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 Posted: Sat May 13, 2006 5:04 pm
If you would like to provide some comments regarding the intro to relativity thread, please do so here.
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Posted: Sat May 13, 2006 5:46 pm
In Australia at least, complex number theory is only taught in the last year of high school at the most advanced level of maths. I would suspect it is also not covered in Algebra II, though I am not at all familiar with the US education system, and admitedly the Aussie system is, well, crap.
Also, perhaps using LaTeX for some of the equations? Perhaps just the more cumbersome ones like cos t = [e^{it} + e^{-it}]/2
I've got LaTeX somewhere I think if you want me to write up the equations in it.
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Posted: Sat May 13, 2006 6:11 pm
Dave the lost In Australia at least, complex number theory is only taught in the last year of high school at the most advanced level of maths. I would suspect it is also not covered in Algebra II, though I am not at all familiar with the US education system, and admitedly the Aussie system is, well, crap. Well, I know for certain that complex numbers themselves are covered in Algebra II, although I'm not so sure about Euler's formula. I don't believe it should present any difficulty to someone already familiar with the basics of complex numbers, though. Dave the lost Also, perhaps using LaTeX for some of the equations? Perhaps just the more cumbersome ones like cos t = [e^{it} + e^{-it}]/2 I've got LaTeX somewhere I think if you want me to write up the equations in it. That's a good idea. I've added some LaTeX-made inlined images to clarify some of the equations. Gah, the image had a typo.
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Posted: Sat May 13, 2006 7:20 pm
Aye, under some of the poorer American systems (among them my school system, Los Angeles Unified) imaginary numbers need not be taught at all. I didn't learn them until I took a mechanics course, and spring oscillations (as well as circuits) required imaginary numbers. Maybe you could describe more about that?
Also, for some, trigonometric identities (or ideas) were not covered adequately in geometry, only in well...trigonometry.
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Posted: Sat May 13, 2006 7:38 pm
Hmm. That's an important omission from schoolwork. I'll rewrite it soon, then.
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Posted: Sun May 14, 2006 7:01 pm
Aye, I'm probably not the best to comment on the "average" American high school student. I went to a barrio school in Los Angeles sweatdrop
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Posted: Sun May 14, 2006 7:51 pm
My geometry course didn't teach trigonometric ratios either, of course I'm not so sure if that's normal or not. The school didn't have a permanent math teacher for my class at the time, and we went through a new substitute every two weeks.
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Posted: Sun May 14, 2006 8:13 pm
VorpalNeko: you're going to teach trigonometry? isn't that a bit cumbersome? Dave the lost: did you do trigonometry? what is it that you don't understand? Perhaps you can ask directly from what VorpalNeko has posted and we can try and explain as best we can here.
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Posted: Mon May 15, 2006 2:42 am
[ Message temporarily off-line ]
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Posted: Mon May 15, 2006 5:44 am
If you know trig, and complex numbers, and you're aquainted with euler's formula... and apparently no one else has complained... then what's the problem?
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Posted: Tue May 16, 2006 4:54 pm
That's the thing; Euler's formula isn't taught in many American high schools. I didn't know it until I had to do spring mechanics last semester.
Aye, I mean things like that. All of the sine/cosine relations, addition and subtraction of angles, and (to an extent) Taylor expansion.
Matrix notation is incredibly useful; the course I'm in now (Linear Algebra) uses it for everything, and it makes life so simple.
I'm sure if anyone has problems with these things they can PM anyone else in the physics guild - especially the moderators - to find out.
Oh, also, matrix notation is not taught in my high school, either. But it's so great to learn.
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Posted: Tue May 16, 2006 7:39 pm
He said he wanted it to be taught with high school level maths.
So I was pointing out bits of the maths that weren't, to the best of my knowledge, high school level.
Just because those people who are currently here now commenting on this thread understand the material, doesn't mean that all present and future guild members have the same understanding.
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Posted: Tue May 16, 2006 10:15 pm
poweroutage VorpalNeko: you're going to teach trigonometry? isn't that a bit cumbersome? Definitely not! I'm assuming that the reader is already familiar with trigonometry. However, a brief review will be beneficial, particularly since I use it as a springboard to hyperbolic trigonometry, which is useful in STR. Dave the lost He said he wanted it to be taught with high school level maths. So I was pointing out bits of the maths that weren't, to the best of my knowledge, high school level. You're right. Matrices were taught in my high school, but since it seems this is not all that common in high school settings, Ill make sure to rewrite it so it is optional (it already is, kind of). I will, however, expect basic knowledge of complex numbers. I should probably write a brief review of how they work, but given that, it seems the only truly new piece of information that is still necessary is Euler's formula. I do not think it is too much to ask those unfamiliar with it to learn how it works (although not necessarily why it works, which would require calculus). If one is familiar with complex numbers and the standard exponential function (which I know is covered in Alg II), it really shouldn't be anything mind-shattering.
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Posted: Thu May 18, 2006 10:53 pm
Wow...this is really making me think of just how much math is required to be able to do physics reasonably well. I realized, while trying to explain an EM problem to someone, that I use multivar calc on a near-daily basis without even thinking about it.
Which leads me to my next suggestion. What about a small topic/forum-thingy that just goes over the math itself, for whichever topics are being done? That way, an inexperienced user can learn the math at their own rate, while the "physics" part of it can be explained without being overly mathematical at any given time? Instead of teaching both at once, you'd just have two topics open.
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Posted: Fri May 19, 2006 10:31 pm
So (if you don't mind sharing) what's your plan of action with the thread? You could generalize the worldline concept into multiple dimensions, but that doesn't seem like your style. Include more on the nature of this method? Springboard straight into relativity?
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