mathwonk's latest activity
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Mmathwonk replied to the thread Undergrad Meaning of division by non-whole real numbers.Interesting question. I haven't thought much about it, but if I understand, I think the point here is that, if one is given a unit...
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Mmathwonk reacted to Roberto Pavani's post in the thread Undergrad Meaning of division by non-whole real numbers with
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As a humble engineer, I think there's both a counting bias and a decimal bias here. We are taught to think of numbers mainly as counts... -
Mmathwonk replied to the thread Undergrad Meaning of division by non-whole real numbers.@Roberto Pavani: As a geometer, I share your point of view, as did Euclid. I.e. real numbers are essentially lengths on a line, (after...
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Mmathwonk replied to the thread Basic skills that kids are lacking.I should have mentioned I was the original referee for Riemann's paper. Unfortunately I rejected it for lack of detail, but they...
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Mmathwonk replied to the thread Basic skills that kids are lacking.Is it possible there are people today who think kids no longer need to know Euclidean geometry!? Or the Riemann - Roch theorem? Perhaps...
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MWhile increasingly rare, there are still situations where they still need to know how to write a check. Analogue clocks are still...
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Mmathwonk replied to the thread Learning linear algebra.Welcome to PF. I recommend Michael Artin's book: Algebra, as a good guide to linear algebra and other topics in algebra. With your...
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Mmathwonk replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.Courant, Differential and Integral Calculus, vol. 1, pp. 352-3.
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M(Apologies if some of this was already said while I was typing it out... had to leave and come back to it...) In most cases when a...
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MYou flunked two semesters of community college? If I'm reading that right, that's not a good sign of potential success at this time...
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Mmathwonk replied to the thread Graduate Zeros of functions analytic in 2 variables.If the z2- partial derivative of f at p is non -zero, then near p, on f=0, z2 is indeed a single valued function of z1; but if both...
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Mmathwonk replied to the thread Graduate Zeros of functions analytic in 2 variables.I don't know if the argument for my statement is of interest, but it is nice and fairly short; namely, Riemann showed for analytic...
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Mmathwonk replied to the thread Graduate Zeros of functions analytic in 2 variables.are z1, z2 complex variables? if so, the zeroes of an analytic function of 2 complex variables are never isolated.
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Mmathwonk replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.It helps to have a definition of e. One definition is that e is the unique base such that the derivative of e^y at y=0 equals 1. Since...
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Mmathwonk replied to the thread Other Collection of Free Online Math Books and Lecture Notes (part 1).short calc is a first course in calc, less than 300 pages, terse, no epsilonics. Undergrad analysis is a 3rd course in calc, very...