Difference between revisions of "LibreOffice-Suite-Math/C3/Set-Operations-Factorials-Cross-reference-equations/English-timed"

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{| border=1
 
{| border=1
!Visual Cues
+
|'''Time'''
!Narration
+
|'''Narration'''
 +
 
 
|-
 
|-
|Show Slide Number 1
+
|00:00
 +
|Welcome to the '''Spoken tutorial''' on '''LibreOffice Math'''.
  
Spoken tutorial on LibreOffice Math
+
|-
 +
|00:04
 +
|In this tutorial, we will learn how to:
  
Learning Objectives
+
|-
 +
|00:07
 +
|Write '''Set operations'''
  
*Write Set operations
+
|-
 +
|00:10
 +
|Write '''Factorial'''s and
  
*Write Factorials
+
|-
 +
|00:12
 +
|'''Cross reference''' equations by numbering.
  
*Cross reference equations by numbering
+
|-
|Welcome to the Spoken tutorial on LibreOffice Math.
+
|00:16
 +
|For this, let us first open our example 'Writer' document that we created in our previous tutorials "MathExample1.odt".
  
In this tutorial, we will learn how to
+
|-
 +
|00:29
 +
|Here, let us go to the end of the document and press '''Control, Enter''' to go to a new page.
  
Write Set operations
+
|-
 +
|00:37
 +
|And type “Set Operations: ” and press  '''Enter''' twice.
  
Write Factorials and
+
|-
 +
|00:42
 +
|Now, let us call '''Math'''.
  
Cross reference equations by numbering
 
 
|-
 
|-
|Open the MathExample1.odt (created in part 2)
+
|00:45
|For this, let us first open our example Writer document that we created in our previous tutorials: MathExample1.odt.
+
|Before we go ahead, let us increase the Font-size to '''18 point'''.
 +
 
 
|-
 
|-
|Scroll to last page, go to the end.
+
|00:51
 +
|Change the '''Alignment''' to the '''Left'''.
  
Press Control  - Enter to go to a new page
+
|-
 +
|00:54
 +
|Let us now learn how to write '''Set operations'''.
  
Type “Set Operations: ” in Writer on this fresh page. Press enter twice.
+
|-
 +
|01:00
 +
|'''Math''' has separate '''mark up''' to represent '''Set'''s which are collections of distinct '''element'''s.
  
Click Insert > Object > Formula
+
|-
|Here let us go to the end of the document and press Control Enter to go to a new page.
+
|01:07
 +
|Let us write four (4) example '''set'''s, in the '''Formula Editor''' window, as shown on the screen:
  
And type “Set Operations: ” and press the Enter key twice.
+
|-
 +
|01:14
 +
|'''Set A''' with 5 elements,
  
Now let us call Math.
 
 
|-
 
|-
|Click Format menu > Font size. Increase size to 18 pt.
+
|01:18
 +
| Set B,Set C,
  
Click Format menu > Alignment, choose left option
+
|-
 +
|01:21
 +
|and Set D with elements each.
  
All pink coloured text goes into Formula Editor Window (FEW in short)
+
|-
 +
|01:26
 +
|Notice that to write the brackets for sets, we can use the '''mark up: lbrace''' and '''rbrace'''.
  
In FEW, copy and paste:
+
|-
 +
|01:35
 +
|Now, we can write '''set operation'''s such as '''union'''s and '''intersection'''s.
  
A ~=~ lbrace 1, 2, 3, 4, 5 rbrace newline
+
|-
 +
|01:42
 +
|First, let us write a '''union operation'''.
  
B ~=~ lbrace 1, 2 rbrace newline
+
|-
 +
|01:46
 +
|The mark-up for '''B union C''' is the same as we read it;
  
C ~=~ lbrace 4, 5 rbrace newline
+
|-
 +
|01:51
 +
|and the resulting set is 1, 2, 6, 4 and 5 which includes all the distinct elements in both sets.
  
D ~=~ lbrace 6, 7 rbrace newline newline
+
|-
|Before we go ahead, let us increase the font size to 18 point.
+
|02:04
 +
|The markup for an '''intersection operation''' is again the same as we read it.
  
Change the alignment to the left.
+
|-
 +
|02:10
 +
|The '''intersection''' includes only the common elements from both the sets.
  
