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Re: MX2 Integration Marathon Yep -xe^{-x^2} by inspection/product rule. For those, its pretty obvious the same exponential has to be in there because we cant obtain that as the derivative of something else. Unless its super hard, you can often guess it from there.

Re: HSC 2014 4U Marathon Lel, was planning on tearing into that post when I finished up with my essential work for today. Am glad Carrotsticks held down the fort. You need to really know what you are talking about to properly formulate questions that guide students through out-of-syllabus...

I would actually say the work is pretty different in undergrad to high school, at least in the case of mathematics where you are finally doing things rigorously and creative approaches are encouraged. First year is super easy though to ease people into it. As for a PhD, well I read lots of...

I was more mocking the OP, but it kind of is unless you have really specific and really high aims. Even then, the step up to postgrad is pretty ridic.

^ this. Knight's tour doesn't really illustrate any interesting concepts, and wouldn't be a memorable example if it wasn't for the fact that you can write it as having chess squares as nodes. My favourite parts of graph theory are actually when you get away from the combinatorial stuff and look...

lol undergrad is nothing too.

There weren't really enough questions in that quiz.

You are a: Left-Leaning Pro-Government Interventionist Cosmopolitan Progressive Collectivism score: 33% Authoritarianism score: 17% Internationalism score: 17% Tribalism score: -33% Liberalism score: 67%

Potentially, but just as a pretty short self-contained article/video. There isn't all that much to them.

Yeah of course, and that kind of stuff leads into statistics...most of which I don't find terribly interesting but things like random walks are pretty cool.

I have roughly ordered the topics by difficulty and how much you would probably need to know beforehand to properly understand the material.

Cool, these are definitely things I would be interested in talking about. I think that Hilbert space theory might be a little hard to motivate and explain to high school students, but well-prepared early undergrads could most likely handle it. One would probably need to have a reasonable...

Cheers, these are very good suggestions :).

Hi all. Sometime over the next couple of months I intend to start a professional blog to help me organise my mathematical writing and practice my exposition. (It will also give me a relatively easy way to answer the dreaded questions from friends on the contents of my research.) Most of this...

Well sure, that is a pretty natural human response to a new environment imo. I can just think of many examples of people (friends/acquaintances/colleagues) whose skillsets were far better suited to one environment than the other. (Eg I found that uni suited me FAR better than high school did...

Pretty strongly disagree with this, but whatever...everyone has their own experiences.

Its pretty different. Uni better rewards independent learning where you have a personal drive for the subject/s. It's pretty hard to do well by just going through the motions, which I find suffices in high school. I've seen plenty of people do amazingly in uni but not at high school, and vice...

Whenever there are factors with multiplicity > 1 in the denominator you will need to do this.

Ssbm.

As an extension, you might find it interesting to try and prove that \frac{Q(N)}{N\log(N)}\rightarrow 1 where Q(N) is the quantity in the question and log is the natural log.