1. Numerical calculations - Revision history

Tek at 13:32, 29 January 2009

2009-01-29T13:32:41Z

←Older revision		Revision as of 13:32, 29 January 2009
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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'''.

Phil: Edited for idiomatic English by Phil Ramsden--some changes made to information about calculators, which at Imperial varies from course to course

2008-12-30T12:21:27Z

Edited for idiomatic English by Phil Ramsden--some changes made to information about calculators, which at Imperial varies from course to course

Eakc07: Minor grammatical changes

2008-10-21T14:48:50Z

Minor grammatical changes

Eakc07: Minor grammatical changes

2008-10-21T14:42:15Z

Minor grammatical changes

←Older revision		Revision as of 14:42, 21 October 2008
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-	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.).	+	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 EURO, 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.	+	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''.)	+	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. Even logarithms can be regarded as a reverse operation to exponentiation. (This you can read about in Part 3 ''Roots and Logarithms''.)


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	Fun puzzles with sound can be found, inter alia, on Puzzel Playground [http://www.puzzles.com/puzzleplayground/Numbers.htm Puzzel Playground ]]]		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.'''	+	''' It is important to note that the material in this section — as well as in other parts of the course — is designed so 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.	+	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. For advanced courses in mathematics one has hardly any use of calculators as the mathematics is more about understanding principles than performing calculations. 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.


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	'''To do well in arithmetic '''		'''To do well in arithmetic '''

-	# Start by reading the section's theory and study the examples.	+	# Start by reading the section's theory and study the examples.
	# Work through the exercises 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		# Work through the exercises 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
	# Then go ahead and answer the questions in the basic test of the section.		# Then go ahead and answer the questions in the basic test of the section.

Eakc07 at 14:34, 21 October 2008

2008-10-21T14:34:58Z

←Older revision		Revision as of 14:34, 21 October 2008
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-	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."	+	Arithmetic is the study of the properties of numbers and the four basic operations: addition, subtraction, multiplication and division. We usually separate mathematics into 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."

Tek at 08:19, 10 September 2008

2008-09-10T08:19:58Z

←Older revision		Revision as of 08:19, 10 September 2008
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-	<div class="inforuta">	+	<div class="inforuta" style="width: 580px;">
	'''To do well in arithmetic '''		'''To do well in arithmetic '''

Tekbot: 1. Numerisk räkning moved to 1. Numerical calculations: Robot: moved page

2008-09-09T12:18:23Z

1. Numerisk räkning moved to 1. Numerical calculations: Robot: moved page

←Older revision

Revision as of 12:18, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T06:18:49Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

←Older revision		Revision as of 06:18, 21 August 2008
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-	[[~~Bild~~:pussel.jpg\|thumb\|250px\|	+	[[Image: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 ]]]		Fun puzzles with sound can be found, inter alia, on Puzzel Playground [http://www.puzzles.com/puzzleplayground/Numbers.htm Puzzel Playground ]]]

Tek: small fixes

2008-08-13T12:38:59Z

small fixes

←Older revision		Revision as of 12:38, 13 August 2008
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	'''		'''

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




-	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."

		+
		+	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.).		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.		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.)	+	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''.)


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	# Start by reading the section's theory and study the examples.		# 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	+	# Work through the exercises 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
	# Then go ahead and answer the questions in the basic test of the section.		# 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.		# 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.

Ian at 07:35, 15 July 2008

2008-07-15T07:35:13Z

←Older revision		Revision as of 07:35, 15 July 2008
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	<div class="inforuta">		<div class="inforuta">
-	'''~~Success with~~ arithmetic '''	+	'''To do well in arithmetic '''

	# Start by reading the section's theory and study the examples.		# Start by reading the section's theory and study the examples.

←Older revision		Revision as of 12:21, 30 December 2008
Line 26:		Line 26:


-	Arithmetic is the study of the properties of numbers and the four basic operations: addition, subtraction, multiplication and division~~. We usually separate mathematics into 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."~~	+	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 EURO~~, amount per guest: 1 / 8 cake, perimeter of the circle: 2 cm.).	+	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.		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.)
-	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~~. Even~~ logarithms can be regarded as a reverse operation to exponentiation. (This you can read about in Part 3 ''Roots and Logarithms''.)	+



	[[Image:pussel.jpg\|thumb\|250px\|		[[Image: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 ]]]	+	Fun puzzles with sound, amongst other things, can be found at [http://www.puzzles.com/puzzleplayground/Numbers.htm Puzzle Playground ]]]

-	''' 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 ~~reader does~~ not need ~~the use of~~ a calculator.'''	+	''' 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.'''

-	~~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. For advanced courses in mathematics one has hardly any use of calculators as the mathematics is more about understanding principles than performing calculations. ~~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.	+	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.


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	# Start by reading the section's theory and study the examples.		# Start by reading the section's theory and study the examples.
-	# Work through the exercises and try to solve them without using a calculator. ~~Make sure~~ 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.	+	# 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.
-	# ~~Then go ahead and~~ answer the questions in the basic test of the section.	+	# 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.	+	# 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 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 ~~this section~~ and can move on to Part 2 of the course.	+	#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.		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 ~~succeed in passing~~ a test at first attempt, it is your ~~last~~ result that appears in the statistics.	+	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.
-	If you feel that you are familiar with the contents of a section you can go ~~directly~~ to the basic and final tests.	+


	</div>		</div>

←Older revision		Revision as of 14:48, 21 October 2008
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	Fun puzzles with sound can be found, inter alia, on Puzzel Playground [http://www.puzzles.com/puzzleplayground/Numbers.htm Puzzel Playground ]]]		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 so that ~~one~~ does not use ~~calculators~~.'''	+	''' 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 reader does not need the use of a calculator.'''

	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. For advanced courses in mathematics one has hardly any use of calculators as the mathematics is more about understanding principles than performing calculations. 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.		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. For advanced courses in mathematics one has hardly any use of calculators as the mathematics is more about understanding principles than performing calculations. 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.
Line 53:		Line 53:

	# Start by reading the section's theory and study the examples.		# Start by reading the section's theory and study the examples.
-	# Work through the exercises 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	+	# Work through the exercises and try to solve them without using a calculator. Make sure 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.
-	# Then go ahead and answer the questions in the basic test of the section.	+	# 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.	+	# 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 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.	+	#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 this section and can move on to Part 2 of the course.



	PS.		PS.
-	You must answer all the questions correctly for both the basic and the final test, ~~but~~ you may do a 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.	+	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 succeed in passing a test at first attempt, it is your last result that appears in the statistics.
-	If you feel that you are familiar with the contents of a section you can go directly to the basic and final tests.	+	If you feel that you are familiar with the contents of a section you can go directly to the basic and final tests.


	</div>		</div>