I think you're confused about the relationship between integration by parts and the chain rule. They aren't.
The fact of the matter is that the problems we are giving the students are not difficult by any stretch of the imagination, unless one is really ill-posed for mathematics. Much like one learns how to do division before one gets a calculator, the same should be true of integration. Aren't you concerned about people learning the numeric way to solve a DE, but then not really understanding what is happening? Lest the problem not converge...
I asked for the notes because I thought it might be like some of my courses, and thus with a.pdf online. For information on what I've studied, go here http://www.sps.uq.edu.au/disciplines/MathsAll.php and then I've studied the following courses: STAT2003, and (the rest all have MATH prefix, so I won't put that there)
The course notes (for those that have them) aren't too hard to find from there if you're particularly driven.
"My computer is doing it" pretty much means you've dropped off the rigour bandwagon. Maybe my problem is that it seems everyone says "calculus" and knows instantly what is being talked about. It's not so clear for me. Really though, calculus, even rigourously, is not difficult at all. Do you mean you were solving PDEs on prescribed contours or something?
Perhaps we'll have to chalk this up to geographical difference then. Where I'm from, engineers are usually the butt of jokes from mathematicians, but just jokes. So they make fun of them, but it's not a serious "engineers suck" sort of thing. On the other hand, the engineers see mathematicians with a sort of mysticism and joke as well.
I'm not sure about your comment about how much engineers and scientists contribute to the economy vs. mathematicians. This seems to be a comment that would be largely subjective due to the definitions of what a "contribution" is, and thus sort of seems pointless to debate.
Good luck with your studies!
No, this is probably incorrect. I'm not purporting to be an expert on pedagogy, but the books need sufficient worked examples to illustrate the basic methods and variations of attack. After that, "answers in the back of the book" serve limited utility. Of course, they can help to an extent ("I'm out by a factor of two", etc.) but they are far from the be-all end-all.
A handy thing about mathematics is that if you're right, you're right. Hence why the "even numbers have solutions only" style is so successful. And much like what the fellow above me said - just check the answer yourself! Integrals, differentiate and so forth. It's only in the higher level maths courses where checking becomes harder than the problem itself, at which stage those who have trouble with mathematics have given up anyway.
psst how did you know you learnt anything if you didn't do problems.
Guys, the exams... aren't hard. They aren't allowed to be hard, they're easier than assignments. One of the most fundamental aspects of learning mathematics is to do the problems. See the cases.
Mathematicians don't think maths is just crunching formulas from a book. The closest you could get to that is people who are into numerical analysis... who are they, you might ask? They are the guys who are making the methods for calculators and computers! We've come full circle, people.
If you think a class with Maple is "rigorous", I'd like to see your course notes if at all possible.
And just because the integrals are uglier, doesn't mean putting them into Maple makes you smarter. I mean, I don't want to say too much until (if) I see your course notes, but uh... that sounds more like a course in teaching you how to talk to Maple, not how to do problems.
Integration by parts isn't... tricky? If that is the level which you are declaring, "Beyond this point, only perverse pederasts shall go" you've set the bar quite low.
Why are we teaching mathematics, when clearly certain parts will never be used by certain people? Why do we teach history, biology, etc. to students at all? No one in the real world will ever ask you, "Who was the first pope?" in the real world.
Hint: Consider athletics. Being able to throw a shotput in a certain way is more or less useless for everyone. Maybe the putter is doing so to show prowess and physical capability?
Second hint: The first hint wasn't there for fun.
We try to teach the engineers, physicists, etc. about where the methods that they are using are actually coming from. Admittedly, this is sometimes a forlorn task, but the same is true of what these demographics try to teach to students not of their field.
Mathematicians are aware that other fields exist, and that approximations are the name of the game in the real world. This is nothing new. Please try to get up to date about how mathematicians think about the world. It's (clearly) not useless if you think about it for a modicum of time, and these notions of "purity" are (usually) in jest to a certain degree. Of course, there are minorities who are obsessed with this notion, but such is true of any field.
This is fine for practical, applied type people. But recall that a picture is but a picture... it gives you an indication of what the equation / object looks like, but sometimes it lies! Think the Dirichlet function (1 for rationals, 0 for irrationals (or vice versa)). A bit boring on a computer, but we know it is slightly less so...
Graphs are good for "hunch feelings" or as a lead. They are not a substitute for actual thinking. Of course, one cannot pull oneself up by the bootstraps, but still... sometimes seeing it will prevent a student from thinking in alternative ways about the question.
I can only speak for my degree, so I study mathematics at the university of Queensland (Australia), and we don't have anything like this. The closest thing to it is that for one of my courses, a first year course that I tutor, if you don't attend the tutorials you miss out on 1% per week. No penalties otherwise.
Try to be understanding. Think of things in this way:
If someone cannot walk -- they have no legs -- you don't make fun of them. If someone cannot think -- they're in a coma -- you don't make fun of them.
