2. Algebra - Revision history

Tek at 13:33, 29 January 2009

Tek — Thu, 29 Jan 2009 13:33:55 GMT

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-	'''Why do we use letters and who were the first to do this? '''
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-	''Watch the video in which the lecturer Lasse Svensson tells us how algebra
-	developed and answers Elins questions about Part 2 of the course.
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	Algebra is the branch of mathematics that is concerned with symbolic expressions and variables, not just calculations with numbers.		Algebra is the branch of mathematics that is concerned with symbolic expressions and variables, not just calculations with numbers.

Phil: Edited for idiom; Phil Ramsden

Phil — Tue, 30 Dec 2008 16:22:17 GMT

Edited for idiom; Phil Ramsden

←Older revision		Revision as of 16:22, 30 December 2008
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	Algebra is the branch of mathematics that is concerned with symbolic expressions and variables, not just calculations with numbers.		Algebra is the branch of mathematics that is concerned with symbolic expressions and variables, not just calculations with numbers.

		+	Algebra is needed in many situations. For example, it can be used to represent situations in which one or more of the quantities is unknown, and hence perhaps to find the values of these quantities. It can also be used to represent geometrical structures, such as curves on the plane.

-	~~Algebra~~ is ~~needed in many situations. For example algebra can~~ be ~~used~~ to ~~describe mathematical problems and to solve equations. Among other things it can~~ ~~describe geometric facts by means~~ of ~~algebraic statements and many problems can~~ be ~~resolved with~~ the ~~help~~ of ~~algebraic operations~~.	+	In some cases, too, we use symbols because it is important that a number be exactly specified; perhaps, for example, a circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to be <math>\sqrt{3}</math>, or the value of a constant is to be exactly <math>\dfrac{1-\ln 2}{3}</math>.

-	In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that a given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to be <math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.

-		+	[[Image:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The solution (''x'',''y'') of these two simultaneous equations corresponds to the common point of these lines, that is their point of intersection. ]]
-	[[Image:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The ~~common~~ solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]	+	Then it may be easier just to call the number, for example, ''a''. In return you must accept that at the end of a calculation, you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.
-	Then it may be easier just to call the number, for example, ''a''. In return you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.	+

	A common situation where algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.		A common situation where algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.


-	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. ~~Which of these~~ is ~~to be considered as~~ ”simple” is sometimes obvious, but it can also depend on what you want to do with the expression.	+	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another, which exactly equivalent mathematically but which is in some sense simpler. What is meant by ”simple” is sometimes obvious, but it can also depend on what you want to do with the expression.

-	When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.	+	When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.


	'''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 — 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~~.''	+	''Calculators are not used at all on some degree courses, and on others their use is limited.''


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	#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 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 3 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 3 of the course.

Eakc07: Minor Grammatical Changes

Eakc07 — Wed, 22 Oct 2008 00:10:31 GMT

Minor Grammatical Changes

Tek at 08:27, 10 September 2008

Tek — Wed, 10 Sep 2008 08:27:46 GMT

←Older revision		Revision as of 08:27, 10 September 2008
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-	<div class="inforuta">	+	<div class="inforuta" style="width:580px;">
	'''To do well in Algebra'''		'''To do well in Algebra'''

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

Tekbot — Thu, 21 Aug 2008 06:18:59 GMT

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

←Older revision		Revision as of 06:18, 21 August 2008
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-	[[~~Bild~~:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The common solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]	+	[[Image:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The common solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]
	Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.		Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.

Tek: small fixes

Tek — Thu, 14 Aug 2008 14:27:05 GMT

small fixes

←Older revision		Revision as of 14:27, 14 August 2008
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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.
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	# 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 3 of the course.		# 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 3 of the course.

-	PS. If you feel that you are very familiar with the contents of a section you can test yourself by going directly to the basic and final tests. You must answer all the questions correctly in a test, but you may do the test several times if you do not succeed at the first attempt. It is your final results which appear in the statistics.	+	P.S. If you feel that you are very familiar with the contents of a section you can test yourself by going directly to the basic and final tests. You must answer all the questions correctly in a test, but you may do the test several times if you do not succeed at the first attempt. It is your final results which appear in the statistics.

	</div>		</div>

Ian at 17:51, 6 August 2008

Ian — Wed, 06 Aug 2008 17:51:58 GMT

←Older revision		Revision as of 17:51, 6 August 2008
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-	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. Which of these ~~are~~ considered as ”simple” is sometimes obvious, but it can also depend on what you want to do with the expression.	+	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. Which of these is to be considered as ”simple” is sometimes obvious, but it can also depend on what you want to do with the expression.

	When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.		When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.
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	'''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 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.''	+	''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.''

