Preparatory Course in Mathematics At the University of Konstanz How to use this manuscript. It is optional and in Konstanz it is held the week before the first term . The intention of this preparatory course is to refresh school mathematics , to compensate for deficits in the mathematical education in special types of high schools and to deliver some additional important topics necessary immediately for the beginning lectures in physics, even before the regular mathematical lectures, hampered by their necessity to give a systematic treatment, are able to provide them. But it is hoped that some students will use the manuscript in subsequent weeks to acquire some more topics by self-education. The author of this manuscript is of opinion that in mathematics memorizing also plays an important role.
Nothing goes into our long-time memory without repetition and without motivation .
In the first reading the Q -units bring a minimum of the material in compact form, which should simply be learnt by heart . An attempt was made to choose exercises that were as simple as possible, while still exemplifying a certain point as clearly as possible. To enhance motivation, an attempt was made to try and find exercises which have real meaning or appeal to the students, so they are confident that they learn for themselves and not for their teachers. However, realistic and important examples have a tendency to be very long and complicated and will therefore distract from the essential point. A student who is very motivated will be better off with so called nonsense examples , which as such, have no real application but will present a certain point with utmost clarity and not at the expense of unneccessary complication by inessentials.