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Mathematics in Engineering Education 1. The Meaning of Mathematics 2. Why Math Education Have to Be Reformed and How It Can Be Done 3. WebCT: Some Possibilities

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1.The Meaning of Mathematics Mathematics occupies a particular place among all the exact sciences. The language, theoretical methods, and logic of physical and engineering sciences are based on mathematics since it concentrates the most important results of exact thinking of scientists and engineers.

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Mathematics helps us: Mathematics helps us: - to understand deeper the mutual correspondence of different approaches to the same problem; - to see relationships between the space-time properties and the conservation laws in Physics; - to predict behaviors of some systems under different conditions; - to analyze the results of experiments, and so on. In particular, the property of time homogeneity implies the law of conservation of energy, while the property of space homogeneity implies the momentum conservation law.

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Mathematics allows to express physical laws in different forms. It gives a way of conversion of one set of statements to another. For instance, the movement of a particle in a gravitation field can be described by applying the gravitation law. On the other hand, this problem can be formulated and solved by making use of the principle of least action, the domain of applicability of which is not restricted by mechanical problems only and extends also over electrodynamics and quantum physics. Many processes being different from the physical point of view, are described by an identical equation, the solution of which does not depend on the physical meaning of the considered phenomenon. Many processes being different from the physical point of view, are described by an identical equation, the solution of which does not depend on the physical meaning of the considered phenomenon.

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One of the basic goals of mathematics is a rigorous proof of a proposition. So mathematics deals with the general structure of argumentation, no matter the physical meaning of the used concepts. Then other sciences apply that ideas in the making and development of theoretical models.

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Future engineers have to study Math because Nature knows and applies mathematics. Future engineers have to study Math because Nature knows and applies mathematics. French physicist Dirac discovered a law of relativistic quantum mechanics since he guesses right the corresponding mathematical equation. Maxwell electrodynamics has been created on the basis of the concept according to which the space was considered as consisting of wheels and pinions. Despite the fact that the model is erroneous, the physical theory expressed in a mathematical form, is true. Maxwell electrodynamics has been created on the basis of the concept according to which the space was considered as consisting of wheels and pinions. Despite the fact that the model is erroneous, the physical theory expressed in a mathematical form, is true. Any fundamental physical law can be formulated in a simple mathematical form and even by means of a few mathematical models. Just that hypothesis stands a better chance to be valid, whose mathematical representation possesses the property of simplicity. Any fundamental physical law can be formulated in a simple mathematical form and even by means of a few mathematical models. Just that hypothesis stands a better chance to be valid, whose mathematical representation possesses the property of simplicity.

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Mathematics Provides the Deep Understanding and Description of Nature. The Great Architect Was Mathematician. If the God knows mathematics then all future engineers must study it well.

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2.Why Math Education Have to Be Reformed and How It Can Be Done In view of the modern tendencies of rapid change in educational activities and level of development of engineering education, international cooperation of universities is becoming an insistent need to provide students new educational opportunities. In view of the modern tendencies of rapid change in educational activities and level of development of engineering education, international cooperation of universities is becoming an insistent need to provide students new educational opportunities. Access to the Internet and computer tools of training change the traditional education concept and result in an appearance of new forms of education such as distance learning, e.g. Access to the Internet and computer tools of training change the traditional education concept and result in an appearance of new forms of education such as distance learning, e.g.

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Mathematics is gaining in greater importance for technical progress, economy, medicine, etc. However, mathematics education of future engineers have to be modified to include the modern Internet-technologies, math software and other computer aids. It is necessary: - to select the fundamental component of mathematics, which provides the ability to reason logically and to apply knowledge to engineering courses; - to pick out the concepts of central importance; - to analyze the existing educational programs, approaches, and methodical materials in view of their correspondence to the modern tendencies of engineering education. Possibly, the most instructive proofs should be combined into separate sections as examples of exact reasoning.

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By making use of the Internet tools and software environment all routine calculating work (in numerical form as well as in symbolical one) could be readdressed to computer programs such as Matlab or Maple, for example. By making use of the Internet tools and software environment all routine calculating work (in numerical form as well as in symbolical one) could be readdressed to computer programs such as Matlab or Maple, for example. Finally, one has to find a balanced combination of the above components. Finally, one has to find a balanced combination of the above components.

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Section 1: The Nature of Science

Section 1: The Nature of Science

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