Let us now learn how to write Set operations.
+
|-
 +
|02:16
 +
|So, the result of '''B intersection D''' is 6.
  
Math has separate mark up to represent Sets, which are collections of distinct elements.
+
|-
 +
|02:23
 +
|And we can also write: '''set C''' is a '''subset''' of '''set A''', as every element in 'C' is in '''set A'''.
  
Let us write 4 example sets in the Formula Editor window as shown on the screen:
+
|-
 +
|02:35
 +
|The '''mark up''' for this is '''C subset A'''.
  
Set A with 5 elements
+
|-
 +
|02:42
 +
|You can learn to write more set operations by exploring the '''Elements''' window, by clicking on the third icon there.
  
Set B
+
|-
 +
|02:51
 +
|Go to '''View > Elements > Set Operations'''.
  
Set C
+
|-
 +
|02:59
 +
|Let us '''save''' our work now.
  
And Set D equal to 6, and 7, with 2 elements each.
 
 
|-
 
|-
|Point mouse over the four sets in Writer gray box
+
|03:02
 +
|Click on '''File > Save'''.
  
In FEW, point mouse over above mark up.
+
|-
 +
|03:06
 +
|Now, let us write '''Factorial function'''s.  
  
In FEW, press enter twice, copy and paste:
+
|-
 +
|03:11
 +
|We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
  
B union C ~=~ lbrace 1, 2, 6, 4, 5 rbrace  newline newline
+
|-
 +
|03:19
 +
|These will help to '''cross reference''' them anywhere within the '''Writer''' document.
  
In FEW, point mouse over ‘Union’ word
+
|-
 +
|03:25
 +
|Let us go to a new page by clicking three times slowly, outside the '''Writer gray box'''.
  
Point mouse over the last formula in Writer gray box
+
|-
 +
|03:33
 +
|Press '''Control, Enter'''.
  
In FEW, press enter twice, copy and paste:
+
|-
 +
|03:36
 +
|Type: “Factorial Function: ” and press '''Enter''' twice.
  
B intersection D ~=~ lbrace 6  rbrace  newline newline
+
|-
 +
|03:42
 +
|Now, we know how to call '''Math'''.
  
Point mouse over the last formula in Writer gray box
+
|-
 +
|03:45
 +
|But, there is another way to bring up the '''Math object''' into the '''Writer'''.
  
In FEW, press enter twice, copy and paste:
+
|-
 +
|03:51
 +
|For this, simply write ‘f n’ on the '''Writer document''' and press '''F3'''.
  
C subset A newline newline
+
|-
 +
|03:59
 +
|We are now seeing a new '''Math object''' that says '''E is equal to m c squared'''
  
Point mouse over the subset symbol in the last formula in Writer gray box
+
|-
 +
|04:07
 +
|and along with that the number one (1), within parentheses, on the right.
  
In FEW, point mouse over the last line.
+
|-
 +
|04:14
 +
|Meaning- we can '''cross reference''' this formula with the number 1, anywhere in this document.  
  
If elements window not visible, click View >Elements.
+
|-
 +
|04:22
 +
|We will learn the details of how to do this later.
  
In the Elements window, click the third icon in the Elements window and slowly mouse over on the elements, to show tool tips.
+
|-
 +
|04:27
 +
|For now, let us double-click on the '''Math object'''.  
  
Click  File > Save.
+
|-
|Notice that to write the brackets for sets, we can use the mark up: lbrace and rbrace.
+
|04:32
 +
|And do the formatting. '''Font size 18''' and ''''Left' Alignment'''.
  
Now we can write set operations such as unions and intersections.
+
|-
 +
|04:40
 +
|Okay, let us now write an example for '''Factorial'''.  
  
First let us write a union operation.  
+
|-
 +
|04:44
 +
|The '''mark up''' ‘fact’ represents the '''factorial''' symbol.
  
The mark up for B union C is the same as we read it;
+
|-
 +
|04:50
 +
|So, let us overwrite the existing formula with ours:
  
and the resulting set is 1, 2, 6, 4, and 5, which includes all the distinct elements in both the sets.
+
|-
 +
|04:55
 +
|'''5 Factorial = 5 into 4 into 3 into 2 into 1 = 120'''.
  
The markup for an intersection operation is again the same as we read it.
+
|-
 +
|05:07
 +
|Notice the '''mark up''' here.
  
