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    Set theory. I loved how it formalised so much, how it constructs the numbers and the arithmetic associated to them we're so familiar with, along with relations and functions. The proofs were fun too.

    (Original post by The Joker ~)
    2 + 2 = fish!!
    YAY!!
    :3
    I have to go with this as well. That's one of the most profound equations I have learned, personally. I have never looked at fish in the same way again.
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    I love Maths - I don't find it interesting but it's a good subject ! Plus it's easy to understand once you've done 10 or more sums on the topic
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    The connections between maths and physics,particularly the connections between geometry and particle physics.
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    When considering planetary waves it can be entirely appropriate to consider the oceans of the world to be "shallow waters".

    Edit: Oops just reread the title, I learnt that nearly 10 years ago not but still find it amusing.

    I learnt that any divisor that can be written in the form (2^m)x(5^n) will give a terminating decimals if the divident is rational. Never underestimate the things you can learn teaching an S1/Year 7 class
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    Probably about how incredibly useful matrices are for computation. I don't regret choosing my subject but I think Computer Science would have been an absolutely fascinating subject to study too. I've got a lot of appreciation for the work they have done to aid scientific computation.
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    taylor's series
    euler's identity
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    Sin^2(x)+Cos^2(x)=1
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    Thinking outside the box to answer STEP questions.

    Also M3 was very interesting.
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    I really liked imaginary numbers, combinatorics and mathematical induction. I just finished high school though...
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    Jesus Christ, everyone answering with scary sounding FM or degree things!
    I feel like a right numpty saying I found Parametric Equations from C4 to be the most interesting thing this year.
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    (Original post by rayquaza17)
    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.
    Not a maths student on a formal basis but vampire numbers look weird and interesting to me
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    (Original post by rayquaza17)
    So what's the most interesting thing you have learned this year? It can be anything at all from any level of mathematics.
    Just an example to show that if you choose maths as a career, you go on learning forever (heaven!)...just this year I learned about:

    (a) Hamiltonian Markov Chain Monte Carlo as used in the STAN Bayesian statistics software.

    (b) Dirichlet stochastic processes as used in non-parametric clustering.
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    Eigenvalues and eigenvectors are probably my favourite thing about this year. Although stuff like defining e^{i\theta}=cos(\theta)+ i sin(\theta) was also pretty interesting. Even if my exam board does use j and not i:erm:
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    De Moivre's theorem and Taylor's/Maclaurin's series.
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    There are some remarkable results in the study of cardinals and the various models they offer. The area is partly interesting because of how many open questions there currently are. A very memorable result is that if \aleph_{\omega}^{\aleph_0}\neq 2^{\aleph_0} then the former must be smaller than \aleph_{ \omega_4}.
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    Uhhh I like adding, multiplying and subtracting because it's all you need in life.


    Yes I am doing Maths A-Level in Sep.
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    (Original post by chloeabeki)
    Jesus Christ, everyone answering with scary sounding FM or degree things!
    I feel like a right numpty saying I found Parametric Equations from C4 to be the most interesting thing this year.
    The more difficult/advanced things aren't always the most interesting! I found parametrics this year one of my favs as well

    I even experimented with them to create this: https://www.desmos.com/calculator/jekx6csxzm
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    Taylor and Maclaurin series
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    Tupper's Self Referential Formula - watch the numberphile video on it; it is very comprehensive.
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    Sometimes the most interesting puzzles are, on the surface of it, the most simple. I bet if we all have a look at the 5 Pirates puzzle and the Monty Hall problem we'll end up arguing
 
 
 
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