If we don't have enough math discussions, we should have more. Less invasions, more equations!
I've been intending for some time to relearn my calculus. Perhaps a "derivation of the week" is in order, at least until I'm at the point where integration, which I find much more gratifying, is again within my grasp.
I've been intending for some time to relearn my calculus. Perhaps a "derivation of the week" is in order, at least until I'm at the point where integration, which I find much more gratifying, is again within my grasp.
I have successfully forgotten the calculus. I think I am the point where the only calculus I can manage is nx^(n-1).
If we don't have enough math discussions, we should have more. Less invasions, more equations!
I've been intending for some time to relearn my calculus. Perhaps a "derivation of the week" is in order, at least until I'm at the point where integration, which I find much more gratifying, is again within my grasp.
Make it more multi purpose by calling it "Math problem of the week". It would be a useful topic for those who are in high school or otherwise wish to relearn math while users who have a great grasp of the subject can help/berate the people asking questions.
I've been intending for some time to relearn my calculus. Perhaps a "derivation of the week" is in order, at least until I'm at the point where integration, which I find much more gratifying, is again within my grasp.
I have successfully forgotten the calculus. I think I am the point where the only calculus I can manage is nx^(n-1).
I'm with you on that. I can think of very few situations in which knowing how to integrate an equation is useful in my life. Somebody go ahead and integrate E. coli for me. Let me know how that works out for you.
I'm with you on that. I can think of very few situations in which knowing how to integrate an equation is useful in my life. Somebody go ahead and integrateE. colifor me. Let me know how that works out for you.
I can think of many situations where calculus would be useful in the computer sciences. However, I am not involved in any of those areas. I am not in the business of making physics engines.
I can think of many situations where calculus would be useful in the computer sciences. However, I am not involved in any of those areas. I am not in the business of making physics engines.
Unfortunately I am. AI and algorithm optimization.
I can think of many situations where calculus would be useful in the computer sciences. However, I am not involved in any of those areas. I am not in the business of making physics engines.
Unfortunately I am. AI and algorithm optimization.
I wholeheartedly support any effort to get people interested in learning math, on their own or otherwise. I would encourage people to not just think about whatever specific applications the derivative of a certain function may have, which for many people could be essentially none. Rather, learning math is important to everyone because the skills trained in the process (considering how to use the tools you have available to solve a new problem, examining the assumptions you make when you give an argument) are so fundamental and universally applicable. Except maybe in flipping burgers.
I actually teach freshman calculus, so if you want some ideas on practice problems, an organized path of study, etc, all you need to do is ask.
I agree. I don't understand why people are so obsessed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
Oh yeah - I taught a semester of freshman calculus as well when I had to substitute for another instructor who was ill. Normally, I taught algebra and trig since I was just part-time.
while not applying the same attitude to art and music.
I did, and still do. I'm a person who'll make money by using his brain, why the bloody hell should I need to learn how to use a figure saw? And why would I need to learn how to play 3 songs when even the kids that are going into music already are way beyond that point. Some classes are pointless, thank god I had an awesome music teacher. I also questioned why I had to write book reports about books that were all the same (at least those on the list) and in a language (Dutch) that does not do the written word justice. Dutch is quick merchant babble, not fit for stories.
As for math, never whined about it being useless, only that it was hard.
I agree. I don't understand why people are so obsessesed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
Oh yeah - I taught a semester of freshman calculus as well when I had to substitute for another instructor who was ill. Normally, I taught algebra and trig since I was just part-time.
Oh sure, that's a great reason to learn it. You should expose yourself to all different sorts of topics; how else are you going to find what interests you.
There does come a point, though, where you start figuring out what you need to know, what has utility in your life, and what interests you. If you give calculus a fair shake, and you find it's not for you, I don't see a problem with not forcing yourself to keep that knowledge.
I agree. I don't understand why people are so obsessesed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
Because, unlike art and music, you really are going to need it in a practical way. It would be a disservice not to tell students what is important for them to learn. I'm not disparaging art or music, indeed appreciating and understanding them is a major part of leading a meaningful life, and I wholeheartedly agree on the virtues of teaching math for the way it encourages you to think.
However, I see people who study history, psychology, medicine and they go "why the f**k didn't they tell me I need math for this s**t!" Anything where the object of your study is associated with human beings necessarily involves at least statistics. If you plan to not go into higher learning and "just" learn a trade, you still need math. I helped out a friend of mine in consulting a businessman on one of his projects, and when I told him that it can not work and showed him the published mathematical proof, he didn't like that at all. Even if you just flip burgers but want to understand why Obama can lead by one point in one poll and 14 in another, you need math skills (granted the US electoral system requires university level math).