The intersection includes only the common elements from both the sets.
+
|-
 +
|05:09
 +
|Let us write our next formula in a new '''Math object''' here.
  
So the result of B intersection D is 6.
+
|-
 +
|05:14
 +
|For this, let us first click outside this '''Writer gray box''' three times slowly.
  
And we can also write: set C is a subset of set A, as every element in C is in set A.
+
|-
 +
|05:23
 +
|Press the down-arrow key two or three times to go to the end of this page.
  
The mark up for this is C subset A.
+
|-
 +
|05:30
 +
|And type ‘f n’ and press '''F3''' to bring up the second '''Math object'''.
  
You can learn to write more set operations, by exploring the Elements window by clicking on the third icon there.
+
|-
 +
|05:37
 +
|Again, we will repeat the formatting
  
Go to View> Elements> Set Operations.
+
|-
 +
|05:46
 +
|and overwrite the existing formula with the '''factorial''' definition:
  
Let us save our work now.  
+
|-
 +
|05:52
 +
|'''n factorial is equal to prod from k = 1 to n of k'''.
  
Click on File>Save.
 
 
|-
 
|-
|Click three times slowly outside right of Writer gray box. Now then click again.
+
|06:01
 +
|Notice the mark-up ‘prod’ which denotes product, similar to '''sigma''' for summation.
  
Press Control  -Enter
+
|-
 
+
|06:10
Type: “Factorial Function: ” and press enter twice
+
|Now, let us introduce a third Math object just like the first two
 
+
Type fn and press F3
+
 
+
Point mouse over E = mc squared in Writer gray box
+
 
+
Point mouse over (1) on the right in Writer gray box
+
 
+
Double click on E = mc squared in Writer gray box
+
 
+
Click Format menu > Font size. Increase size to 18 pt.
+
 
+
Click Format menu > Alignment, chooses left option
+
|Now let us write Factorial functions.
+
 
+
We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
+
 
+
These will help to cross reference them anywhere within the Writer document.
+
 
+
Let us go to a new page by clicking three times slowly outside the Writer gray box.
+
 
+
Press Control  -Enter.
+
 
+
Type “Factorial Function: ” and press enter twice.
+
 
+
Now, we know how to call Math.
+
 
+
But there is another way to bring up the Math object into the Writer.
+
 
+
For this simply write ‘f n’ on the Writer document and press F3.
+
 
+
We are now seeing a new Math object that says E is equal to m c squared;
+
 
+
and along with that, the number one within parentheses, on the right.
+
 
+
Meaning, we can cross reference this formula with the number 1 anywhere in this document; we will learn the details of how to do this later.
+
 
+
For now, let us double click on the Math object
+
  
And do the formatting. Font size 18 and Left Alignment.
 
 
|-
 
|-
|In FEW, overwrite existing formula. So press Control + A to select all, then copy and paste:
+
|06:20
 +
|and rewrite the factorial definition as two conditional formulae, as shown on the screen.
  
fact 5 = 5 times 4 times 3 times 2 times 1  = 120
 
 
In FEW, point mouse over ‘fact’ word in the last line
 
 
Click outside this Writer gray box three times slowly
 
 
Press the down arrow key two or three times to go to the end of this page.
 
 
Type ‘fn’ and press F3
 
 
Double click on E = mc squared in Writer gray box
 
 
Click Format menu > Font size. Increase size to 18 pt.
 
 
Click Format menu > Alignment, chooses left option
 
 
In FEW, overwrite existing formula. So press Control  - A to select all, then copy and paste:
 
 
fact n ~=~ prod from k = 1 to n k newline
 
 
In FEW, point mouse over ‘prod’ word in the last line
 
 
Click outside this second Writer gray box three times slowly
 
 
Press the down arrow key two or three times to go to the end of this page.
 
 
Type ‘fn’ and press F3
 
 
Double click on E = mc squared in Writer gray box
 
 
Click Format menu > Font size. Increase size to 18 pt.
 
 
Click Format menu > Alignment, chooses left option
 
 
In FEW, overwrite existing formula.
 
 
So press Control + A to select all, then copy and paste:
 
 
fact n ~=~ left lbrace binom{1 ~ "if n = 0"}{fact(n-1) `times` n ~ " if n > 0 "} right none newline newline
 
 
Point mouse over this formula in  Writer gray box
 
 
In FEW, point mouse over ‘binom’ word in the last line
 
|Okay, let us now write an example for Factorial.
 
