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Integral calculus from the modern viewpoint [closed]
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This is a soft question.
What is the purpose of teaching techniques of integration at the college level?
More specifically, in the sense of putting integration into practice, what value does teaching these techniques serve in a world which increasingly depends on approximation and computer algebra systems?
If the use of these techniques in practice is limited, then what should integral calculus be teaching in order to make the content imparted by the class more actionable?
I am assuming that, in general, the students of integral calculus will not go on to be mathematicians.
integration soft-question approximation education riemann-integration
asked Jul 25 at 15:59
Chickenmancer
3,007621
closed as off-topic by Xander Henderson, Adrian Keister, Lord Shark the Unknown, Arnaud Mortier, Parcly Taxel Jul 25 at 16:09
- This question does not appear to be about math within the scope defined in the help center.
add a comment |Â
up vote
1
down vote
favorite
This is a soft question.
What is the purpose of teaching techniques of integration at the college level?
More specifically, in the sense of putting integration into practice, what value does teaching these techniques serve in a world which increasingly depends on approximation and computer algebra systems?
If the use of these techniques in practice is limited, then what should integral calculus be teaching in order to make the content imparted by the class more actionable?
I am assuming that, in general, the students of integral calculus will not go on to be mathematicians.
integration soft-question approximation education riemann-integration
asked Jul 25 at 15:59
Chickenmancer
3,007621
closed as off-topic by Xander Henderson, Adrian Keister, Lord Shark the Unknown, Arnaud Mortier, Parcly Taxel Jul 25 at 16:09
- This question does not appear to be about math within the scope defined in the help center.
11
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This is a soft question.
What is the purpose of teaching techniques of integration at the college level?
More specifically, in the sense of putting integration into practice, what value does teaching these techniques serve in a world which increasingly depends on approximation and computer algebra systems?
If the use of these techniques in practice is limited, then what should integral calculus be teaching in order to make the content imparted by the class more actionable?
I am assuming that, in general, the students of integral calculus will not go on to be mathematicians.
integration soft-question approximation education riemann-integration
asked Jul 25 at 15:59
Chickenmancer
3,007621
This is a soft question.
What is the purpose of teaching techniques of integration at the college level?
More specifically, in the sense of putting integration into practice, what value does teaching these techniques serve in a world which increasingly depends on approximation and computer algebra systems?
If the use of these techniques in practice is limited, then what should integral calculus be teaching in order to make the content imparted by the class more actionable?
I am assuming that, in general, the students of integral calculus will not go on to be mathematicians.
integration soft-question approximation education riemann-integration
asked Jul 25 at 15:59
Chickenmancer
3,007621
asked Jul 25 at 15:59
Chickenmancer
3,007621
asked Jul 25 at 15:59
Chickenmancer
3,007621
asked Jul 25 at 15:59
Chickenmancer
3,007621
3,007621
closed as off-topic by Xander Henderson, Adrian Keister, Lord Shark the Unknown, Arnaud Mortier, Parcly Taxel Jul 25 at 16:09
- This question does not appear to be about math within the scope defined in the help center.
closed as off-topic by Xander Henderson, Adrian Keister, Lord Shark the Unknown, Arnaud Mortier, Parcly Taxel Jul 25 at 16:09
- This question does not appear to be about math within the scope defined in the help center.
11
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30
add a comment |Â
11
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30
11
11
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30
add a comment |Â
1 Answer
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0
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Your perspective is the general perspective of most students.There's nothing wrong in thinking that way, but what you don't yet realize or know is that 'mathematics is not for mathematicians only'.
It's more like a general subject and if you want my answer to be precise rather than general I would give the following points against your perspective:
As I have already mentioned it's not for mathematicians only,math is used in economics,computer science,engineering,science and to be precise everywhere.Even in sports also, you might have observed coaches doing some work on papers while game is on, well they do math to figure out what's best for the team.
