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Author Topic: Are some people born good at maths?  (Read 12272 times)

Offline cheryl j

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Are some people born good at maths?
« on: 01/02/2012 20:09:25 »
I love science. But I always hated maths. I was not good at it, and as a kid I thought it was boring. I was never a "puzzle person" who liked solving a question for the challenge of solving it. Also, I was slow at numbers, could not "hold numbers" in my head or solve things without writing it down. And I could never do those SAT questions where you are supposed to figure out the next number in a sequence.

 It was only when I took chemistry and physics in highschool that I developed any appreciation for or enjoyment of maths at all. And really, I only liked physics and chemistry because it helped me understand biology better, which is what I really loved.

But to this day, maths haunts me, because I feel like I missed out on some other way of understanding or experiencing the world, like a deaf person who can't hear music. Especially when maths people talk about the beauty or "elegance" of an equation, and I have no idea what they mean. The other thing I don't understand is when maths people talk about having an instinct or a "feel" for how certain mathematical things work. I'm ashamed to admit I took an entire course in calculus and had no idea why it was invented or what the point of it was. I just copied the steps the professor did on the black board, and tried to duplicate it on the test.

I don't think I am a stupid person, but I have to admit, when it comes to maths, I feel like part of my brain never developed at all. The biologist in me would like to know what differences there are in the brains of people who are good at maths and those who are not, and if it can be changed, or its hardwired.
« Last Edit: 03/02/2012 22:08:46 by chris »


 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #1 on: 02/02/2012 06:11:24 »
I have heard that some people, even many people, have a hard time with abstraction.

The point of maths is (more or less) that you abstract patterns from real world things and try to work on the patterns independently from the the thing you took the pattern from. To the extent that you can do that, you can use the same maths across different many places; places where you wouldn't normally expect there to be any connections.

Numbers aren't actually that much to do with higher mathematics, at the very highest levels it's more like a foreign language, so it may even be that you would be bad at the lowest levels, but good at the higher levels.

The other thing is, that's nobody really, really good at maths, since mathematicians have managed to prove that maths is infinitely hard; so there's always an equation so hard that no mathematician will ever prove it.
 

Offline CliffordK

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Re: Math -what am I missing out on.
« Reply #2 on: 02/02/2012 08:28:49 »
Personally I think the terms "Language of Mathematics" is overused, and believe that one needs to mix mathematical proofs with empirical evidence.

For example, setting the volume of a Black Hole to zero doesn't mean that it in fact exists.

And, while I used to like mathematics, I do have a bad habit of jumping to the answer and ignoring the derivation. 

Everything depends on what you wish to do, and are comfortable with.  I do find that algebra and trigonometry is much more useful for my current needs than calculus.  And, I probably learned more about Algebra in Calculus than I did in Algebra.  However, it doesn't hurt to at least understand the basic slopes, areas, and state changes that one derives with calculus.

If I need to solve a series of linear equations, I'm much more likely to use brute force than complex matrix transformations.

A year or so ago I thought I'd try some science fiction writing.
While I'm not convinced that the speed of light is an absolute limit, it quickly became obvious how difficult of a task it is to get anywhere near the speed of light.  And, my aspirations to become a science fiction writer soon became Epsilon!!!!  So much for Math actually helping a person   [xx(]
 

Offline krool1969

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Re: Math -what am I missing out on.
« Reply #3 on: 02/02/2012 08:44:42 »
I don't think you're to blame for your lack of understanding. For many people, myself included, it takes a good teacher to really understand math. Unfortunatly good math teachers are very rare. It's easy to teach someone who already understands a basic consept. But if your brain doesn't quite "get it" it makes teaching a lot harder. The teacher must think outside the box.
 

Offline graham.d

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Re: Math -what am I missing out on.
« Reply #4 on: 02/02/2012 10:00:43 »
Even great mathematicians say that, at some point, they hit a ceiling. It is also the case that the ceiling gets lower as you get older, at least for very advanced mathematics - I think people peak in their early twenties. I agree with Krool1969, a good teacher makes a difference to us normal mortals. To the exceptionally gifted it seems they are able to get beyond a teacher's abilities quite quickly.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #5 on: 02/02/2012 21:20:00 »
Especially when math people talk about the beauty or "elegance" of an equation, and I have no idea what they mean.
Usually they just mean it's a short equation(!) Often the symbols take several pages to understand though, so the elegance is sometimes illusory. And you shouldn't assume that the mathematicians are consistent about it, and I've seen equations that are shorter and more useful that many mathematicians didn't like, for historical reasons only.
 

