WHO LOVES MATH <3

[mandy]

Is anyone here doing all three math: Further, Methods and Specialist?
How are you finding it? Is it all too much ? Because I may do it next year, and I wanna know how it is ..

Hope that you don't have annoying teachers that do book checks, and do only the amount of homework you really have to do. I basically only did exercises for probability in Methods because everything else was basically covered in spesh (which did involve a lot of work), or I would have understood it from in-class teaching and didn't require further conceptual understanding or practise. Basically, don't do maths homework for the sake of satisfying your syllabus, but instead focus on what you can gain from it.

So you're saying it's better to simply listen and concentrate in class, and only do questions when I actually need practise? That sounds good.
And luckily, I don't have annoying-book-checking teachers, rofl. They just set the hw and never speak of it again. Don't even know if thats a good or bad thing!

It depends on the person. I know that I probably understand concepts faster than most people so this is by no means a strategy that will suit everyone. But yes, that's how you should work in general with most subjects. If you understand the conceptual stuff behind it well enough, you won't need that much practise. Well, not of the dodgy textbook-grind variety at least...exam preparation gets a bit different though for the analysis questions though which many people might not have the capability to work out the methods to solve them the first time around and require some experience beforehand.

Yes, thats like me. I can do the normal questions really easily, but when it comes to analysis questions, it takes me awhile to figure out what they want me to do :S It's horrible and such a waste of my life.

[TrueTears]

Is anyone here doing all three math: Further, Methods and Specialist?
How are you finding it? Is it all too much ? Because I may do it next year, and I wanna know how it is ..

Hope that you don't have annoying teachers that do book checks, and do only the amount of homework you really have to do. I basically only did exercises for probability in Methods because everything else was basically covered in spesh (which did involve a lot of work), or I would have understood it from in-class teaching and didn't require further conceptual understanding or practise. Basically, don't do maths homework for the sake of satisfying your syllabus, but instead focus on what you can gain from it.

So you're saying it's better to simply listen and concentrate in class, and only do questions when I actually need practise? That sounds good.
And luckily, I don't have annoying-book-checking teachers, rofl. They just set the hw and never speak of it again. Don't even know if thats a good or bad thing!

It depends on the person. I know that I probably understand concepts faster than most people so this is by no means a strategy that will suit everyone. But yes, that's how you should work in general with most subjects. If you understand the conceptual stuff behind it well enough, you won't need that much practise. Well, not of the dodgy textbook-grind variety at least...exam preparation gets a bit different though for the analysis questions though which many people might not have the capability to work out the methods to solve them the first time around and require some experience beforehand.

Yes, thats like me. I can do the normal questions really easily, but when it comes to analysis questions, it takes me awhile to figure out what they want me to do :S It's horrible and such a waste of my life.

Practise makes perfect.

[kamil9876]

Loving it. Whenever I am supposed to study on my breaks in the library or eat lunch/go to lectures  I always forget to do so because all these maddog random books - like most recently, Gauss' Disquisitiones Arithmeticae - or some Olympiad problems take control over me.

[monokekie]

when i m good at maths i love maths, when i am bad at maths i hate maths.

the more effort you put into this subject, the more you will love it.

[IntoTheNewWorld]

I can't even do textbook questions. When I can't do a question for a while, I quit and go do some physix instead.

[zzdfa]

i loves math <3

literally the only time i have the willpower to spend time on other subjects  is when i have to do an assignment. any other time, there's always a nagging maths problem in the back of my head that i HAVE to solve first.

like most recently, Gauss' Disquisitiones Arithmeticae

hawt. which translation are you reading? i've started skimming through "Visual Complex Analysis" lately (theres a link to the pdf in ahmad's maths links thread). I wanted to see why everyone claims that Complex Analysis is the most beautiful branch of mathematics. from what ive seen so far it is pretty hot (e.g. geometric interpretation of e^(ix) = cosx+isin(x) )

or some Olympiad problems take control over me.

Putnam problems are also fun, if you want to try using your uni maths knowledge the same way you use elementary stuff in olympiad problems.