Math is perceived as a hard subject. Harder than music, art, languages, etc. which all have clear motivators like becoming a rock star, drawing comics and traveling. Math's motivator is not obvious, and that is why we have to advocate, explain and "justify" the teaching of it. If you aim to lead an informed life then you need math!
Math makes you not become a redneck (and any proof to the contrary will be gladly accepted).
I agree. I don't understand why people are so obsessesed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
Because, unlike art and music, you really are going to need it in a practical way.
In my opinion, that makes it even better. However, the attitude I'm getting at is the "I'm not going to learn _____ because I'll never need it" attitude. I think people should want to learn math even if they think they won't need it, if for no other reason than that it is beautiful.
Math makes you not become a redneck (and any proof to the contrary will be gladly accepted).
QFT.
I agree. I don't understand why people are so obsessed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
Oh yeah - I taught a semester of freshman calculus as well when I had to substitute for another instructor who was ill. Normally, I taught algebra and trig since I was just part-time.
Oh sure, that's a great reason tolearnit. You should expose yourself to all different sorts of topics; how else are you going to find what interests you.
There does come a point, though, where you start figuring out what you need to know, what has utility in your life, and what interests you. If you give calculus a fair shake, and you find it's not for you, I don't see a problem with not forcing yourself to keep that knowledge.
So, do you just forget Starry Night after you've taken art appreciation? Do you forget Beethoven's 8th Symphony after you hear a lecture about how it's supposed to sound like a metronome? Do you forget Ethan Frome after you've written a book report about it?
Of course, if you don't think it's pretty, you're entitled to your opinion. I wouldn't advocate "forcing" it. It's just that I don't understand how you could stay away from it after you see how pretty it is.
Of course, if you don't think it's pretty, you're entitled to your opinion. I wouldn't advocate "forcing" it. It's just that I don't understand how you could stay away from it after you see how pretty it is.
And if you're not into beauty, how about mind bending, bat shit crazy, f**king awesome. Hands up who can tell me why 1+2+3+... (all the way up to infinity) = -1/12? Anyone? No peeking at Wikipedia! Double points for mentioning the real world physics experiment that proves it (well not exactly that series but a similar infinite series 1^3+2^3+3^3+...).
Maybe the proof could be the first "Math problem of the week".
I tried to mash up a Taylor series to match 1+2+3+..., but all I got was Which is just a convoluted way to prove that 1+2+3+... = infinity, =D. Still, it beats peeking.
Of course, it was obvious I'd get that with a divergent series, so I just looked up Ramanujan summation after that. Still, that seemed more like merely a question of knowledge than would be preferred.
So, do you just forgetStarry Nightafter you've taken art appreciation? Do you forget Beethoven's 8th Symphony after you hear a lecture about how it's supposed to sound like a metronome? Do you forgetEthan Fromeafter you've written a book report about it?
Of course, if you don't think it's pretty, you're entitled to your opinion. I wouldn't advocate "forcing" it. It's just that I don't understand how you could stay away from it after you see how pretty it is.
Sure, if it's no longer useful to you. If you reach a point in your life where knowing a particular piece of information is no longer useful, I see no problem in allowing yourself to forget that knowledge and replacing it with something that is useful to you.
As I said, earlier in your education, you should expose yourself to as many different things as possible to find your interests. Once you find that interest, though, you'll tend to learn information pursuant to said interest.
There exists today more information than we can ever learn. This problem is near and dear to me as a scientist; we generate more data today than we can ever analyze. Multiple scientists could dedicate the next 40 years of their careers to analyzing the data my laboratory generated last month. It's absurd. It's no longer possible to know everything, so rather than focusing on learning more and more information, we need to learn how to process said information. Part of that is filtering out what information you do and don't need.
Calculus is exceedingly important on the whole; it's not important that every person on earth know how to find the third derivative of an equation.
Calculus is exceedingly important on the whole; it's not important that every person on earth know how to find the third derivative of an equation.
I understand what you are saying, and I respect that opinion. However, that's not quite what I was saying.
I'm saying that it doesn't have to be important. The people who watch Project Runway probably wouldn't say it was important, but they wouldn't care whether it was important. They'd say it was fun and entertaining and that's why they watch it. My point is that math can be fun and entertaining (and more artsy) as well, so I think people should do math more often because it's fun and entertaining (and pretty as well).