 
The mark up ‘fact’ represents the factorial symbol.
 
 
So let us overwrite the existing formula with ours:
 
 
5 Factorial = 5 into 4 into 3 into 2 into 1 = 120.
 
 
Notice the mark up here.
 
 
Let us write our next formula in a new Math object here.
 
 
For this, let us first click outside this Writer gray box three times slowly.
 
 
Press the down arrow key two or three times to go to the end of this page.
 
 
And type ‘f n’ and press F3 to bring up the second Math object.
 
 
Again, we will repeat the formatting
 
 
and overwrite the existing formula with the factorial definition:
 
 
N factorial is equal to prod from k = 1 to n of k.
 
 
Notice the mark up ‘prod’ which denotes product, similar to sigma for summation.
 
 
Now, let us introduce a third Math object just like the first two
 
 
and rewrite the factorial definition as two conditional formulae as shown on the screen.
 
 
Notice the mark up ‘binom’, which displays a vertical stack of two elements and helps with better alignment.
 
 
|-
 
|-
|Click three times outside Writer gray box, press Control + Enter
+
|06:30
 
+
|Notice the '''mark up''' ‘binom’ which displays a vertical stack of two elements and helps with better alignment.
Type: An example of factorial is provided here:
+
 
+
Click Insert menu > Cross reference
+
 
+
In the popup, click on Text in the Type list
+
  
Click on first item in the Selection list on the right
+
|-
 
+
|06:42
Click Reference in the ‘Insert reference to’ list , click on Insert once and click on close
+
 
+
Point mouse over (1).
+
 
+
Click on (1).
+
 
+
Point mouse over the formula numbered 1.
+
 
+
Click File > Save
+
 
|Let us now see how we can cross reference these formulae.
 
|Let us now see how we can cross reference these formulae.
  
For this, let us go to a new page
+
|-
 +
|06:47
 +
|For this, let us go to a new page
  
and type: An example of factorial is provided here:
+
|-
 +
|06:51
 +
|and type: "An example of factorial is provided here:"
  
Now let us click on the Insert menu, and on Cross reference.  
+
|-
 +
|06:59
 +
|Now, let us click on the '''Insert''' menu and on '''Cross reference'''.  
  
In the new popup, let us select “Text” in the Type list.
+
|-
 +
|07:06
 +
|In the new pop-up, let us select '''Text''' in the '''Type''' list.
  
Then choose the first item in the Selection list denoting the first factorial formula we wrote.
+
|-
 +
|07:12
 +
|Then choose the first item in the '''Selection''' list denoting the first factorial formula we wrote.
  
Now choose Reference in the ‘Insert reference to’ list and click on Insert once and close.
+
|-
 +
|07:21
 +
|Now choose '''Reference''' in the '''‘Insert reference to’''' list and click on '''Insert''' once and close.
  
So the number one in parentheses has appeared next to our text. And we are done.
+
|-
 +
|07:31
 +
|So, the number one (1) in parentheses has appeared next to our text. And we are done.
  
Let us test it by simply clicking on this number;
+
|-
 +
|07:39
 +
|Let us test it by simply clicking on this number
  
And notice that the cursor has jumped to the location where we wrote the first formula.
+
|-
 
+
|07:43
So this is how we can cross reference Math formulae anywhere within the Writer document.
+
|and notice that the cursor has jumped to the location where we wrote the first formula.
  
Let us save our work.
 
 
|-
 
|-
|Show Slide Number 2
+
|07:51
 +
|So, this is how we can '''cross reference''' Math formulae anywhere within the '''Writer document'''.
  
References for Math:
+
|-
 
+
|07:58
Guide:
+
|Let us '''save''' our work.
  
http://www.libreoffice.org/get-help/documentation/
+
|-
 
+
|08:01
http://help.libreoffice.org/Math/Welcome_to_the_Math_Help
+
 
|Here are some reference links for Math:
 
|Here are some reference links for Math:
  
Download guides at libreoffice.org documentation link.
+
|-
 +
|08:06
 +
|Download '''Guide''' at 'libreoffice.org documentation' link.
  