If someone cannot walk well -- they have cerebral palsy -- you don't make fun of them. If someone cannot think well -- they have a learning disability -- you don't make fun of them.
I guess it's all about magnitudes. Personally, I think I think pretty well. This is no reason to make fun of other people, or to exploit them. Another example: beauty. Some people are born beautiful. Others are born ugly. Only in certain circumstances can one transition from ugliness to beauty. No one "willfully" chose to be ugly. Now change the appropriate words with "erudite" and "stupid", and what do you see?
Perhaps if you want me to help you a little more to understand, I'm definitely willing.
Hmm, it seems that (from your point of view) this sobretism is inexplicably linked with evangelism. However, it doesn't appear to me at least that this is a necessary criterion for other addictions. Is this the defining characteristic?
Sorry for such short responses -- I study mathematics, not social science, so I'm not so great with writing long texts.
(a lot of friends I formerly had were "straight edge", and some were pretty fanatical. Most were mellow, cool guys but, but others...hmm)
Is this actually a thing? It's a very interesting idea -- I'm someone who I guess is "addicted to sobreity", except for coffee. I'd like to read about it is all.
You're showing a level of myopia seen normally only in engineers -- please think more. Think long and hard about how Twitter is useful. I, like you, don't use/need it, but I can certainly see a hole it fills / a hole it overlaps with.
It's really not that difficult, please just think a little harder.
When you go to a beach and there are ships going out to see, note they don't shrink into the horizon, but they drop off, ie. the world is round and not flat. Showing the Earth revolves around the Sun obviously takes time observation though.
Anyway, that's just for personal interest. We have to take someone else's word on most things, which is fine! It's better than knowing everything, really -- it creates dependencies on eachother. And you don't kill the horse you're riding on (maybe not the best metaphor, as they're riding you. Horses all the way down!)
Slashdot Mirror
I mean, I know headlines can't convey everything, but it seems a few leaps have been made...
That's not true, and further, it's inhumane. Please try to avoid encouraging the death of people.
I think you're confused about the relationship between integration by parts and the chain rule. They aren't.
The fact of the matter is that the problems we are giving the students are not difficult by any stretch of the imagination, unless one is really ill-posed for mathematics. Much like one learns how to do division before one gets a calculator, the same should be true of integration. Aren't you concerned about people learning the numeric way to solve a DE, but then not really understanding what is happening? Lest the problem not converge...
I asked for the notes because I thought it might be like some of my courses, and thus with a .pdf online. For information on what I've studied, go here http://www.sps.uq.edu.au/disciplines/MathsAll.php and then I've studied the following courses: STAT2003, and (the rest all have MATH prefix, so I won't put that there)
1051, 1052, 1061, 2000, 2100, 2302, 3301, 2301, 2400, 3401, 3090.
The course notes (for those that have them) aren't too hard to find from there if you're particularly driven.
"My computer is doing it" pretty much means you've dropped off the rigour bandwagon. Maybe my problem is that it seems everyone says "calculus" and knows instantly what is being talked about. It's not so clear for me. Really though, calculus, even rigourously, is not difficult at all. Do you mean you were solving PDEs on prescribed contours or something?
Perhaps we'll have to chalk this up to geographical difference then. Where I'm from, engineers are usually the butt of jokes from mathematicians, but just jokes. So they make fun of them, but it's not a serious "engineers suck" sort of thing. On the other hand, the engineers see mathematicians with a sort of mysticism and joke as well. I'm not sure about your comment about how much engineers and scientists contribute to the economy vs. mathematicians. This seems to be a comment that would be largely subjective due to the definitions of what a "contribution" is, and thus sort of seems pointless to debate. Good luck with your studies!
Note that this is from your physics teachers, not your maths teachers. I'm not disagreeing with what is happening, but just keep that in mind.
No, this is probably incorrect. I'm not purporting to be an expert on pedagogy, but the books need sufficient worked examples to illustrate the basic methods and variations of attack. After that, "answers in the back of the book" serve limited utility. Of course, they can help to an extent ("I'm out by a factor of two", etc.) but they are far from the be-all end-all. A handy thing about mathematics is that if you're right, you're right. Hence why the "even numbers have solutions only" style is so successful. And much like what the fellow above me said - just check the answer yourself! Integrals, differentiate and so forth. It's only in the higher level maths courses where checking becomes harder than the problem itself, at which stage those who have trouble with mathematics have given up anyway.
psst how did you know you learnt anything if you didn't do problems. Guys, the exams... aren't hard. They aren't allowed to be hard, they're easier than assignments. One of the most fundamental aspects of learning mathematics is to do the problems. See the cases. Mathematicians don't think maths is just crunching formulas from a book. The closest you could get to that is people who are into numerical analysis... who are they, you might ask? They are the guys who are making the methods for calculators and computers! We've come full circle, people.
