Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) Hardcover – January 1, 1964 by Walter Rudin (Author) › Visit Amazon's Walter Rudin Page. Find all the books, read about the author, and more. See search results for this author. Are you an author?

Principles Of Mathematical Analysis Pdf
Principles Of Mathematical Analysis Solutions
Principles Of Mathematical Analysis Solution

The paper pays attention to using in the preparation process of the future bachelors of mathematics an effective learning tool such as a computer. Its use is disclosed in the training materials of the course 'Mathematical Analysis', during the introduction of such concepts as the limit of a numerical sequence or function and their fixing. Information and communication technologies in teaching represent an effective means of increasing the productivity of the learning process, which allows finding new ways of solving urgent pedagogical problems and ensuring optimal management of the educational process. Information and communication technologies are indispensable tools by which teachers can qualitatively change the methods of teaching and organize the forms of the educational process in a new way, raise the level of the studied material, develop the individual traits of the trainees more qualitatively, and organize independent work.

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Today we are witnessing how computerization penetrates into all aspects of our lives. There are practically no spheres of activity, wherever computers are not used: financial operations, engineering, communications and printing, modeling and construction of new facilities and more. It is difficult to imagine our life without these operating and multifunction tools. Therefore, it is important to teach various computer skills at all levels of the education system.

Using computer technology in education is a powerful new stimulus for the further development of the teaching science. There is a need for research to find new and effective techniques, methods of using computer technology that expand the possibilities of the educational process.

In recent years, pedagogical and methodological developments demonstrate the comprehensive implementation of information and communication tools in education and science. Today, many leading pedagogues turn increasingly to the use of these tools in the modern educational process, among them:

M.P. Lapchik, V.A. Dalinger, K.A. Zuev, N.V. Sholokhov, P.I. Sovertkov, I.V. Robert, S.I. Shapiro, Gershunskiy and others. Most of them take the consideration of various approaches to the use of computer technology as a learning

The computer can act as a subject of study, as a learning tool, and as a tool for scientific research. In this connection, it solves the following problems: execution of complex computing operations, analysis of the experimental results, the construction and interpretation of mathematical models, and so on.

Applications of the computer in the learning activities are mainly limited to its use as a ―big calculator‖, ―information textbook‖ tool for controlling students’ knowledge and less – as a performer of other functions. Moreover, its advantages and opportunities for learning are generally not fully disclosed. When using the computer [1], students master the learning material at their own speed, their knowledge are objectively evaluated, simultaneous feedback is carried out, they get a wide range of information to be provided in a variety of images. On the other hand, using the computer, teacher can take into account the individuality of students, pay more attention to them, get rid of routine work when searching for information, include various exercises, while spending a minimum of time for creating tasks, and as a result, spend more time for improving his intellectual level and professional skill.

No doubt, such use of computer solves many educational and psychological problems during the learning. However, the possibilities of this technical tool are much broader. In addition, information technologies have a significant impact not only on the learning process, but also on the development and education of students. They stimulate and create motivation, provide the dynamism of the learning process, stimulate learning and cognitive activity. Information technologies alone cannot always ensure efficiency of learning, but they can be a means of improving the current educational process [2].

The primary role in realization of these possibilities falls on the shoulders of teachers of higher educational institutions. In this connection, it is necessary to pay the due attention in pedagogical higher educational institutes not only to teachers of computer skills, but also to teachers of other disciplines (of humanitarian and natural–mathematical cycles) in their training the basics of modeling with the use of the application software. Teachers must be not only subject teachers, but also teachers having basics of didactics and new technologies of education.

M.P. Lapchik [3] noted that the computer science is not so much the content as the methodology. For this reason, all the teachers – as in general all the experts – must become teachers of computer skills; and computer literacy of young people must be formed in a constant communication with the computers in the classroom in all subjects, and during all the years of schooling. However, there is a need for advanced study of computer science as a specialty.

One can use such effective technical tool as the computer in all stages of study. Its use should not be limited to the laboratory studies; one can use it during lectures, practical lessons, tests, and coursework and diploma projects.

When the perception of the new academic content, computer can simulate the abstract objects, processes, phenomena, process the information quickly and accurately, etc.

In the process of understanding and generalization, computer can make a demonstrational analysis of the relationships, dependencies, etc.; it can monitor students’ independent work, formulate conclusions, hypotheses and prognoses.

When fixing the educational material, computer serves as a generator of problem situations; manages students’ independent work; analyzes the level of assimilation.

In the application of knowledge, computer can serve as a simulator for formation of skills and abilities; provide differentiated support and control for the learners [4].

Principles Of Mathematical Analysis Pdf

Turning on the computer in the learning process should not be chaotic and aimless. Each lesson must be thought-out; the involvement of information and communication tools must be justified by the objectives, demands of the subject, time expenditures. The development of skills in working with technical equipment must be carried out regularly throughout the course of study in high school.

The computer as a learning tool has another important advantage – its ability to represent various types of dependencies, numerical relations, and so on, in a visual form. At the lesson, the realization of obviousness principle takes place in a qualitatively different level. In addition, of particular interest is modeling of the phenomena that are inaccessible to direct observation, as well as phenomena whose description has not developed adequate mathematical apparatus, and which cannot be demonstrated within the classroom without the help of a computer.

Visualization has been not received the due attention in traditional higher education. It has been found that a person gets 90% of information about the surrounding reality through the visual analyzer, 9% – with the help of hearing, and 1% – with the help of touch. All this proves once again that the active use of the visual analyzer provides new, grea