1. Numerische Berechnungen

Aus Online Mathematik Brückenkurs 1

What is a number and who invented the four basic arithmetic operations?

Watch the video in which the lecturer Lasse Svensson tells us how arithmetic developed and answers Elins questions.

This first part of the course is about numerical calculations, that is, calculations with numbers. Another name for this is arithmetic.

Arithmetic is the study of the properties of numbers and the four basic operations: addition, subtraction, multiplication and division. We usually separate mathematics in different branches or areas, and arithmetic is one of those branches. Other branches are, for example, algebra, geometry and the theory of functions. The word arithmetic comes from the Greek "arithmos" meaning "number" and the ending -ic, means "knowledge". Thus the original meaning was "knowledge of numbers."

We begin with a discussion of various kinds of numbers and the usual basic operations. The numbers originated in measurements of various kinds (in the animal enclosure: 17 sheep, credit: -250 EURO, per guest: 1 / 8 cake, perimeter of the circle: 2 cm.).

The basic arithmetic operations are structured in a hierarchy that begins with addition and its opposite, subtraction. Following on from addition we have multiplication, which is addition repeated several times. The opposite operation to multiplication is division.

If one continues in the same way the next operation is exponentiation or raising to a power, which is a multiplication repeated several times. The reverse operation to this is to take the root of a number. Even logarithms can be regarded as a reverse operation to exponentiation. (This you can read about in Part 3 Roots and Logarithms.)

Fun puzzles with sound can be found, inter alia, on Puzzel Playground Puzzel Playground

It is important to note that the material in this section — as well as in other parts of the course — is designed that one does not use calculators.

When you get to university, you will not be allowed to use calculators during your "exams", at least this is true for the basic courses. In advanced courses in mathematics one has hardly any use of calculators, as the mathematics is more about understanding principles than performing calculation. For example, it is more important to understand why 7 + 3 is the same as 3 + 7, than to be able to carry out the additions and obtain the answer 10.