Offline Geezer

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Re: Math -what am I missing out on.
« Reply #6 on: 02/02/2012 21:38:41 »

I'm ashamed to admit I took an entire course in calculus and had no idea why it was invented or what the point of it was.


I don't  think you are alone! We did some calculus in high school, but I didn't see the point in it until later when I got into engineering. When I understood how it could be applied to solve real problems, the light bulb went on. I suspect our teacher didn't have much sense of how it could be applied either.
 

Offline David Cooper

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Re: Math -what am I missing out on.
« Reply #7 on: 02/02/2012 22:11:58 »
If you get a dud teacher who doesn't explain calculus properly, it's their fault and not yours. I had a completely useless teacher who completely failed to explain what calculus was or how it worked: it was like trying to learn a foreign language without being allowed to know what any of the words mean and being asked to create gramatically correct sentences out of all the empty pieces. I have tried to find something on the Web that teaches calculus many times since then and have found nothing - it either leads up to it and fails to deliver, or it dives in at the deep end and drowns you in stuff you can't understand. (I haven't been able to test the Khan Academy videos as I don't have a fast enough connection or sufficient monthly bandwidth to be able to watch videos.) I don't think the problem can be that I'm simply useless at maths, and here's why: I have written gravity simulation programs like http://www.magicschoolbook.com/science/inner-planets.html and http://www.magicschoolbook.com/science/sun2saturn.html, and I've also written this scientific calculator http://www.magicschoolbook.com/maths/3.html. More evidence of my ability is that I've written this operating system directly in machine code without using assembler http://www.magicschoolbook.com/computing/os-project.html. But I still haven't found out how to do calculus. All I'd need to see to understand how it works are some simple examples of how to apply it to some real problems to get real answers out, and preferably all done through normal language without turning everything into alien squiggles.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #8 on: 02/02/2012 22:34:37 »
The main point of maths is to turn it into alien squiggles.

Well, not alien, maths is a foreign language, and if you lose the sense of what it means, you'll not be able to do good maths. But you should always remember that maths is about patterns, not about the thing you're trying to do maths on, and the patterns have a life of their own.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #9 on: 02/02/2012 22:40:58 »
To be honest, even Newton had problems with calculus, and he invented it!

Newton got hung up on the examples he used to derive it; calculus was invented to deal with the motion of planets and things, so everything was about rates of change with respect to time.

Leibnitz was more general, he allowed rates of change with respect to anything, like 'how does gravity change with the distance away from a planet',  but Newton couldn't get his head around those kinds of rates of change, only the rates with respect to time; his examples always were speeds (rate of change of distance with time) and accelerations (rate of change of speed with time). He called them 'fluxions'.

So the calculus we use comes from Leibnitz.
« Last Edit: 02/02/2012 22:42:33 by wolfekeeper »
 

Offline David Cooper

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Re: Math -what am I missing out on.
« Reply #10 on: 02/02/2012 23:05:19 »
The main point of maths is to turn it into alien squiggles.

It's fine to use alien squiggles after the maths that lies behind them has been explained to the point that you have a proper understanding of it, but many teachers go straight into dx/dy which doesn't appear to have anything to do with dividing the upper by the lower term, then change the d into greek for some reason, and then they start hurling barless "f"s around and talking about limits without ever demonstrating that any of it can do anything useful. Before long, the teacher takes to writing something complex on the board and asking you to simplify it. When she finally demonstrates how it should be done, she generates something twice as complex as the thing she was claiming to simplify, and none of it appears to make any sense because she hasn't explained it. Everyone else in the class either gets their parents to pay for tutoring or they just give up.

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Well, not alien, maths is a foreign language, and if you lose the sense of what it means, you'll not be able to do good maths.

It wasn't losing the sense of it that was the problem - it was trying to get the sense of it in the first place. My "teacher" didn't give me anything to lose.

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But you should always remember that maths is about patterns, not about the thing you're trying to do maths on, and the patterns have a life of their own.

