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What's the most interesting thing you have learned this year in maths?

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1. I did some work in dimensional analysis in second semester, and I find it amazing that from some basic knowledge and a photo of the explosion, we can estimate the energy released from the first atomic bomb explosion. You can read this if you are interested: http://www.atmosp.physics.utoronto.c...imensional.pdf

So what's the most interesting thing you have learned this year? It can be anything at all from any level of mathematics.
2. The Fibonacci sequence is quite interesting and its links to the financial markets
3. Calculating the Age of the Universe from Hubble's Constant.
4. Abel's impossibility theorem: There is no solution in radicals to polynomial equations of degree five or higher with arbitrary coefficients. Probably because it took a lot of machinery and was built up for ages and ages just to arrive at this result that I was aware of for a while but never had any idea why. (tbh I am still trying to fully understand it so maybe I can't say I have learned it rather learning it). I remember being told a story by someone at Warwick that GI Taylor shocked everyone by telling them how powerful the bomb just on the back of a piece of paper and they didn't know how to react because they thought they had kept it highly classified and didn't realise it was possible to estimate haaaa.
5. I would probably say the Baire Category Theorem. Not a massively high tech result but so useful, and with some very pretty consequences.
6. when you have e^-n, as n approaches infinity then e^-n approaches 0 but don't understand at all why....
7. (Original post by fefssdf)
when you have e^-n, as n approaches infinity then e^-n approaches 0 but don't understand at all why....
e^(-n) = 1/e^n.
Now, as n approaches infinity, the e^n approaches infinity - you can see this by considering the graph y=e^x, which continuously increases as x increases.
Thus 1/e^n approaches 1/infinity, i.e. zero.
8. (Original post by HapaxOromenon3)
e^(-n) = 1/e^n.
Now, as n approaches infinity, the e^n approaches infinity - you can see this by considering the graph y=e^x, which continuously increases as x increases.
Thus 1/e^n approaches 1/infinity, i.e. zero.
ohhhh interesting - thanks for clearing this up aha
9. (Original post by fefssdf)
when you have e^-n, as n approaches infinity then e^-n approaches 0 but don't understand at all why....
e^-n = 1/(e^n)

so when n approaches infinity, e^n also approaches infinity

1 divided by a very big number (a.k.a infinity) is 0

so 1/(e^n) approaches 0
10. (Original post by lyamlim97)
e^-n = 1/(e^n)

so when n approaches infinity, e^n also approaches infinity

1 divided by a very big number (a.k.a infinity) is 0

so 1/(e^n) approaches 0
thanks yo !
11. Most of it was just fairly interesting and not close to mindblowing. I guess the Riemann Series Theorem was the best. Most of analysis 2 (dealing with continuity, differentiation, power series) was very interesting to me but nothing sticks out.
12. Nothing I did this year was particularly interesting, although I am enjoying learning about group theory atm, especially cyclic groups

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13. 2 + 2 = fish!!
YAY!!
:3
14. Runge-Katta methods for numerically solving complex ordinary differential equations.
15. Pretty much all the A2 pure modules I did this year. (and M3 relative velocity)
16. I learned about binomial and Poisson distributions. I have really begun to enjoy statistics.

(I'm still at school not at uni)
17. Statistics rules I'm technically not at uni yet either, but I'm studying maths/stats
18. nothing -.-

I wish the syllabus was better
19. (Original post by Student403)
nothing -.-

I wish the syllabus was better
Are you doing GCSE, A Level, or Uni?
20. (Original post by rayquaza17)
Are you doing GCSE, A Level, or Uni?
Just finished A2 - I really liked the dimensional analysis you posted. Learnt a much more basic version of that this year.. Shame school didn't teach it

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