1. Numerical calculations
From Förberedande kurs i matematik 1
(Edited for idiomatic English by Phil Ramsden--some changes made to information about calculators, which at Imperial varies from course to course) |
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| - | '''What is a number and who invented the four basic arithmetic operations? | ||
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| - | Watch the video in which the lecturer Lasse Svensson tells us how arithmetic developed and answers Elins questions. | ||
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This first part of the course is about numerical calculations, that is, calculations with numbers. Another name for this is '''arithmetic'''. | This first part of the course is about numerical calculations, that is, calculations with numbers. Another name for this is '''arithmetic'''. | ||
Current revision
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. The word arithmetic comes from the Greek "arithmos" meaning "number".
We begin with a discussion of various kinds of numbers and the usual basic operations. The numbers originated in measurements of various kinds (animals in an enclosure: 17 sheep, credit: -£250, amount 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 can be considered as a multiplication repeated several times. The reverse operation to this is to take the root of a number; alternatively, logarithms can be regarded as a reverse operation to exponentiation. (This you can read about in Part 3 Roots and Logarithms.)
It is important to note that the material in this section — as well as in other parts of the course — has been designed so that you do not need a calculator.
Mathematics at university is more about understanding principles than performing calculations. To take a very simple 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.
To do well in arithmetic
- Start by reading the section's theory and study the examples.
- Work through the exercises and try to solve them without using a calculator. Check whether that you have the right answer by clicking on the answer button. If your answer is incorrect you can click on the solution button to see what went wrong.
- Go on to answer the questions in the basic test of the section.
- If you get stuck on a point, check to see if someone else has discussed the point in the forum belonging to the section. If not, take up the point yourself. Your teacher (or a student) will respond to your question within a few hours.
- When you have finished with the exercises and the basic test in a section you should take the final test to get a pass for the section. The requirement here is to answer correctly three questions in a row before you can move on to the next section.
- When you have answered all the questions correctly in both the basic and the final test of this section you will have a pass for it, and can move on to Part 2 of the course.
PS. You must answer all the questions correctly for both the basic and the final test; however, you may do a test several times. Even if you do not pass a test at the first attempt it is your most recent result that appears in the statistics. If you feel that you are familiar with the contents of a section you can go straight to the basic and final tests.