The people who worked out calculus did it to solve specific problems and they knew exactly what those problems were. Why shouldn't everyone else be allowed to start off at the same point where there are clear problems there to be solved and where they can see a mathematical process generate answers. It should be possible to program a computer to solve these problems without having to type alien squiggles in at all - all of it must be possible using nothing more than a standard CPU instruction set.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #11 on: 03/02/2012 00:38:01 »
No, in the alien squiggle language, dy/dx is actually dividing something by something.

But it's not just divide one by the other, it's defined as the limit of dividing dy/dx as you take dx towards zero.

Limits are answers where you find that the answer gets closer and closer to something, without ever quite getting there, (if it actually got there the maths usually explodes, but that doesn't matter!!) But not every equation tends to a limit, some don't converge to a limit at all, and some give you a different answer depending on which side of the limit you start from.

For example:

y = (x+1)/x

y tends to 1/x as x tends to 0, but when you get to 0, it explodes! If you don't believe me, try plugging in a small x and seeing what y is, you'll find it's very close, and gets closer the smaller x is. The reason is, is because when x is small x+1 in the numerator is basically 1, but x in the denominator is still significant to the answer.

That's what calculus is all about, it's based on limits. dy/dx is short hand for saying take dx towards zero and dy with it, what do you get when you divide them.. in the limit?

So for example in your gravity simulation dx/dt is the speed of a body; if you set dt very small, how fast is the body moving? dx/dt! It's just distance (dx) over time (dt), speed!

It turns out, like with the (1+x)/x case above, with calculus you can solve some important equations exactly using limits, but don't worry, many equations are still impossible to solve!
 

Offline Geezer

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Re: Math -what am I missing out on.
« Reply #12 on: 03/02/2012 07:32:04 »

That's what calculus is all about, it's based on limits. dy/dx is short hand for saying take dx towards zero and dy with it, what do you get when you divide them.. in the limit?


There you go. That is not what calculus is "all about".

dy/dx is simply a method of determining the slope of something at a particular place on the slope. The "limits" are simply an artifact of the method employed.

I'm not suggesting that "limits" are not required, but the whole point of calculus was to solve practical problems. Limits fell out of that, not the other way around.

This is precisely why so many people become disenchanted when mathematicians ennoble the method rather than the purpose. 
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #13 on: 03/02/2012 07:51:53 »
Well, if as you say and I say, limits are required to do the job, then they're required to do the job.

I don't think it's possible to do calculus without limits, and having some understanding of them; I think everyone that has ever done calculus gets shown a right-angle triangle of sides dy and dx and is asked to imagine what happens as you make that triangle ever-so-small. That's just exactly the same as taking the limit.
 

Offline Geezer

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Re: Math -what am I missing out on.
« Reply #14 on: 03/02/2012 08:12:12 »
Well, if as you say and I say, limits are required to do the job, then they're required to do the job.

I don't think it's possible to do calculus without limits, and having some understanding of them; I think everyone that has ever done calculus gets shown a right-angle triangle of sides dy and dx and is asked to imagine what happens as you make that triangle ever-so-small. That's just exactly the same as taking the limit.

Of course it is, but the entire purpose of the exercise is to determine the slope (the rate of change of something with respect to something else) during a very small change in either one of them. That's why the differentiation was invented.

Ironically, Newton didn't think it was any big deal. He just cooked it up as a method to help him solve some problems.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #15 on: 03/02/2012 08:30:55 »
The people who worked out calculus did it to solve specific problems and they knew exactly what those problems were. Why shouldn't everyone else be allowed to start off at the same point where there are clear problems there to be solved and where they can see a mathematical process generate answers.
Yes, most people learn general processes by starting with the specific and learning how to generalise them.
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It should be possible to program a computer to solve these problems without having to type alien squiggles in at all - all of it must be possible using nothing more than a standard CPU instruction set.
Both yes, and no. Mainly no.

Normal calculus takes an equation, and changes the equation 'differentiating' or 'integrating' to give new equations. Computers can do that, but those are very definitely alien squiggles it's manipulating, you type them in in that form, and you get them back in that form.

The other way to do it is not to use true calculus, but to use small deltas. So you divide the problem up into small chunks, but you do not take it down to the infinitesimal limit. If the distances between the chunks are small enough, this approximates to using calculus. That's done rather a lot, it's called 'finite element analysis' and similar names.
 

Offline Geezer

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Re: Math -what am I missing out on.
« Reply #16 on: 03/02/2012 08:48:27 »

Computers can do that, but those are very definitely alien squiggles it's manipulating, you type them in in that form, and you get them back in that form.