If you think a class with Maple is "rigorous", I'd like to see your course notes if at all possible. And just because the integrals are uglier, doesn't mean putting them into Maple makes you smarter. I mean, I don't want to say too much until (if) I see your course notes, but uh... that sounds more like a course in teaching you how to talk to Maple, not how to do problems.
Integration by parts isn't... tricky? If that is the level which you are declaring, "Beyond this point, only perverse pederasts shall go" you've set the bar quite low. Why are we teaching mathematics, when clearly certain parts will never be used by certain people? Why do we teach history, biology, etc. to students at all? No one in the real world will ever ask you, "Who was the first pope?" in the real world. Hint: Consider athletics. Being able to throw a shotput in a certain way is more or less useless for everyone. Maybe the putter is doing so to show prowess and physical capability? Second hint: The first hint wasn't there for fun.
We try to teach the engineers, physicists, etc. about where the methods that they are using are actually coming from. Admittedly, this is sometimes a forlorn task, but the same is true of what these demographics try to teach to students not of their field. Mathematicians are aware that other fields exist, and that approximations are the name of the game in the real world. This is nothing new. Please try to get up to date about how mathematicians think about the world. It's (clearly) not useless if you think about it for a modicum of time, and these notions of "purity" are (usually) in jest to a certain degree. Of course, there are minorities who are obsessed with this notion, but such is true of any field.
This is fine for practical, applied type people. But recall that a picture is but a picture... it gives you an indication of what the equation / object looks like, but sometimes it lies! Think the Dirichlet function (1 for rationals, 0 for irrationals (or vice versa)). A bit boring on a computer, but we know it is slightly less so... Graphs are good for "hunch feelings" or as a lead. They are not a substitute for actual thinking. Of course, one cannot pull oneself up by the bootstraps, but still... sometimes seeing it will prevent a student from thinking in alternative ways about the question.
We will begin with the firemen, then the math teachers, and so on in that fashion ...
I can only speak for my degree, so I study mathematics at the university of Queensland (Australia), and we don't have anything like this. The closest thing to it is that for one of my courses, a first year course that I tutor, if you don't attend the tutorials you miss out on 1% per week. No penalties otherwise.
Try to be understanding. Think of things in this way:
If someone cannot walk -- they have no legs -- you don't make fun of them.
If someone cannot think -- they're in a coma -- you don't make fun of them.
If someone cannot walk well -- they have cerebral palsy -- you don't make fun of them.
If someone cannot think well -- they have a learning disability -- you don't make fun of them.
I guess it's all about magnitudes. Personally, I think I think pretty well. This is no reason to make fun of other people, or to exploit them. Another example: beauty. Some people are born beautiful. Others are born ugly. Only in certain circumstances can one transition from ugliness to beauty. No one "willfully" chose to be ugly. Now change the appropriate words with "erudite" and "stupid", and what do you see?
Perhaps if you want me to help you a little more to understand, I'm definitely willing.
Thanks,
Sam.
Doors open! Get 'em, boys!
I don't mean to insult you (but I will):
psst 'you cant prove a negative' is a negative, dont spread it around mmk
Hmm, it seems that (from your point of view) this sobretism is inexplicably linked with evangelism. However, it doesn't appear to me at least that this is a necessary criterion for other addictions. Is this the defining characteristic?
Sorry for such short responses -- I study mathematics, not social science, so I'm not so great with writing long texts.
(a lot of friends I formerly had were "straight edge", and some were pretty fanatical. Most were mellow, cool guys but, but others...hmm)
Thanks,
Sam.
Is this actually a thing? It's a very interesting idea -- I'm someone who I guess is "addicted to sobreity", except for coffee. I'd like to read about it is all.
Thanks if you reply,
Sam.
terms that a computer programmer or biologist could follow
no
I can't understand how people think they have the right to enforce their own judgement over other people's judgement. ohhhhh shiiiiiiiiii
You're showing a level of myopia seen normally only in engineers -- please think more. Think long and hard about how Twitter is useful. I, like you, don't use/need it, but I can certainly see a hole it fills / a hole it overlaps with.
It's really not that difficult, please just think a little harder.
Guy, I think most slashdotters should be worried about their BMI.
Haha what.
Look, guy, I just asked four guys if they were homosexuals. 3/4 said yes, so clearly that's representative of everything!
Yeah, I see what you're getting at, but please don't put your anecdotal evidence in your post. It's (at best) fluff.
When you go to a beach and there are ships going out to see, note they don't shrink into the horizon, but they drop off, ie. the world is round and not flat. Showing the Earth revolves around the Sun obviously takes time observation though.
Anyway, that's just for personal interest. We have to take someone else's word on most things, which is fine! It's better than knowing everything, really -- it creates dependencies on eachother. And you don't kill the horse you're riding on (maybe not the best metaphor, as they're riding you. Horses all the way down!)