You can also visit help.libreoffice.org/Math for more information on Math
 
 
|-
 
|-
|Show Slide Number 3
+
|08:14
 +
|You can also visit the following website for more information on Math.
  
Math mark up assignment:
+
|-
 
+
|08:20
1. Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
+
 
+
2. Write the results of  subtraction of set B from set A
+
 
+
3. Cross reference the second and third factorial formulae in the example document in the Writer document
+
 
|And finally, here is an assignment for you. Use the Writer document.
 
|And finally, here is an assignment for you. Use the Writer document.
  
1. Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C
+
|-
 +
|08:25
 +
|Using the example '''Set'''s in this tutorial: check if '''A union ( B union C) is equal to (A union B) union C'''.
  
2. Write the results of A minus B
+
|-
 +
|08:40
 +
|Write the results of '''A minus B'''
  
3. And cross reference the second and third factorial formulae in the Writer document
 
 
|-
 
|-
|Show Slide Number 3
+
|08:43
 +
|and cross reference the second and third '''factorial''' formulae in the Writer document.
  
Summary:
+
|-
 +
|08:51
 +
|This brings us to the end of this tutorial on '''Sets, Factorials''' and '''Cross Referencing''' in '''LibreOffice Math'''.
  
*Write Set operations
+
|-
 +
|08:59
 +
|To summarize, we learned how to:
  
*Write Factorials and
+
|-
 +
|09:03
 +
|Write '''Set''' operations
  
*Cross reference equations by numbering
+
|-
|This brings us to the end of this tutorial on Sets, Factorials and Cross Referencing in LibreOffice Math.
+
|09:05
 +
|Write '''Factorial'''s and  
  
To summarize, we learned how to:
+
|-
 +
|09:08
 +
|'''Cross reference''' equations by numbering.
  
Write Set operations
+
|-
 +
|09:11
 +
|'''Spoken Tutorial''' project is a part of the '''Talk to a Teacher''' project, supported by the National Mission on Education through ICT, MHRD, Government of India.
  
Write Factorials and
+
|-
 +
|09:23
 +
|This project is coordinated by http://spoken-tutorial.org.
 +
 
 +
|-
 +
|09:27
 +
|More information on the same is available at the following link.
  
Cross reference equations by numbering
 
 
|-
 
|-
|Acknowledgement Slide
+
|09:32
|Spoken Tutorial Project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.
+
|This script has been contributed by Priya Suresh, Desicrew Solutions. And this is Saundarya, desicrew solutions,  signing off.
This project is co-ordinated by http://spoken-tutorial.org.
+
Thanks for joining.
More information on the same is available at the following link http://spoken-tutorial.org/NMEICT-Intro.
+
This script has been contributed by Priya Suresh, Desicrew Solutions, and this is (the name of the narrator and affiliation
+
and place) signing off. Thanks for joining.
+