Only because the computer translates them to and from mathematical hieroglyphs in the process. The computer is only capable of operating on a series of very mundane mathematical expressions.

Analog computers did implement calculus in hardware, but I don't think any of the digital variety do that. 
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #17 on: 03/02/2012 17:44:52 »
Well analogue computers and finite element analysis are pretty much both branches of signal processing, whereas calculus is a branch of mathematics, it's purely to do with equations.

Analogue computers and finite element analysis can both do very much the same thing, except that one is sampled and the other is continuous, but that doesn't matter provided the Nyquist criteria is satisfied.
 

Offline David Cooper

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Re: Math -what am I missing out on.
« Reply #18 on: 03/02/2012 22:06:30 »
Limits are answers where you find that the answer gets closer and closer to something, without ever quite getting there, (if it actually got there the maths usually explodes, but that doesn't matter!!) But not every equation tends to a limit, some don't converge to a limit at all, and some give you a different answer depending on which side of the limit you start from.

I thought the whole purpose of calculus was the it could get to an exact answer at some point rather than just getting a good approximation. For example, if you're trying to calculate the slope of a curve through a point, you can calculate the slope of a line and make that line shorter and shorter to get a closer and closer approximation of the slope at the point, but you can't do anything useful with a line of zero length. I was led to believe that calculus would somehow enable you to get an exact value for the slope at a point, but I never saw any evidence that this was actually possible during hundreds of hours of watching a teacher fail to explain how calculus was meant to be done.

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For example:

y = (x+1)/x

y tends to 1/x as x tends to 0, but when you get to 0, it explodes! If you don't believe me, try plugging in a small x and seeing what y is, you'll find it's very close, and gets closer the smaller x is. The reason is, is because when x is small x+1 in the numerator is basically 1, but x in the denominator is still significant to the answer.

I can see what happens with different numbers in that, but I can't relate it to anything in the real world, and that's a large part of my problem - I can handle the abstract once I've seen it being applied to something real, but so long as it is nothing but abstract it is impossible for me to tie it to anything in my head.

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So for example in your gravity simulation dx/dt is the speed of a body; if you set dt very small, how fast is the body moving? dx/dt! It's just distance (dx) over time (dt), speed!

It would be helpful if this stuff was taught by retaining words in the early stages so that you can remember what things are meant to be. Why not just write dist/time? And why does it suddenly go Greek with delta replacing d? The trouble I have with calculus is may be mainly down to a teacher introducing symbols and never restating what they're supposed to mean.

It should be possible to program a computer to solve these problems without having to type alien squiggles in at all - all of it must be possible using nothing more than a standard CPU instruction set.
Both yes, and no. Mainly no.

Normal calculus takes an equation, and changes the equation 'differentiating' or 'integrating' to give new equations. Computers can do that, but those are very definitely alien squiggles it's manipulating, you type them in in that form, and you get them back in that form.

If it can be done at all, it must be possible for a computer to do the job with a set of very simple instructions. It has to be able to turn the squiggle version of the problem into something it can handle through those simple instructions, and that simply requires someone to program it to decode the squiggles. My problem is that no one has ever told me how to decode the squiggles in a way that's intelligible to anyone who doesn't already know how to do it.

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The other way to do it is not to use true calculus, but to use small deltas. So you divide the problem up into small chunks, but you do not take it down to the infinitesimal limit. If the distances between the chunks are small enough, this approximates to using calculus. That's done rather a lot, it's called 'finite element analysis' and similar names.

If a human can work out exact answers using calculus, why would a machine not solve problems the same way? If a human can do it, it ought to be dead easy for a machine. Maybe it's faster to do it with approximations and that might matter in something like graphics for computer games where precise answers may be unnecessary.
 

Offline wolfekeeper

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Re: Math -what am I missing out on.
« Reply #19 on: 03/02/2012 22:20:00 »
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So for example in your gravity simulation dx/dt is the speed of a body; if you set dt very small, how fast is the body moving? dx/dt! It's just distance (dx) over time (dt), speed!

It would be helpful if this stuff was taught by retaining words in the early stages so that you can remember what things are meant to be. Why not just write dist/time?
Because if you do dist/time, that's actually the average speed. What you're trying to calculate is the speed at a particular instant in time. For example, a car that is accelerating may travel 100 metres in 10 seconds, but it wasn't going at 10m/s the whole way. At the beginning it was stationary, at the end it was going at (say) 20 m/s.