It makes you smart:you might say what has an actor or a musician got to do with math?...well although no practical application in the specified fields,math makes you smart I.e helps you increase your Iq
If you are so much deep on why integrals?... I would say that integrals form basis for many fields,even in computer science and economics.
- Look at integrals form this perspective: Newton is a famous figure and what is he famous for? Well gravity and calculus and let me see why is he famous and what makes him a genius(and you should develop that interest in studying one of the famous works ever done by a human mind)...you know what's cool about calculus? I read somewhere(sorry I don't know the source,it was long ago) that newton wanted to explain motion and gravity very badly and for doing so he needed math,but the math at his time wasn't good enough so he invented math(calculus)to understand his physics... Thug life right?
Suggestion: Look at math as a beautiful way to understand nature or a fun game, but not as a burden or inevitable problem.
answered Jul 25 at 16:08
Banchin
112
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Your perspective is the general perspective of most students.There's nothing wrong in thinking that way, but what you don't yet realize or know is that 'mathematics is not for mathematicians only'.
It's more like a general subject and if you want my answer to be precise rather than general I would give the following points against your perspective:
As I have already mentioned it's not for mathematicians only,math is used in economics,computer science,engineering,science and to be precise everywhere.Even in sports also, you might have observed coaches doing some work on papers while game is on, well they do math to figure out what's best for the team.
It makes you smart:you might say what has an actor or a musician got to do with math?...well although no practical application in the specified fields,math makes you smart I.e helps you increase your Iq
If you are so much deep on why integrals?... I would say that integrals form basis for many fields,even in computer science and economics.
- Look at integrals form this perspective: Newton is a famous figure and what is he famous for? Well gravity and calculus and let me see why is he famous and what makes him a genius(and you should develop that interest in studying one of the famous works ever done by a human mind)...you know what's cool about calculus? I read somewhere(sorry I don't know the source,it was long ago) that newton wanted to explain motion and gravity very badly and for doing so he needed math,but the math at his time wasn't good enough so he invented math(calculus)to understand his physics... Thug life right?
Suggestion: Look at math as a beautiful way to understand nature or a fun game, but not as a burden or inevitable problem.
answered Jul 25 at 16:08
Banchin
112
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
add a comment |Â
up vote
0
down vote
Your perspective is the general perspective of most students.There's nothing wrong in thinking that way, but what you don't yet realize or know is that 'mathematics is not for mathematicians only'.
It's more like a general subject and if you want my answer to be precise rather than general I would give the following points against your perspective:
As I have already mentioned it's not for mathematicians only,math is used in economics,computer science,engineering,science and to be precise everywhere.Even in sports also, you might have observed coaches doing some work on papers while game is on, well they do math to figure out what's best for the team.
It makes you smart:you might say what has an actor or a musician got to do with math?...well although no practical application in the specified fields,math makes you smart I.e helps you increase your Iq
If you are so much deep on why integrals?... I would say that integrals form basis for many fields,even in computer science and economics.
- Look at integrals form this perspective: Newton is a famous figure and what is he famous for? Well gravity and calculus and let me see why is he famous and what makes him a genius(and you should develop that interest in studying one of the famous works ever done by a human mind)...you know what's cool about calculus? I read somewhere(sorry I don't know the source,it was long ago) that newton wanted to explain motion and gravity very badly and for doing so he needed math,but the math at his time wasn't good enough so he invented math(calculus)to understand his physics... Thug life right?
Suggestion: Look at math as a beautiful way to understand nature or a fun game, but not as a burden or inevitable problem.
answered Jul 25 at 16:08
Banchin
112
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Your perspective is the general perspective of most students.There's nothing wrong in thinking that way, but what you don't yet realize or know is that 'mathematics is not for mathematicians only'.
It's more like a general subject and if you want my answer to be precise rather than general I would give the following points against your perspective:
As I have already mentioned it's not for mathematicians only,math is used in economics,computer science,engineering,science and to be precise everywhere.Even in sports also, you might have observed coaches doing some work on papers while game is on, well they do math to figure out what's best for the team.