Calculus is exceedingly important on the whole; it's not important that every person on earth know how to find the third derivative of an equation.
I understand what you are saying, and I respect that opinion. However, that's not quite whatIwas saying.
I'm saying that it doesn't have to be important. The people who watchProject Runwayprobably wouldn't say it was important, but they wouldn'tcarewhether it was important. They'd say it was fun and entertaining and that's why they watch it. My point is that math can be fun and entertaining (and more artsy) as well, so I think people should do math more often because it's fun and entertaining (and pretty as well).
I see that point. Some math is certainly fun and entertaining, but not everyone is going to see it that way. Of course, you need to learn some of it to be exposed to it, and you punk high school kids need to learn your calculus. I think it's just inevitable that people are going to eventually forget the things that they don't think are important to them. Sometimes that can be sad - I wish some information was never lost - but it seems inevitable to me.
In my opinion, that makes it even better. However, the attitude I'm getting at is the "I'm not going to learn _____ because I'll never need it" attitude. I think people should want to learn math even if they think they won't need it, if for no other reason than that it is beautiful.
People tend to get scared off of math because of this point:
how about mind bending, bat shit crazy, f**king awesome.
Day after day, I hear plenty of kids complaining about how they're never going to need Calculus. A lot of the kids are just lazy or scared to get into the uglier problems of math, so they stray away from it. Also, my math teacher makes us find a real life application regarding the current chapter we're on before we start on the chapter. I don't think many kids take it to heart, but it's an interesting exercise to answer the question of "when I am going to need this?"
"why the f**k didn't they tell me I need math for this s**t!"
For the record, no one here cares if you swear. No need to censor yourself.
I agree. I don't understand why people are so obsessed with the need to justify math education by "when are we ever going to need it?", while not applying the same attitude to art and music. Math is beautiful in and of itself and, in my view, that beauty is justification enough for learning it and playing with it.
People do ask the same things about other subjects. I remember my own very vocal criticism of my high school's 1 semester art requirement to graduate, and I was not the only one. The problem was, and in my experience almost always is, the student asking 'why do we need to learn this' lacks the perspective to realize that all these things really are important, the connection is just not as direct as what they are looking for. Most subjects taught in school are taught not because of some need to put these specific pieces of knowledge into the heads of young people, but to teach important life skills. For example, the arts, especially literature, teach you how to draw and defend conclusions reached from imperfect/ambiguous information. History teaches you perspective that helps give a fuller understanding of current events that are relevant to everybody.
Incidentally, I think that an ideal first problem for this forum in particular would be one that illustrates how accepting a different set of axioms completely changes what kind of conclusions you can make, and even how you approach problems. I wish I could think of something good right now.
Incidentally, I think that an ideal first problem for this forum in particular would be one that illustrates how accepting a different set of axioms completely changes what kind of conclusions you can make, and even how you approach problems. I wish I could think of something good right now.
You need to learn all the subjects in school, and a few others they don't teach in school, so that you don't get your ass handed to you when you come into a forum like this one.
This isn't a complaint against Palin as much as it is a complaint against people who don't know what they are talking about. In her last speech, Palin scoffed at funding for fruit fly research. Now, she's supposed to be this big proponent of research into dhildren's disabilities, so why doesn't she know that fruit fly research has led to some pretty big advance in understanding autism? Sigh.
What would she consider a more proper avenue of research? Finding a new poultice that will drive out the autism demons?
Of course, if you don't think it's pretty, you're entitled to your opinion. I wouldn't advocate "forcing" it. It's just that I don't understand how you could stay away from it after you see how pretty it is.
And if you're not into beauty, how about mind bending, bat shit crazy, f**king awesome. Hands up who can tell me why 1+2+3+... (all the way up to infinity) = -1/12? Anyone? No peeking at Wikipedia! Double points for mentioning the real world physics experiment that proves it (well not exactly that series but a similar infinite series 1^3+2^3+3^3+...).
Maybe the proof could be the first "Math problem of the week".
That's a pretty understandable feeling when looking at something like Ramanujan sums (which is the topic Timo was referring to) for the first time. Which incidentally, I think is a very poor way to introduce new people to math, because you very quickly get into things like Bernoulli numbers or the zeta function, which are extremely interesting to mathematicians, but possibly too abstract to be appreciated by laymen.
Something on the easy side that may be appreciable by those with a more engineery mindset is a problem like "Find the roots of x2-1000x-1000 and explain why they have those values. Use the result to estimate the roots of x2-10100x-10100, and approximate the error this estimate gives."