How would you work out the speed at the end of the course, if it wasn't accelerating completely uniformly?

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And why does it suddenly go Greek with delta replacing d? The trouble I have with calculus is may be mainly down to a teacher introducing symbols and never restating what they're supposed to mean.
Delta means it's not a limit, it's a real number you could type into your calculator, like 0.0001, it's just a small number.

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Normal calculus takes an equation, and changes the equation 'differentiating' or 'integrating' to give new equations. Computers can do that, but those are very definitely alien squiggles it's manipulating, you type them in in that form, and you get them back in that form.

If it can be done at all, it must be possible for a computer to do the job with a set of very simple instructions. It has to be able to turn the squiggle version of the problem into something it can handle through those simple instructions, and that simply requires someone to program it to decode the squiggles.
No, it doesn't decode them, it treats them as squiggles and messes around with the squiggles. It doesn't have a clue what the squiggles really mean.
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The other way to do it is not to use true calculus, but to use small deltas. So you divide the problem up into small chunks, but you do not take it down to the infinitesimal limit. If the distances between the chunks are small enough, this approximates to using calculus. That's done rather a lot, it's called 'finite element analysis' and similar names.
If a human can work out exact answers using calculus, why would a machine not solve problems the same way? If a human can do it, it ought to be dead easy for a machine. Maybe it's faster to do it with approximations and that might matter in something like graphics for computer games where precise answers may be unnecessary.
In most real-world cases humans can't work out exact answers either. Maths only works in certain situations, mostly the ones you get shown in school! Usually in the full glorious complexity of real life you can't solve the maths, and you have to use approximations, and you aren't always sure that the approximations are valid either. Still, where the maths works well, it's really, really, really, really useful.
« Last Edit: 03/02/2012 22:22:29 by wolfekeeper »
 

Offline wolfekeeper

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Re: Are some people born good at maths?
« Reply #20 on: 03/02/2012 22:33:53 »
Limits are answers where you find that the answer gets closer and closer to something, without ever quite getting there, (if it actually got there the maths usually explodes, but that doesn't matter!!) But not every equation tends to a limit, some don't converge to a limit at all, and some give you a different answer depending on which side of the limit you start from.

I thought the whole purpose of calculus was the it could get to an exact answer at some point rather than just getting a good approximation. For example, if you're trying to calculate the slope of a curve through a point, you can calculate the slope of a line and make that line shorter and shorter to get a closer and closer approximation of the slope at the point, but you can't do anything useful with a line of zero length. I was led to believe that calculus would somehow enable you to get an exact value for the slope at a point, but I never saw any evidence that this was actually possible during hundreds of hours of watching a teacher fail to explain how calculus was meant to be done.
You take the limit of the gradient as the line length tends to zero, and you get the answer; that's the gradient at that point.

The answer is exact, the limit of something (when it's soluble) is an EXACT answer, it's not approximate.

The approximation gets better and better as the line length gets shorter, and the limit is precise.

1+1/2+1/4+... the limit of that is 2. It's exactly 2. Likewise the limit of the gradient is the actual gradient at that point (by definition- they define it that way!!)

How do we know it's right? That the gradient really is that? Probably, mathematicians don't, really. But they find that the answers always make sense, they're always self consistent, so it doesn't matter. But really it's pretty obvious that it ought to work.
 

Offline David Cooper

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Re: Are some people born good at maths?
« Reply #21 on: 03/02/2012 23:45:42 »
It would be helpful if this stuff was taught by retaining words in the early stages so that you can remember what things are meant to be. Why not just write dist/time?
Because if you do dist/time, that's actually the average speed.

Then so is dx/dy. If the d has some function other than being a constant, wouldn't it be better to have a special symbol for whatever it's supposed to be to avoid confusion? What does the d actually mean?

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What you're trying to calculate is the speed at a particular instant in time. For example, a car that is accelerating may travel 100 metres in 10 seconds, but it wasn't going at 10m/s the whole way. At the beginning it was stationary, at the end it was going at (say) 20 m/s.

How would you work out the speed at the end of the course, if it wasn't accelerating completely uniformly?

I probably couldn't, but I can imagine that there might be a way to do it if you had a formula to describe the acceleration.