Ian at 13:36, 17 July 2008

Ian — Thu, 17 Jul 2008 13:36:02 GMT

←Older revision		Revision as of 13:36, 17 July 2008
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	\|}		\|}

-	'''Why do we use letters ~~letters~~ and who were the first to do this? '''	+	'''Why do we use letters and who were the first to do this? '''


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	Algebra is needed in many situations. For example algebra can be used to describe mathematical problems and to solve equations. Among other things it can describe geometric facts by means of algebraic statements, and many problems can be resolved with the help of algebraic operations.		Algebra is needed in many situations. For example algebra can be used to describe mathematical problems and to solve equations. Among other things it can describe geometric facts by means of algebraic statements, and many problems can be resolved with the help of algebraic operations.

-	In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to ~~b e~~<math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.	+	In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that a given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to be <math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.


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	Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.		Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.

-	A common situation where it algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.	+	A common situation where algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.


-	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. Which of these are considered as ”simple”is sometimes obvious, but it can also depend on what you want to do with the expression.	+	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. Which of these are considered as ”simple” is sometimes obvious, but it can also depend on what you want to do with the expression.

	When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.		When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.

Ian at 07:34, 15 July 2008

Ian — Tue, 15 Jul 2008 07:34:30 GMT

←Older revision		Revision as of 07:34, 15 July 2008
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	<div class="inforuta">		<div class="inforuta">
-	'''To ~~succeed you with~~ Algebra'''	+	'''To do well in Algebra'''

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

Ian at 13:48, 10 July 2008

Ian — Thu, 10 Jul 2008 13:48:50 GMT

←Older revision		Revision as of 13:48, 10 July 2008
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	\|}		\|}

-	'''~~Varför räknar vi med bokstäver och vem kom på detta~~?'''	+	'''Why do we use letters letters and who were the first to do this? '''


-	''~~Titta på videon där universitetslektor~~ Lasse Svensson ~~berättar om hur algebran utvecklats och svarar på~~ Elins ~~frågor om Del~~ 2 ~~i kursen~~.''	+	''Watch the video in which the lecturer Lasse Svensson tells us how algebra
		+	developed and answers Elins questions about Part 2 of the course.


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-	Algebra ~~är den gren av matematiken som behandlar räkning med symboliska uttryck och variabler och inte bara räkning med tal~~.	+	Algebra is the branch of mathematics which works with symbolic expressions and variables, and not just calculations with numbers.


-	Algebra ~~behövs i många situationer, t.ex~~. ~~kan~~ algebra ~~användas till att beskriva matematiska problem och till att lösa ekvationer~~. ~~Det går bland annat att beskriva geometriska fakta med hjälp av algebraiska påståenden~~, ~~och många problem går att lösa med hjälp av algebraiska operationer~~.	+	Algebra is needed in many situations. For example algebra can be used to describe mathematical problems and to solve equations. Among other things it can describe geometric facts by means of algebraic statements, and many problems can be resolved with the help of algebraic operations.

		+	In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to b e<math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.

-	I en del fall kan man inte räkna ut värdet av ett uttryck till ett numeriskt värde. Anledningen kan vara att uttrycket innehåller obekanta parametrar eller variabler. Det kan också vara så att det är viktigt att ett tal är exakt angivet, t.ex. att en viss cirkel har en omkrets som är exakt <math>4\pi</math>, eller hypotenusans längd för en triangel är <math>\sqrt{3}</math>, eller varför inte att värdet på en konstant är <math>\dfrac{1-\ln 2}{3}</math>.

		+	[[Bild:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The common solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]
		+	Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.

-	~~[[Bild:grafisk lösning~~.~~gif\|thumb\|250px\|En linjär ekvation med två obekanta kan ses som en linje i ett koordinatsystem. Den gemensamma lösningen (''x''~~,~~''y'') till dessa ekvationer motsvaras då av den gemensamma punkten för dessa linjer, dvs. skärningspunkten.]]~~	+	A common situation where it algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.
-	~~Då kan det vara enklast att i uträkningarna kalla talet för exempelvis ''a''. Som svar kan man också acceptera att man inte kommer fram till ett numeriskt värde~~, ~~utan i stället får ett uttryck som innehåller ''a''~~.	+

-	En vanlig situation där man kan behöva algebra är förenkling. Det är ofta mycket viktigt att förenkla ett uttryck, t.ex. innan man skall derivera, eller när man löser en ekvation.

		+	Simplification reduces the risk of careless mistakes and avoids unnecessary work. To simplify means to transform an expression from one form to another. Which of these are considered as ”simple”is sometimes obvious, but it can also depend on what you want to do with the expression.

-	~~Genom att förenkla minskar man risken för slarvfel och man slipper onödigt arbete~~. ~~Att förenkla innebär att skriva om ett uttryck från en form till en annan~~. ~~Vilken form som betraktas som ”enkel” är ibland uppenbart~~, ~~men det kan också bero på vad man vill göra med uttrycket~~.	+	When differentiating, it may be advantageous to transform the expression into a sum of a number of terms. On the other hand when we solve an equation, it may be advantageous to reformulate the expression as a product of a number of factors. Therefore, one needs to be proficient in converting expressions into different forms.


