scholarly journals STOCHASTIC PROBLEMS AND APPLIED ORIENTATION IN MATHEMATICS TEACHING

Author(s):  
Irina М. Kozyrieva ◽  

The article deals with some aspects of the study of the discipline “Probability theory and mathematical statistics” by the students of economic specialties through the solution of practical exercises. The main aim of learning the course is to form the skills to apply the knowledge gained to the tasks in economics. The concept of teaching probability theory and mathematical statistics is a process in which stochastic concepts and ideas serve as a mathematical apparatus for solving specific problems. Nowadays it is traditional to acquaint students with certain sections of applied mathematics, including probability theory and mathematical statistics, as purely abstract theories. However, as the best we consider another approach, according to which “a more adequate solution will be to acquaint the students with the methods of mathematical models construction”. In solving the problems of an applied nature, students get an idea of the necessity and universality of mathematics and its methods. The value of stochastic problems is determined predominantly not by the apparatus used in the process of their solution, but by the ability to demonstrate the process of usage of mathematics in solution of non-mathematical problems. It is shown how, with the help of applied tasks, to familiarize students with real examples of application of stochastic ideas and methods, as well as to make it possible to organize specific activities necessary in the process of application of mathematics. The student, researching a mathematical problem, formulates different questions and problems, then “transforms” them into the notions of mathematics, in order to solve them by mathematical methods, and then adapt the solution to the real problem, which was set at the beginning of the learning activity. This process is a process of constructing a mathematical (probabilistic) model of a real situation, which can be considered a mathematical activity in a broad sense. Among the traditional stochastic problems there are many typically mathematical (intramodel) tasks of such a kind, which were formulated by means of non-mathematical terms. It is necessary to note that the real problems of an applied nature are rare in mathematics because the stage of formalization (construction of a mathematical model of a non-mathematical situation) requires to have a deep knowledge and mathematical culture. This fact generated the problem of selection of tasks of applied nature that can be used in teaching. The paper presents a number of examples where students are shown how, with the help of some modification, a number of traditional problems of probability theory (formulated in the language of nonmathematical terms) can be developed into the tasks of applied nature. Expanding the range of such tasks during the study of mathematics would have a positive effect on students’ attitudes to this discipline and would increase their motivation to learn. Besides, the role of stochastic issues in mathematics and general education would become more multifaceted. For the university teachers of mathematics working with the students of economic specialties the most important thing is the formation of students’ mathematical skills to use the mathematical apparatus in their future professional activities.

1971 ◽  
Vol 27 (4) ◽  
pp. 434-452
Author(s):  
Hugh T. Kerr

“If there is fault to find with education, and if the system appears to be breaking down, we assume that the first place to look for trouble must be teaching and the teacher. … My own research on general education began with teaching as the primary focus. But I have come to see that the real problem in education today is not teaching and the teacher but learning and the student. The big question is not how to teach but who the student is and how he learns. … Until today, the big question has always been content-oriented: ‘What is education?’ But now high school, college, university, and graduate students are asking a different kind of question: ‘What is education for?’ When translated into the area of theological education, this becomes a ‘professional’ question”.


Author(s):  
А. Лыгин ◽  
A. Lygin ◽  
Ан. Лыгин ◽  
An. Lygin ◽  
А. Хабидов ◽  
...  

In the paper the possibility of using Dean’s equilibrium beach profile formula for a large man-made lake coastal conditions was studied. A stringent test of its adequate use was made based on mathematical statistics. The calculations were performed for the real bottom profile of the Novosibirsk reservoir beach.


Author(s):  
Matthew Rendall

It is sometimes argued in support of discounting future costs and benefits that if we gave the same weight to the future as to the present, we would invest nearly all our income, but never spend it. Rather than enjoying the fruits of our investments, we would always do better to reinvest them. Undiscounted utilitarianism (UU), so the argument goes, is collectively self-defeating. This attempted reductio ad absurdum fails. Regardless of whether each generation successfully followed UU, or merely attempted to follow it, we could never get trapped in endless saving. The real problem is different: without the ability to foresee the end of the world, UU cannot tell us how much to save. Discounting is a defensible response, but only when coupled with a rule against risking catastrophe.


1984 ◽  
Vol 16 (1) ◽  
pp. 19-19
Author(s):  
V. Klemeš

Most of what is routinely labeled ‘stochastic hydrology’ does not contain any hydrology at all and could be more properly identified as the fitting of stochastic models to samples of data of hydrologic origin. T0 engage in this enterprise, no hydrologic knowledge is necessary, nor do the results contribute to hydrologic knowledge. Moreover, the bulk of the current stochastic hydrology does not appreciably enhance the quality of water management decisions-an aim which provided the original impetus for its development. It seems that the mainstream of stochastic hydrology follows in the steps of ‘dam theory’, the only difference being that while the latter has become a self-contained branch of pure probability theory, the former is on the way to becoming a branch of pure mathematical statistics.


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