence. By appropriate generalizations, the many and varied details are organized into a more manageable framework. Work within particular areas of detail then becomes the area of specialists. Put another way, the drive to abstraction is the desire to unify diverse instances under a single conceptual framework. Beginning with the abstraction of the number concept from the specific things being counted, mathe...

Math is about the study of formal systems, the study of what can be deduced from formal systems: given some axioms and some rules of manipulation, what follows?

The article looks at the premise that children are encouraged to talk and the reasons why this might be effective in helping them understand concepts better by involving the input of their peers.

It is shown that a deep going view of mathematical essence can be reached through a comprehensive study of the subject.

This article looks at why talk is important for young children learning mathematics, how talk fosters mathematical understanding and the importance of having something to talk about by relating maths to real situations. It then looks at the revealing comments of some four and five year old children talking about simple number activities linked to a favourite rhyming story song they had been singing.

Numération Les nombres < 999 999 (vers le cycle 3) Utiliser les maths pour questionner le monde (frise historique, massifs montagneux) Calculs Comprendre le sens de la division : partages Diviser en ligne Technique opératoire de la division par 1 chiffre Calcul mental Tables de x2 à x11 RITUELS ceintures Ajouter au-delà de 999 Soustraire au-delà de 999 Calculer la moitié de multiples de 10 Calculer la moitié de nombres quelconques Calculer des tiers, des quarts Diviser par 10, 5, 25, 50 Connaître les relations entre 5, 10, 25, 50 et 100 Connaître les relations entre 15, 30 et 60 Espace et Géom...

A more accurate title is “What is mathematics education for?” but the shorter one is more attention-getting and allows me more generality. My answer will become apparent soon, as will my answer to the subquestion of why the public supports mathematics education as much as it does. So that there is no confusion, let me say that by “mathematics” I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic. There is no question about what arithmetic is for or why it is supported. Society cannot proceed without it. Addition, subtraction, multiplication, d...

Marian Small is a professor in the Faculty of Education, University of New Brunswick, Fredericton, NB E3B 6E3. She teaches graduate and undergraduate courses in the areas of mathematics education and computers in the curriculum. dents opportunities to experiment with mathematics. Virtually all current text series offer some laboratory experiences using manipulative materials, some number-pattern exploration experiences, and digressions about special topics like mathematics in cooking or sports for those who are more interested. However, fewer attempts have been made to offer opportunities for ...

Examples from the author’s personal experience illustrate how mathematical chemistry applies graph theory and discrete mathematics to chemical problems, without involving intermediate physics. In molecular graphs, vertices represent atoms and whose edges represent covalent bonds. In reaction graphs vertices represent molecules or ions and edges symbolize elementary reaction steps.

This paper is dealing with an optimization problem by using the meta heuristic approach in which the demand of delivery customer can be met by a relatively large number of pickup customers and by optimal tour the authors mean the shortest trajectory or the minimum distance among the nodes of wireless sensors.

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of mathematics and a paradigm for education, namely Learn to structure.