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.
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.
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
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.
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.
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.ca/people/codoban/PHY138/Mechanics/dimensional.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
Eigenvalues and eigenvectors are probably my favourite thing about this year. Although stuff like defining eiθ=cos(θ)+isin(θ) was also pretty interesting. Even if my exam board does use j and not i
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 ℵωℵ0=2ℵ0 then the former must be smaller than ℵω4.
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
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