It makes you smart:you might say what has an actor or a musician got to do with math?...well although no practical application in the specified fields,math makes you smart I.e helps you increase your Iq
If you are so much deep on why integrals?... I would say that integrals form basis for many fields,even in computer science and economics.
- Look at integrals form this perspective: Newton is a famous figure and what is he famous for? Well gravity and calculus and let me see why is he famous and what makes him a genius(and you should develop that interest in studying one of the famous works ever done by a human mind)...you know what's cool about calculus? I read somewhere(sorry I don't know the source,it was long ago) that newton wanted to explain motion and gravity very badly and for doing so he needed math,but the math at his time wasn't good enough so he invented math(calculus)to understand his physics... Thug life right?
Suggestion: Look at math as a beautiful way to understand nature or a fun game, but not as a burden or inevitable problem.
answered Jul 25 at 16:08
Banchin
112
Your perspective is the general perspective of most students.There's nothing wrong in thinking that way, but what you don't yet realize or know is that 'mathematics is not for mathematicians only'.
It's more like a general subject and if you want my answer to be precise rather than general I would give the following points against your perspective:
As I have already mentioned it's not for mathematicians only,math is used in economics,computer science,engineering,science and to be precise everywhere.Even in sports also, you might have observed coaches doing some work on papers while game is on, well they do math to figure out what's best for the team.
It makes you smart:you might say what has an actor or a musician got to do with math?...well although no practical application in the specified fields,math makes you smart I.e helps you increase your Iq
If you are so much deep on why integrals?... I would say that integrals form basis for many fields,even in computer science and economics.
- Look at integrals form this perspective: Newton is a famous figure and what is he famous for? Well gravity and calculus and let me see why is he famous and what makes him a genius(and you should develop that interest in studying one of the famous works ever done by a human mind)...you know what's cool about calculus? I read somewhere(sorry I don't know the source,it was long ago) that newton wanted to explain motion and gravity very badly and for doing so he needed math,but the math at his time wasn't good enough so he invented math(calculus)to understand his physics... Thug life right?
Suggestion: Look at math as a beautiful way to understand nature or a fun game, but not as a burden or inevitable problem.
answered Jul 25 at 16:08
Banchin
112
edited Jul 25 at 16:16
answered Jul 25 at 16:08
Banchin
112
answered Jul 25 at 16:08
Banchin
112
answered Jul 25 at 16:08
Banchin
112
112
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
add a comment |Â
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
The economists, engineers, computer scientists, and biologists I have discussed this question with say they have all either used CAS systems, or approximation techniques to get their answers. That is, outside of academia, I don't have concrete examples as to when anyone will, say, compute the antiderivative of an elementary function in practice. I see your point, that a student may ask this same question. I am asking it on their behalf, so I can better motivate the purpose of these techniques in the classroom, rather than saying "just learn it."
– Chickenmancer
Jul 25 at 18:27
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
Just ask them if they know these calculus stuff(anti derivative and more)... I'm pretty sure that they would say yes,moreover ask someone who is very effective with his work,he would 'definitely(a 100%)'say yes.
– Banchin
Jul 27 at 7:07
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
It's like this... If you wish to be an athlete( let's say running) and being a runner requires you to have legs( like approximations and CAS) and it isn't necessary for you to have hands(integrals and stuff).But,a person with hands runs faster than the one without them... Similarly if you have knowledge of integrals and deeper stuff you can be better in your fields(like economics, computer science and more).. Sry I can't provode any applications of integrals specifically in economics and computer science...but I think they do play a role
– Banchin
Jul 27 at 8:14
add a comment |Â
11
I'm voting to close this question as off-topic because I think that it would be much better suited for the Mathematics Educators SE sister site.
– Xander Henderson
Jul 25 at 16:02
Possible duplicate of math.stackexchange.com/questions/188933/…
– Paul
Jul 25 at 16:03
@XanderHenderson You're right. I didn't think to look for an education related SE.
– Chickenmancer
Jul 25 at 18:30