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And why does it suddenly go Greek with delta replacing d? The trouble I have with calculus is may be mainly down to a teacher introducing symbols and never restating what they're supposed to mean.
Delta means it's not a limit, it's a real number you could type into your calculator, like 0.0001, it's just a small number.

I should have asked what the d meant first and then asked what it meant to replace it with delta.

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No, it doesn't decode them, it treats them as squiggles and messes around with the squiggles. It doesn't have a clue what the squiggles really mean.

At some point it has to take numbers in and at some point it has to produce answers as numbers, and in between those points it has to do something that I've never seen set out clearly, and some of that will involve crunching numbers. I have no doubt I could write a program to do it all too, but I have never seen anyone set out a real problem and illustrate how to solve it in rational steps. All I've ever seen is a teacher repeatedly assert that something can be done and then repeatedly fail to demonstrate how.

You take the limit of the gradient as the line length tends to zero, and you get the answer; that's the gradient at that point.

The answer is exact, the limit of something (when it's soluble) is an EXACT answer, it's not approximate.

The approximation gets better and better as the line length gets shorter, and the limit is precise.

1+1/2+1/4+... the limit of that is 2. It's exactly 2. Likewise the limit of the gradient is the actual gradient at that point (by definition- they define it that way!!)

I can see that it's exactly 2 in this case, but I can't see a process that would enable a machine to work that out. You can add up lots of smaller and smaller fractions and see that it appears to be heading for 2, but if calculus doesn't involve a guess at some stage, there needs to be some point at which the exact answer 2 comes out of an actual calculation.

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How do we know it's right? That the gradient really is that? Probably, mathematicians don't, really. But they find that the answers always make sense, they're always self consistent, so it doesn't matter. But really it's pretty obvious that it ought to work.

With that example (can't see any calculus in it) you can calculate the 2 easily enough through reasoning and see that the total would be exactly 2 if you could add an infinite number of fractions with each half the size of the one before, but in most cases I can't see that it would be possible to reason your way to an exact answer so easily.
 

Offline wolfekeeper

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Re: Are some people born good at maths?
« Reply #22 on: 04/02/2012 00:02:14 »
It would be helpful if this stuff was taught by retaining words in the early stages so that you can remember what things are meant to be. Why not just write dist/time?
Because if you do dist/time, that's actually the average speed.

Then so is dx/dy. If the d has some function other than being a constant, wouldn't it be better to have a special symbol for whatever it's supposed to be to avoid confusion? What does the d actually mean?
It means you've taken delta x/delta y to the infinitesimally small limit.
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What you're trying to calculate is the speed at a particular instant in time. For example, a car that is accelerating may travel 100 metres in 10 seconds, but it wasn't going at 10m/s the whole way. At the beginning it was stationary, at the end it was going at (say) 20 m/s.

How would you work out the speed at the end of the course, if it wasn't accelerating completely uniformly?

I probably couldn't, but I can imagine that there might be a way to do it if you had a formula to describe the acceleration.
Yes, Ok, if I give you the acceleration, but what if I give you an equation of its position:

x = 0.5 t^3 + 3 t^2

what speed is it going at, at time t=10?
 

Offline Geezer

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Re: Are some people born good at maths?
« Reply #23 on: 04/02/2012 01:18:39 »

x = 0.5 t^3 + 3 t^2

what speed is it going at, at time t=10?

Oh dear! It's been a while. Without looking up anything on the internet, or cracking a book
 
x = 0.5 t^3 + 3 t^2
 
so,
 
dx/dt = 1.5 t^2 + 6 t
 
(probably wrong!)
 

Offline David Cooper

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Re: Are some people born good at maths?
« Reply #24 on: 04/02/2012 22:39:03 »
Yes, Ok, if I give you the acceleration, but what if I give you an equation of its position:

x = 0.5 t^3 + 3 t^2

what speed is it going at, at time t=10?

I wouldn't know where to start with that.

dx/dt = 1.5 t^2 + 6 t

I can do differentiation and integration without any difficulty, but I've never been shown how to apply them to any kind of meaningful problem. Like I said before, doing this stuff at school was like being made to learn a language without ever being allowed to know what any of the words mean, so I've got the algorithms in my head (or at least some of them), but I haven't a clue what can be gained by applying them to anything.
 

The Naked Scientists Forum

Re: Are some people born good at maths?
« Reply #24 on: 04/02/2012 22:39:03 »

 

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