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1 What Is The Future of The Traditional Concept of Mathematical Education – Evolution or Degradation? Outline of The Project of The International Cooperation Between Tomsk Polytechnic University and Hochschule Wismar – University of Technology, Business and Design Presentation is prepared by Valery Konev

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2 Goals: 1. To Discuss Some Teaching-Learning Problems in Mathematics 2. To Analyze Capabilities of The Modern Informational Technologies 3. To Give a Demonstration of The Joint- Development Project “Mathematical Background Required by Higher Education”

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3 The Subjects Being Discussed Current Status of Mathematics in Engineering Education Basic Features of Computer Systems for Advanced Mathematics Some Advantages of Web-Based Teaching Tools Fragments of the Course “Math Background Required by Higher Education”.

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4 Part 1: Status of Mathematics in Engineering Education The traditional teaching concept in mathematics has come into conflict with the reality, that shows itself, for example, in form of decreasing the general level of math culture. Many people treat classic mathematics lightly, referring to the possibilities of modern computer software, which are unbounded practically. If to mention also about the Internet that provided the access to new sources of information (as well as to new learning forms), then one has no choice but to make the following conclusion: Classic Mathematics dies a natural death… Long live computer soft!

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5 When a former Russian President Boris Eltsin was in poor health, many politicians discussed: “Who would be a new President?” Then one of the Russian politicians said: “Don’t hurry to bury Eltsin. Just Eltsin will take a chill at the time of your funeral procession”. We can rephrase the above quote: Nobody will not wait the end of classic mathematics. However, the tradition teaching-learning process needs to be reformed to include the modern Internet-technologies, math software and other computer aids.

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6 Let us analyze some different points of view. All people can be subdivided into two groups, the first of which consists of persons who do not understand mathematics. Let us name them “Contra”. The rest persons like mathematics, and they form the second group named “Pro”.

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7 The point of view of the group “Contra”: Mathematics is some helpful means which is used by other sciences. We have only to carry out the simplest manipulations or calculations of expressions and to write down solutions of equations. Engineers do not need rigorous proofs of mathematical statements as well as complicated transformations due to a new kind of symbolic computer language that could manipulate the very wide range of objects involved in technical computing using only a fairly small number of basic primitives. Computer systems have become a standard tool for both development and production. In many cases one can set up calculation by adapting some appropriate examples from HELP.

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8 The point of view of the group “Pro”: The ability to reproduce some manipulations with expressions or functions has relation only to the simplest mathematics, since such actions require only trivial logic. Mathematics possesses by a particular attraction due its logic. Unfortunately, many modern rule-based tutorials give occasions to hate mathematics. It is very difficult to study a subject, the matter of which consists only in definitions, rules and formulations of theorems. Only a small part of students is able to pick out the key points of the subject and to orient in this information stream consisting of definitions and naked facts. The many do not understand the intrinsic logic of mathematics, and so they do not like mathematics.

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9 The highest level of mathematical culture is necessary in order to solve serious engineering problems. Itself procedure of proving propositions forms the level of thinking, that is, rigorous mathematical proofs have to consider as an end in itself. However, proofs of theorems become a thing of the past in mathematical courses intended even for engineering specialties. Similar interpretation of mathematics has an influence like the narcotic effect: The illusion of the well-being and the paralysis of creative thinking in the future. The result will not keep waiting itself.

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10 As a matter of fact the “Contra” does not understand the true meaning of the learning process in mathematics. Any computer systems cannot replace the basic mathematical knowledge as tools for engineers to master technological needs currently and in the future. The fundamental component of mathematics keeps its importance, since it develops the ability to reason logically and to apply knowledge to special engineering courses. Mathematicians make a typical mistake assuming that everybody knows the true meaning of mathematics because they know it. It is necessary to educate the public using all possibilities. Otherwise, the generation of “slightly educated” engineers will appear on the scene.

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11 Some Advantages of Web-Based Teaching Tools

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14 The Structure of The Course Links refer to proofs, explanations, graphic illustrations, examples or some additional information, each of which has its own system of links.

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15 Part 2: Basic Features of Computer Systems for Advanced Mathematics Maple and Mathematica Each of these systems is the integrated powerful, high-level, interactive environment for technical computing. They have a profound effect on the way computers are used in many technical and other fields. The main concept: to create once and for all a single system that could handle all the various aspects of technical computing in a coherent and unified way. At first, the systems was oriented mainly in the physical sciences, engineering and mathematics. But over the years, they have become important in a remarkably wide range of fields. The systems have played a crucial role in many important discoveries, and has been the basis for thousands of technical papers. In engineering, the systems have become a standard tool for both development and production, and by now many of the world's important new products rely at one stage or another in their design on Mathematica or Maple.

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16 What Can We Do to Bridge a Gap between the Real Level of Math Knowledge and Math Background Required by Higher Education? First of all we could combine together the best features of traditional courses, Web-based tools, and computer soft. It is very important to find a balanced combination of tools based on new information technologies and the classic approach to math education. We should analyse the existing educational programs, approaches, and methodical materials in view of their correspondence to the modern tendencies of engineering education and to pick out the conceptions of central importance.

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17 Thank you very much for your attention! Are you ready to continue? A cup of tea or coffee? Let us go on to the next question.

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Copyright © Cengage Learning. All rights reserved. CHAPTER 11 ANALYSIS OF ALGORITHM EFFICIENCY ANALYSIS OF ALGORITHM EFFICIENCY.

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