>>5
Delta/epsilon = real analysis. The AP exam does not require any delta/epsilon proofs. The OP was concerned about the exams. What moar do you want?
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Anonymous2007-08-06 9:55 ID:CgiLuVld
The Riemann integral is less powerful than the Lebesgue integral. But I don't think anywhere actually teaches Lebesgue instead of Riemann, which is sad.
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Anonymous2007-08-06 11:26 ID:PJ/OPBHl
>>8
In the US, Lebesgue may not be taught until early graduate courses. It's kind of sad. The schools with stronger math departments teach Lebesgue near the end of the undergrad stream.
Of course, most applied disciplines don't bother with these classes. Engineers usually only take enough mathematics to get a "feel" for PDEs and (possibly) complex variables.
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Anonymous2007-08-06 13:35 ID:CgiLuVld
>>9
I'm surprised to hear it's taught anywhere at all: in the UK it's more or less unheard of unless you are in a specific research discipline that requires it. (I've a friend in complex dynamics and a friend in probability, and Riemann just doesn't cut it quite alot of the time so they need him; but they wouldn't otherwise I'm quite sure.)
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Anonymous2007-08-06 14:42 ID:emjTBNJl
>>10
I'm doing maths at Cambridge uni, just completed my first year. It was mentioned to us as an alternative, during Analysis1 lectures, but that was all I've heard. Analysis2 may go into it a little, I'm not certain.
At any point in the English higher education of mathematics, Americans can be as much as about 5 years behind.
And Russians seem to do very well.
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Anonymous2007-08-06 16:09 ID:0r/V7sqW
eastern european fag here. it's taught at uni level in the 3rd (of 4) year in a mandatory one semester course called 'measure theory'. it's also mentioned in analysis 1 (ooh look you can integrate over \Sigma_Q too bad most of you won't get there)
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Anonymous2007-08-06 18:34 ID:gbRGY1Cl
Lebesgue integration is taught as one of the first topics in the Honors Analysis I course for first and second years at UChicago, which is an american uni.
And Lebesgue isn't the only integral. There's Darboux, Stieltjies, Bochner, Daniell, Ito, That other Russian faggot who did the other stochastic integral that chooses the midpoint instead of the endpoint in its integral definition (Ito integration chooses the endpoint for you newfags)... Lebesgue integral just happens to be one of the most convenient.
At its most general, an integral with respect to a measure is simply a linear functional from a function spcae with elements taking values on the measure space into this space. That's all. (Well, that's the Daniell view of integration, at least.)
SO LIGHTEN THE FUCK UP ABOUT LEBESGUE ITS NOT NECESSARILY THE BEST OR MOST GENERAL
I've only taken the first semester test (I think that's AB right?) but I got a 5 on it and I think what helped me the most was taking a couple of the previous calculus tests to find out what I didn't know how to do and then figuring out how to do it. I had trouble with free response problems that were like your filling up a tank with this equation and you need to find out how fast the volume is increasing and how fast the hight of the water is increasing, but after doing 2 or 3 of those problems and spending some time on them I remembered how to do it on the real test.
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Anonymous2007-08-07 8:51 ID:EuXbTt0p
calculus B.C. (before christ) was all about GILGAMESH
lol what'd you get?
I've also just finished first year maths at trinity.
They did mention that we'd do lebesgue, probably in IB.
They said that it would integrate a function that is defined as 0 on all irrational points and 1 on all rational points between 0 and 1.
Common sense says the integral is 1, but it's undefined in riemann.
They probably either missed the lecture or weren't listening too hard, it was a real offhand comment
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4tran2007-08-07 13:42 ID:EMpy3LO8
>>19
I thought common sense would say that the integral is 0, since there are an uncountably infinite # of irrational numbers >> a countably infinite # of ratinal numbers?
#11 here, sorry this is a bit overdue, I keep skipping over this thread because it's so boring! I didn't know there were any other 4channers from my year in uni, except another one that I know from Clare. Yeah I'm from Clare by the way, ha.
Nice work on the S in STEP 3. I got I in STEP3 and S in STEP2. How'd your exams go?
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Anonymous2007-08-08 4:11 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH
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Anonymous2007-08-08 4:12 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH
Name:
Anonymous2007-08-08 4:12 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH
Name:
Anonymous2007-08-08 4:12 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH
Name:
Anonymous2007-08-08 4:12 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH
Name:
Anonymous2007-08-08 4:12 ID:eIzj6N2n
calculus B.C. (before christ) was all about GILGAMESH