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The Geniuses' Thread
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Unfortunately I'm not nearly studious enough to use anything but my notes and supplements but I can give some of the recommended texts for some of my modules.
We're recommended Calculus - A Complete Course by Robert A. Adams for my Diff. & Integral Calculus module. However it's worth noting that the module is more about explaining where the basics of calculus come from. Honestly it feels more like LC level with a bit more depth (and designed to seem more confusing than it is).
Ah fair enough, I'll look elsewhere for Calculus (although maybe the "more depth" part is worth looking at), actually may repost this in the Maths forum now and check back tomorrow, I'd probably get more answers there.Another module I have is about problem solving. While it's mostly only about utilising techniques and forming strategies for solving problems it does teach a bit of number theory. Unfortuntaley it assumes you already know a few things, most of which can be explained by wikipedia if you're bothered.
Anyhow he recommends "The Art and Craft of Problem Solving" by Paul Zeitz or "How to Solve it" by George Polya. I'm going to check out the former when I get the chance but I don't imagine either explains a lot about Number Theory itself. "Elemetary Number Theory" by Gareth A. Jones was something that was mentioned in my Number Theory module last semester so I'd say it's definitely something to look into.
Heard quite a few good things said about "How to Solve it", think I actually had a a PDF of it once but never really got around to starting it. Might get it again :P.I'm afraid I'm a bit useless on the graph theory front, it's a second year module in my case for some reason. Let the fact that I haven't tried learning it independently be a testament to my laziness.
I only really saw it incidentally to be honest :P.
At some computer nerd thing at which it was mentioned, saw it and immediately decided it was the coolest form of Maths, as it's all graphical and useful
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Don't think there are much dedicated books on it, seems to be a fairly small field, it'd probably get a few chapters in some books on relatred subjects more often than books to itself.0 -
Are you looking for more proof-y calculus (i.e. analysis) or are you just looking for problems/solutions-y calculus (i.e plain old calculus :P)?
We've done two courses involving calculus this year. One was called "Advanced Calculus" (oh the ironing) in which we uses Thomas' Calculus - that course was the straight problems one. We've also done an Analysis course this year (it basically builds up to doing the fundamental theorem of calculus etc), and Spivaks Calculus was the recommended textbook.
Neither are particularly difficult courses though, but the books may prove moreso!
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Are you looking for more proof-y calculus (i.e. analysis) or are you just looking for problems/solutions-y calculus (i.e plain old calculus :P)?
We've done two courses involving calculus this year. One was called "Advanced Calculus" (oh the ironing) in which we uses Thomas' Calculus - that course was the straight problems one. We've also done an Analysis course this year (it basically builds up to doing the fundamental theorem of calculus etc), and Spivaks Calculus was the recommended textbook.
Neither are particularly difficult courses though, but the books may prove moreso!
Either/Both :P. Proof-y would be a bit more interesting IMO, but what fun is maths without problems?
Looking at getting those books now, Thomas' one doesn't seem to be a problem to get. Wait found the other one too, spelled his name wrong >.>0 -
Either/Both :P. Proof-y would be a bit more interesting IMO, but what fun is maths without problems?
Looking at getting those books now, Thomas' one doesn't seem to be a problem to get. Wait found the other one too, spelled his name wrong >.>
Proof-y is infinitely cooler. Problems are just applications of proofs.. ¬.¬
Hopefully you'll find them interesting. I'll have a think and see if I can find anything useful for you! 0 -
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I'd recommend reading Fermat's Last Theorem. I found it very interesting. It pretty much gives you a whole history of Maths and some of the stuff in it gets pretty complicated. Definitely a lighter read than the rest, you won't need to have a pen and paper beside you for it!
For those interested, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two (thank you, Wikipedia).
As for textbooks, we were recommended Adams as mentioned earlier, but I don't think I ever used it once. If I ever need a Maths book it's Engineering Mathematics by K.A. Stroud. A massive book, it has pretty much everything you'd ever need! And if you need more, there's Advanced Engineering Mathematics by K.A. Stroud!
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D4RK ONION wrote: »9x-7i>3(3x-7u), solve for i
9x - 7i>9x - 21u
nines cancel.
-7i>-21u
change inequality when you change signs
i<3u
Oh very clever.
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EED wrote:it was not being used as an imaginary number! very clearly!!! it is just being used as a symbol the same as x and u!
The person who showed it me's words not mine 0 -
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