Latest revision as of 10:30, 24 March 2017

Time Narration
00:00 Welcome to the Spoken tutorial on LibreOffice Math.
00:04 In this tutorial, we will learn how to:
00:07 Write Set operations
00:10 Write Factorials and
00:12 Cross reference equations by numbering.
00:16 For this, let us first open our example 'Writer' document that we created in our previous tutorials "MathExample1.odt".
00:29 Here, let us go to the end of the document and press Control, Enter to go to a new page.
00:37 And type “Set Operations: ” and press Enter twice.
00:42 Now, let us call Math.
00:45 Before we go ahead, let us increase the Font-size to 18 point.
00:51 Change the Alignment to the Left.
00:54 Let us now learn how to write Set operations.
01:00 Math has separate mark up to represent Sets which are collections of distinct elements.
01:07 Let us write four (4) example sets, in the Formula Editor window, as shown on the screen:
01:14 Set A with 5 elements,
01:18 Set B,Set C,
01:21 and Set D with elements each.
01:26 Notice that to write the brackets for sets, we can use the mark up: lbrace and rbrace.
01:35 Now, we can write set operations such as unions and intersections.
01:42 First, let us write a union operation.
01:46 The mark-up for B union C is the same as we read it;
01:51 and the resulting set is 1, 2, 6, 4 and 5 which includes all the distinct elements in both sets.
02:04 The markup for an intersection operation is again the same as we read it.
02:10 The intersection includes only the common elements from both the sets.
02:16 So, the result of B intersection D is 6.
02:23 And we can also write: set C is a subset of set A, as every element in 'C' is in set A.
02:35 The mark up for this is C subset A.
02:42 You can learn to write more set operations by exploring the Elements window, by clicking on the third icon there.
02:51 Go to View > Elements > Set Operations.
02:59 Let us save our work now.
03:02 Click on File > Save.
03:06 Now, let us write Factorial functions.
03:11 We will designate numbers 1 to 3 for the three formulae we are going to write shortly.
03:19 These will help to cross reference them anywhere within the Writer document.
03:25 Let us go to a new page by clicking three times slowly, outside the Writer gray box.
03:33 Press Control, Enter.
03:36 Type: “Factorial Function: ” and press Enter twice.
03:42 Now, we know how to call Math.
03:45 But, there is another way to bring up the Math object into the Writer.
03:51 For this, simply write ‘f n’ on the Writer document and press F3.
03:59 We are now seeing a new Math object that says E is equal to m c squared
04:07 and along with that the number one (1), within parentheses, on the right.
04:14 Meaning- we can cross reference this formula with the number 1, anywhere in this document.
04:22 We will learn the details of how to do this later.
04:27 For now, let us double-click on the Math object.
04:32 And do the formatting. Font size 18 and 'Left' Alignment.
04:40 Okay, let us now write an example for Factorial.
04:44 The mark up ‘fact’ represents the factorial symbol.
04:50 So, let us overwrite the existing formula with ours:
04:55 5 Factorial = 5 into 4 into 3 into 2 into 1 = 120.
05:07 Notice the mark up here.
05:09 Let us write our next formula in a new Math object here.
05:14 For this, let us first click outside this Writer gray box three times slowly.
05:23 Press the down-arrow key two or three times to go to the end of this page.
05:30 And type ‘f n’ and press F3 to bring up the second Math object.
05:37 Again, we will repeat the formatting
05:46 and overwrite the existing formula with the factorial definition:
05:52 n factorial is equal to prod from k = 1 to n of k.
06:01 Notice the mark-up ‘prod’ which denotes product, similar to sigma for summation.
06:10 Now, let us introduce a third Math object just like the first two
06:20 and rewrite the factorial definition as two conditional formulae, as shown on the screen.
06:30 Notice the mark up ‘binom’ which displays a vertical stack of two elements and helps with better alignment.
06:42 Let us now see how we can cross reference these formulae.
06:47 For this, let us go to a new page
06:51 and type: "An example of factorial is provided here:"
06:59 Now, let us click on the Insert menu and on Cross reference.
07:06 In the new pop-up, let us select Text in the Type list.
07:12 Then choose the first item in the Selection list denoting the first factorial formula we wrote.
07:21 Now choose Reference in the ‘Insert reference to’ list and click on Insert once and close.
07:31 So, the number one (1) in parentheses has appeared next to our text. And we are done.
07:39 Let us test it by simply clicking on this number
07:43 and notice that the cursor has jumped to the location where we wrote the first formula.
07:51 So, this is how we can cross reference Math formulae anywhere within the Writer document.
07:58 Let us save our work.
08:01 Here are some reference links for Math:
08:06 Download Guide at 'libreoffice.org documentation' link.
08:14 You can also visit the following website for more information on Math.
08:20 And finally, here is an assignment for you. Use the Writer document.
08:25 Using the example Sets in this tutorial: check if A union ( B union C) is equal to (A union B) union C.
08:40 Write the results of A minus B
08:43 and cross reference the second and third factorial formulae in the Writer document.
08:51 This brings us to the end of this tutorial on Sets, Factorials and Cross Referencing in LibreOffice Math.
08:59 To summarize, we learned how to:
09:03 Write Set operations
09:05 Write Factorials and
09:08 Cross reference equations by numbering.
09:11 Spoken Tutorial project is a part of the Talk to a Teacher project, supported by the National Mission on Education through ICT, MHRD, Government of India.
09:23 This project is coordinated by http://spoken-tutorial.org.
09:27 More information on the same is available at the following link.
09:32 This script has been contributed by Priya Suresh, Desicrew Solutions. And this is Saundarya, desicrew solutions, signing off.

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Jyotisolanki, Krupali, Minal, PoojaMoolya, Pratik kamble, Ranjana, Sandhya.np14, Sneha