-	När man deriverar kan det vara fördelaktigt att formulera uttrycket som en summa av ett antal termer. När man löser en ekvation kan det vara fördelaktigt att formulera det som en produkt av ett antal faktorer. Därför behöver man kunna omvandla uttryck mellan olika former.	+	'''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.''
-	''~~'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.'''~~	+
-		+
-	~~''När du kommer till högskolan kommer du nämligen inte att få använda miniräknare på dina~~ "~~tentor~~"~~, åtminstone inte på grundkurserna~~.''	+


	<div class="inforuta">		<div class="inforuta">
-	'''~~Så här lyckas du med Algebran~~'''	+	'''To succeed you with Algebra'''

-	#~~Börja med att läsa genomgången till ett avsnitt och tänka igenom exemplen~~.	+	# Start by reading the section's theory and study the examples.
-	#~~Arbeta sedan med övningsuppgifterna och försök att lösa dem utan miniräknare~~. ~~Kontrollera att du kommit fram till rätt svar genom att klicka på svarsknappen~~. ~~Har du inte det~~, ~~så kan du klicka på lösningsknappen, för att se hur du ska göra.~~	+	#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.
-	# ~~Skulle du fastna~~, ~~se efter om någon ställt en fråga om just detta i avsnittets~~ forum. ~~Ställ annars en fråga om du undrar över något~~. ~~Din lärare~~ (~~eller en studiekamrat~~) ~~kommer att besvara den inom några timmar~~.	+	# 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.
-	#~~När du är klar med övningsuppgifterna och grundproven i ett avsnitt så ska du göra slutprovet för att bli godkänd på avsnittet~~. ~~Där gäller det att svara rätt på tre frågor i följd för att kunna gå vidare~~.	+	#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.
-	#~~När du fått alla rätt på både grundprov och slutprov, så är du godkänd på den delen och kan gå vidare till Del~~ 3 ~~i kursen~~.	+	# 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 3 of the course.

-	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~~.	+	PS. If you feel that you are very familiar with the contents of a section you can test yourself by going directly to the basic and final tests. You must answer all the questions correctly in a test, but you may do the test several times if you do not succeed at the first attempt. It is your final results which appear in the statistics.

	</div>		</div>

←Older revision		Revision as of 00:10, 22 October 2008
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-	Algebra is the branch of mathematics ~~which works~~ with symbolic expressions and variables, ~~and~~ not just calculations with numbers.	+	Algebra is the branch of mathematics that is concerned with symbolic expressions and variables, not just calculations with numbers.


-	Algebra is needed in many situations. For example algebra can be used to describe mathematical problems and to solve equations. Among other things it can describe geometric facts by means of algebraic statements, and many problems can be resolved with the help of algebraic operations.	+	Algebra is needed in many situations. For example algebra can be used to describe mathematical problems and to solve equations. Among other things it can describe geometric facts by means of algebraic statements and many problems can be resolved with the help of algebraic operations.

	In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that a given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to be <math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.		In some cases the value of an expression does not simplify to a numeric value. The reason may be that the expression includes unknown parameters or variables. It may also be that it is important that a number be exactly specified, such as that a given circle is to have a circumference of exactly <math>4\pi</math> units, or the hypotenuse of a triangle is to be <math>\sqrt{3}</math>, or even that the value of a constant is to be <math>\dfrac{1-\ln 2}{3}</math>.
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	[[Image:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The common solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]		[[Image:grafisk lösning.gif\|thumb\|250px\|A linear equation with two unknowns can be interpreted as a straight line in a coordinate system. The common solution (''x'',''y'') to these two equations corresponds to the common point of these lines, that is their point of intersection. ]]
-	Then it may be easier just to call the number, for example, ''a''. In return, you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.	+	Then it may be easier just to call the number, for example, ''a''. In return you must accept that you may not arrive at a numerical value, but instead may finish up with an expression that contains ''a''.

	A common situation where algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.		A common situation where algebra may be necessary is simplification. It is often very important to simplify an expression, such as before differentiation, or when an equation is to be solved.
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-	'''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.''		''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.''
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	# 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 3 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 3 of the course.

-	P.S. If you feel that you are very familiar with the contents of a section you can test yourself by going directly to the basic and final tests. You must answer all the questions correctly in a test, but you may do the test several times if you do not succeed at the first attempt. It is your final results ~~which~~ appear in the statistics.	+	P.S. If you feel that you are very familiar with the contents of a section you can test yourself by going directly to the basic and final tests. You must answer all the questions correctly in a test, but you may do the test several times if you do not succeed at the first attempt. It is your final results that will appear in the statistics.

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