Mathematics for Engineers: Indispensable and Superfluous. We discuss the basic mathematics syllabus of an engineering school syllabus that usually consists of calculus, linear algebra, numerical methods, probability and statistics. During the first two university years a lot of teaching time in basic mathematical courses is spent on repeating topics more or less known from the secondary school, such as systems of linear equations, calculus, probability and statistics. Consequently, littletime is left for advanced topics important theoretically and practically, such as equations of mathematical physics, vector and tensor analysis, theory of variations, algebra, theory of functions, functional analysis and numerical methods. As a result, in their third and fourth university years, students interested in theoretical aspects of engineering, have to spend a lot of time on special courses in the topics mentioned above. These difficulties are partly caused by the fact, that scientific and engineering students have as mathematics teachers pure mathematicians, hardly interested in application. The situation can change if: a) the university has more confidence in high school education (checked by entry examinations); b) future engineers and scientists should be taught mathematics by applied mathematicians or theoretical physicists and engineers, who could better choose from their own experience what chapters of mathematics would be useful to their disciples.
Role of Mathematical Modeling and Applications in University Mathematics Service Courses: An Across-Countries Study. Mathematical modeling skills are very important both for students majoring in mathematics and for those needing mathematics for other subjects. Many academics and practitioners consider them as the most useful skills which non-maths major students should develop while studying mathematical courses. The aim of this study is to find out what university students who are studying mathematics as a service course think about the role of the mathematical modeling process and application problems in their studies. For this purpose a questionnaire was given to more than 500 students from 14 universities in 9 countries (UK, New Zealand, Australia, Russia, Ukraine, Finland, France, South Africa, Spain). The research was not a comparison of countries or universities: the sample size is too small. An across-countries approach was chosen to reduce the affect of differences in education systems, curricula, cultures. A particular attempt was made to reveal the hardest step of the mathematical modeling process for the students.
Reform of the Mathematics Education for the Faculty of Engineering. Nowadays, students' mathematics ability is tending to become lower and the level is tending to vary widely. Also most students can hardly identify any purpose in learning mathematics, even while computer and network technology is rapidly developing. Consequently, it is time for us to change the ideas, methods, and contents of mathematics education. The fundamental concepts of reform in mathematics education at our university are as follows: The contents of mathematics programs are decided based upon the policy of each department, and the necessary mathematics contents selected by each department are taught during the most appropriate periods of undergraduate and graduate education. This we call the "wedge style" curriculum. We demonstrate how this concept and the use of computers and networks are changing the teaching methods as well as curricula and syllabi of mathematics in our university, while letting mathematicians acquire rich knowledge of related science and engineering.
Smoother Transition from Secondary to Tertiary Level: Demand for Adaptation and Renovation of School and University Mathematics Education in Sweden. Alarming news about falling, if not collapsing, knowledge of mathematics among beginners in engineering education was splashed on the front page of one of the leading Swedish morning papers in October 1997. The lack of mathematical skill of students entering the tertiary level appears to be an increasing problem in many countries and it seems to be more or less independent of the educational system. In April 1998 the Swedish government asked the National Agency for Higher Education to (a) find out if there is a discrepancy between the actual mathematical knowledge of secondary school leavers and the requirements of the universities; (b) discuss the reasons for this discrepancy (if it exists); (c) suggest action to be taken in order to improve the situation; and (d) study the experience of other countries. There is obviously no single quick fix that could remedy the situation. What is needed is a number of different long- and short-term actions, both on the university and on the school level. Some of suggestions made by the Committee concern the schools, some the universities, some demand action on a central level and some on a local level.
Some Numerical Approaches in Teaching Differential Geometry. The theory of curves and surfaces was established long ago. Yet applying the general theory to individual objects is not easy. This is because it is not possible in general to solve differential equations explicitly. Hence, the examples appearing in this field have been confined to a small group of calculable objects. However, computers do these numerical calculations easily, and this makes it possible for us to deal with a wide range of examples. I use computers not only to calculate geometric quantities or to draw geometric objects, but also to visualize the basic notions of differential geometry and to perform experiments in geometry making use of computer graphics, animations in particular. Through these examples, I would like to suggest a new possibility for utilizing computers in teaching differential geometry.
China Mathematical Contest in Modeling (CMCM) and the Reform of Mathematics Education in China's Universities. In the last five years mathematics education reform in China has been greatly influenced by the China Mathematical Contest in Modeling (CMCM). This presentation will address (1) problems and difficulties in mathematics teaching in China's universities and the need for reform; (2) eight years of the China Mathematical Contest in Modeling; (3) impact of CMCM on mathematics teaching in China's universities, including (a) setup of new courses such as mathematical modeling, mathematical experimentation, etc; and (b) activities of mathematical modeling; and (4) questions we need to address further.