1. Numerische Berechnungen
Aus Online Mathematik Brückenkurs 1
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| - | '''Vad är ett tal och vem hittade på de olika räknesätten?''' | + | '''What is a number and who invented in the four basic arithmetic operations ? |
| + | Vad är ett tal och vem hittade på de olika räknesätten?''' | ||
| - | Titta på videon där universitetslektor Lasse Svensson berättar om hur aritmetiken utvecklats och svarar på Elins frågor. | ||
| + | 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. on 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 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." | ||
| - | Denna första del av kursen handlar om numerisk räkning, dvs. räkning med tal. Ett annat namn för detta är '''aritmetik'''. | ||
| + | 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 then, 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.) | |
| - | Räkneoperationerna är uppbyggda i en hierarki som börjar med addition och dess omvändning subtraktion. Utifrån addition kommer multiplikation, som är en addition upprepad flera gånger. Den omvända operationen till multiplikation är division. | ||
| + | [[Bild:pussel.jpg|thumb|250px| | ||
| + | Fun puzzles with sound can be found, inter alia, on Puzzel Playground [http://www.puzzles.com/puzzleplayground/Numbers.htm 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 been hardly any use of calculators, as the mathematics is more about understanding principles 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. | ||
| - | [[Bild:pussel.jpg|thumb|250px|Roliga pussel med tal hittar du bland annat på [http://www.puzzles.com/puzzleplayground/Numbers.htm Puzzel Playground ]]] | ||
| - | '''Observera att materialet i denna kursdel — liksom i övriga delar av kursen — är utformat för att man ska arbeta med det utan hjälp av miniräknare.''' | ||
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| - | När du kommer till högskolan kommer du nämligen ''inte'' att få använda miniräknare på dina "tentor", åtminstone inte på grundkurserna. På högre kurser i matematik har man knappast någon användning för miniräknare, eftersom matematiken då mer handlar om att förstå principer än att utföra räkneoperationer. Det är exempelvis viktigare att förstå varför 7 + 3 är detsamma som 3 + 7, än att kunna utföra additionen och få fram svaret 10. | ||
<div class="inforuta"> | <div class="inforuta"> | ||
| - | ''' | + | '''Success with arithmetic ''' |
| - | # | + | # Start by reading the section's theory and study the examples. |
| - | # | + | # Work through the practice questions and try to solve them without using a calculator. Make sure that you have the right answer by clicking on the answer button. If you do not have it, you can click on the solution button to see what went wrong |
| - | # Gå därefter vidare och svara på frågorna i grundprovet som hör till avsnittet. | + | |
| - | # | + | |
| - | # | + | # Gå därefter vidare och svara på frågorna i grundprovet som hör till avsnittet. Then go ahead and 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 are 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 correctly all questions in both the basic and the final test of this section you will have a pass for this section and can move on to Part 2 of the course. | ||
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| + | PS. | ||
| + | If you feel that you know the contents of a section you can test to go directly to basic and final tests. You must answer all the questions correctlyfor both tests, but you may do the test several times. Even if you do not succeed in passing a test at first attempt, it is your last results, which appear in the statistics. | ||
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| - | PS. Tycker du att innehållet i ett avsnitt känns väldigt bekant, så kan du testa att gå direkt till grundprovet och slutprovet. Du måste få alla rätt på ett prov, men kan göra om provet flera gånger, om du inte lyckas på första försöket. Det är ditt senaste resultat som visas i statistiken. | ||
</div> | </div> | ||
Version vom 14:45, 1. Jul. 2008
| \displaystyle \text{@(a class="image" href="http://smaug.nti.se/temp/KTH/film3.html" target="_blank")@(img src="http://wiki.math.se/wikis/2008/forberedandematte1/img_auth.php/0/00/Lars_och_Elin.jpg" alt="Film om tal")@(/img)@(/a)} |
What is a number and who invented in the four basic arithmetic operations ? Vad är ett tal och vem hittade på de olika räknesätten?
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. on 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 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 then, 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.)
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 been hardly any use of calculators, as the mathematics is more about understanding principles 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.
Success with arithmetic
- Start by reading the section's theory and study the examples.
- Work through the practice questions and try to solve them without using a calculator. Make sure that you have the right answer by clicking on the answer button. If you do not have it, you can click on the solution button to see what went wrong
- Gå därefter vidare och svara på frågorna i grundprovet som hör till avsnittet. Then go ahead and 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 are 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 correctly all questions in both the basic and the final test of this section you will have a pass for this section and can move on to Part 2 of the course.
PS. If you feel that you know the contents of a section you can test to go directly to basic and final tests. You must answer all the questions correctlyfor both tests, but you may do the test several times. Even if you do not succeed in passing a test at first attempt, it is your last results, which appear in the statistics.