Comments
Death to non-finitistism!
Gödel, Gödel, GÖDEL!
Ahem, yes, please implement LaTeX in the forums.
It could be an early Cristmans present.
I would encourage people to not just think about whatever specific applications the derivative of a certain function may have, which for many people could be essentially none. Rather, learning math is important to everyone because the skills trained in the process (considering how to use the tools you have available to solve a new problem, examining the assumptions you make when you give an argument) are so fundamental and universally applicable.
Except maybe in flipping burgers.
I actually teach freshman calculus, so if you want some ideas on practice problems, an organized path of study, etc, all you need to do is ask.
Oh yeah - I taught a semester of freshman calculus as well when I had to substitute for another instructor who was ill. Normally, I taught algebra and trig since I was just part-time.
As for math, never whined about it being useless, only that it was hard.
There does come a point, though, where you start figuring out what you need to know, what has utility in your life, and what interests you. If you give calculus a fair shake, and you find it's not for you, I don't see a problem with not forcing yourself to keep that knowledge.
However, I see people who study history, psychology, medicine and they go "why the f**k didn't they tell me I need math for this s**t!" Anything where the object of your study is associated with human beings necessarily involves at least statistics. If you plan to not go into higher learning and "just" learn a trade, you still need math. I helped out a friend of mine in consulting a businessman on one of his projects, and when I told him that it can not work and showed him the published mathematical proof, he didn't like that at all. Even if you just flip burgers but want to understand why Obama can lead by one point in one poll and 14 in another, you need math skills (granted the US electoral system requires university level math).
Math is perceived as a hard subject. Harder than music, art, languages, etc. which all have clear motivators like becoming a rock star, drawing comics and traveling. Math's motivator is not obvious, and that is why we have to advocate, explain and "justify" the teaching of it. If you aim to lead an informed life then you need math!
Math makes you not become a redneck (and any proof to the contrary will be gladly accepted).
Of course, if you don't think it's pretty, you're entitled to your opinion. I wouldn't advocate "forcing" it. It's just that I don't understand how you could stay away from it after you see how pretty it is.
Maybe the proof could be the first "Math problem of the week".
Which is just a convoluted way to prove that 1+2+3+... = infinity, =D.
Still, it beats peeking.
Of course, it was obvious I'd get that with a divergent series, so I just looked up Ramanujan summation after that. Still, that seemed more like merely a question of knowledge than would be preferred.
As I said, earlier in your education, you should expose yourself to as many different things as possible to find your interests. Once you find that interest, though, you'll tend to learn information pursuant to said interest.
There exists today more information than we can ever learn. This problem is near and dear to me as a scientist; we generate more data today than we can ever analyze. Multiple scientists could dedicate the next 40 years of their careers to analyzing the data my laboratory generated last month. It's absurd. It's no longer possible to know everything, so rather than focusing on learning more and more information, we need to learn how to process said information. Part of that is filtering out what information you do and don't need.
Calculus is exceedingly important on the whole; it's not important that every person on earth know how to find the third derivative of an equation.
I'm saying that it doesn't have to be important. The people who watch Project Runway probably wouldn't say it was important, but they wouldn't care whether it was important. They'd say it was fun and entertaining and that's why they watch it. My point is that math can be fun and entertaining (and more artsy) as well, so I think people should do math more often because it's fun and entertaining (and pretty as well).
Also, my math teacher makes us find a real life application regarding the current chapter we're on before we start on the chapter. I don't think many kids take it to heart, but it's an interesting exercise to answer the question of "when I am going to need this?" For the record, no one here cares if you swear. No need to censor yourself.
Most subjects taught in school are taught not because of some need to put these specific pieces of knowledge into the heads of young people, but to teach important life skills. For example, the arts, especially literature, teach you how to draw and defend conclusions reached from imperfect/ambiguous information. History teaches you perspective that helps give a fuller understanding of current events that are relevant to everybody.
Incidentally, I think that an ideal first problem for this forum in particular would be one that illustrates how accepting a different set of axioms completely changes what kind of conclusions you can make, and even how you approach problems. I wish I could think of something good right now.
What would she consider a more proper avenue of research? Finding a new poultice that will drive out the autism demons?
Something on the easy side that may be appreciable by those with a more engineery mindset is a problem like "Find the roots of x2-1000x-1000 and explain why they have those values. Use the result to estimate the roots of x2-10100x-10100, and approximate the error this estimate gives."