Split analysis/linear algebra course..
[URL]http://www.newcastle.edu.au/course/MATH1210.html[/URL]
Have my exam in... ~8.5hours
Going over the exam in my head, I realise that I got an answer correct for the wrong reasons..
We had the complex number [; (z)^{10} ;], where [; z = 1 - \sqrt{3}i ;],
I worked out the Argument to be [; -\frac{\pi}{3} ;] and the modulus to be 2.
My exam brain, doped on Redbull read this as, [; \frac{2\pi}{3} ;], not the actual value of [; \frac{5\pi}{3} ;]
So, in blissful ignorance, I get [;z = 2e^{\frac{2\pi i}{3}} ;]
Hence, [; (z)^{10} = 1024e^{\frac{20\pi i}{3}} ;]
With nothing short of amazement: [; \frac{20\pi}{3} = \frac{2\pi}{3} ;], and [; \frac{50\pi}{3} = \frac{2\pi}{3} ;]
Moral of the story folks, I'm glad that I don't do engineering. :eng101:
Here is an IMPORTANT question for the mathematicians of FP:
How do you end a proof? Just end it? Write QED? Draw the little square? If it's the square, filled or unfilled?
For me it's unfilled square.
Tombstone - Filled in.
reddit sure looks different than it usually does
bigger avatars too
filled square with two dashes on each side
for my horribly unrigorous differential-raping physics proofs
Nothing. I don't see why I would put anything at the end of it, really. Usually, if you redact it decently its outlines are obvious enough that one can identify that the proof is complete. Or just finish with the initial statement, which usually is whatever the proof is trying to demonstrate.
Yeah I usually just write down that all the steps of the proof imply whatever the initial statement was.
I had this brilliant idea yesterday to digitalize all my single variable calculus notes and create an "online course" if you can call it that.
Wrote 1 article and got bored to death.
I've done that before, or something like that. Typing up study guides which cover all the course material in LaTeX is nice.
Yesterday I thought how a torus was a circle something something another circle in the context of my limited knowledge of topology.
Apparently it's
[; S^1 \times S^1 ;]
close enough.
Going on a weeklong cruise in a couple of weeks and since I'm going to study engineering at uni in autumn I thought it would be a good idea to kindle my interest for maths/physics. Since there will probably be a good share of boring nights I'm currently looking for books that contain a good portion of actual math just in a popular science kind of presentation. Does anyone have any recommendations?
[QUOTE=FPSMango;41147689]Going on a weeklong cruise in a couple of weeks and since I'm going to study engineering at uni in autumn I thought it would be a good idea to kindle my interest for maths/physics. Since there will probably be a good share of boring nights I'm currently looking for books that contain a good portion of actual math just in a popular science kind of presentation. Does anyone have any recommendations?[/QUOTE]
Anything by Julian Havil. I really liked [i]The Irrationals[/i].
[QUOTE=FPSMango;41147689]Going on a weeklong cruise in a couple of weeks and since I'm going to study engineering at uni in autumn I thought it would be a good idea to kindle my interest for maths/physics. Since there will probably be a good share of boring nights I'm currently looking for books that contain a good portion of actual math just in a popular science kind of presentation. Does anyone have any recommendations?[/QUOTE]
here's looking at euclid
(alex's adventures in numberland is the UK title)
its great really
I dunno if I've posted this before but if anyone is interested in learning algebraic topology, Allen Hatcher's textbook (probably the most widely used) is available for free! Legally!
[url]http://www.math.cornell.edu/~hatcher/AT/ATpage.html[/url]
This may be sort of a weird question to ask in a maths forum, especially since I probably know the answer; but what exactly is topology, and how would it best be used in a real-world application?
I know that you can use it for certain number puzzles
[QUOTE=mastoner20;41203437]This may be sort of a weird question to ask in a maths forum, especially since I probably know the answer; but what exactly is topology, and how would it best be used in a real-world application?[/QUOTE]
Topology is the study of shape, in a very abstract sense. It builds up a lot of basic properties that spaces can have (like compactness, connectedness, separability, etc.) and uses them to describe given spaces.
I'm not sure of a lot of the applications of topology outside of physics (I don't think there are a ton, it's sort of on the edge of very abstract mathematics) but it does show up in string theory, quantum field theory, and in certain mathematical formulations of classical mechanics.
I see. So sort of a combination of geometry with probability?
Probability? No.
[editline]26th June 2013[/editline]
Wikipedia's overview is pretty good.
[url]https://en.wikipedia.org/wiki/Topology[/url]
Oh, oh, I see. I was thinking probability in a sense of 'what's the likelihood of two things being connected' type of thing, for some reason. I can see how that'd be a really interesting topic to study. How advanced would the book you mentioned be for an undergrad where introductory discrete mathematics is the highest math course they have completed, would you say?
Too advanced. You really need a course in general topology before you tackle Hatcher. Algebraic topology builds on basic general topology. Munkres is a very good introduction to general topology, but for that you're probably going to want to have some experience with rigorous proofs and maybe advanced calculus.
You may want to glance through the early sections of the book though. There are some neat topology proofs in there, like the Borsuk-Ulam theorem: at any given time there is at least one pair of points on directly opposite sides of the earth with exactly the same temperature and barometric pressure simultaneously! (assuming temperature and pressure are continuous) Which is to say, you have two points, a and b, and if you draw a line between them it will pass through the center of the earth. At some point in time, temp[sub]a[/sub] = temp[sub]b[/sub] and pres[sub]a[/sub] = pres[sub]b[/sub]. My original wording was a bit confusing.
Is there an irrational number which is its own irrationality measure?
[QUOTE=Krinkels;41226823]Is there an irrational number which is its own irrationality measure?[/QUOTE]
[url]http://math.stackexchange.com/questions/91210/is-there-any-real-number-except-1-which-is-equal-to-its-own-irrationality-measur[/url]
An infinite number of them in fact, and they are dense on [2,infinity)
It's possible to construct them because in some sense the irrationality measure only cares about the 'end' of the continued fraction, so you can make it arbitrarily close then construct the remaining terms as required.
[QUOTE=Joey90;41241833][url]http://math.stackexchange.com/questions/91210/is-there-any-real-number-except-1-which-is-equal-to-its-own-irrationality-measur[/url]
An infinite number of them in fact, and they are dense on [2,infinity)
It's possible to construct them because in some sense the irrationality measure only cares about the 'end' of the continued fraction, so you can make it arbitrarily close then construct the remaining terms as required.[/QUOTE]
Neat!
So I saw The Killing Fields 0/10 was not actually a feature film about generators of isometries on manifolds.
[img]https://dl.dropboxusercontent.com/u/11323379/yeyweryw.png[/img]
Been stuck with this equation for some time now, could someone give me a hand as to how I'm suppose to solve it?
Well your first step should be to factorise the numerators of the first two terms, so they become 2(x^2 +2x) + 1 and 2(x^2 +2x) - 1. Then replace all the 'x^2 + 2x's in the equation with 't', and solve the partial fractions. From there you should end up with a quadratic, which you can solve to get 2 values of t. Then just replace 't' with 'x^2 + 2x' for each value, solve the quadratics, and you'll get your values of x.
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