[kamil9876]

hah yeah I like the very elementary olympiad problems(not neccesarily easy, just ones with simple notions like number theory(check out the partition problem in Fun Questions)). I think I've done a Putnam problem or two before, they're quite cool . But when it comes to uni knowledge I probably like to focus more on rigour and reading/appreciating elegance rather than trying to use my own creativity since there has been a lot more thought put into the stuff there. But once that is down pat bring on the creativity

[humph]

Read Apostol's Introduction to Analytic Number Theory if you're interested in more fancy number theory - you do need some complex analysis, but it's a pretty well-written book so you can get by well enough without it.

[QuantumJG]

Is anyone here doing all three math: Further, Methods and Specialist?
How are you finding it? Is it all too much ? Because I may do it next year, and I wanna know how it is ..

I love maths!!!

I am planning on doing a major in something related to it.

[/0]

I like it, but prefer learning theory to problem-solving. There's so much to learn, and such little time to learn it in. I guess that's more sciency than mathsy but yeah whatever.

[humph]

I like it, but prefer learning theory to problem-solving. There's so much to learn, and such little time to learn it in. I guess that's more sciency than mathsy but yeah whatever.

Not at all - I'm much more of a theory person than a problem-solver (though this forum is definitely biased towards the latter, as is VCE in general). I don't think that's more sciency than mathsy; mathematicians such as Grothendieck are famous for devoting their entire lives to mapping out entirely new areas of mathematics and creating whole new theories, while solving absolutely no problems whatsoever. University subjects tend to be much more about theory than problem-solving, in any case, though of course there has to be a certain element of it for assessment purposes.

[kamil9876]

What is this dichotomy of theory and problem solving? Although I do agree that there are differences between the two, they are not on opposite sides of some scale. I think it's insulting to problem solving to say that VCE is biased towards it since VCE mostly consists of exercises rather than real, nice problems. Wrestling with a problem forces you to be creative and hence look out for things when doing theory, rather than just doing theory by sticking to strict definitions and deducing things from axioms and definitions that have probably been formulated by the real creator who only introduced it after he solved the more complex aspects. Hence an unnatural view of the subject. Although sometimes the problems too are contrived in such a way that the trick/answer was invented and hidden before the problem was formulated.

Of course this all boils down to what kind of problem solving is being compared to what kind of theory learning, so I can agree with both views depending on the situation. However it's good to learn some problem solving without being hardcore IMO-competitive, just to get the mind working and be more alert and creative with theory. Simpy, I don't like how some people are filled with dry theory but not real, natural mathematicians in soul.

[humph]

What is this dichotomy of theory and problem solving? Although I do agree that there are differences between the two, they are not on opposite sides of some scale. I think it's insulting to problem solving to say that VCE is biased towards it since VCE mostly consists of exercises rather than real, nice problems. Wrestling with a problem forces you to be creative and hence look out for things when doing theory, rather than just doing theory by sticking to strict definitions and deducing things from axioms and definitions that have probably been formulated by the real creator who only introduced it after he solved the more complex aspects. Hence an unnatural view of the subject. Although sometimes the problems too are contrived in such a way that the trick/answer was invented and hidden before the problem was formulated.

Of course this all boils down to what kind of problem solving is being compared to what kind of theory learning, so I can agree with both views depending on the situation. However it's good to learn some problem solving without being hardcore IMO-competitive, just to get the mind working and be more alert and creative with theory. Simpy, I don't like how some people are filled with dry theory but not real, natural mathematicians in soul.

Heh. Without realising it, you're very biased towards the problem-solving side; many mathematicians would still consider people filled with dry theory to be "real, natural mathematicians in soul." There's a massive difference between the mathematical careers of, say, Erdos vs. Grothendieck - the former motivated completely by solving problems, the latter completely by abstraction and creating new areas of mathematics. I don't think many in the mathematical community would say that one is more or less of a mathematician than the other though, but there definitely is a divide between those who tackle certain problems and those who work more generally in extending a field of mathematics (e.g. those who try to solve the Riemann hypothesis compared to those who generalise the notion of the prime number theorem to number fields and conjecture a similar hypothesis for that case).
Of course, it is possible to do both at once - Perelman is famous for solving a difficult problem (the Poincaré conjecture), but in doing so he unearthed an important new area of mathematics, by defining the Perelman flow on a Riemannian manifold. It's certainly the case that new theorems, definitions, and ideas can be unearthed when trying to solve a problem; in fact, it's quite unusual for a paper detailing the proof of some result not to contain some nontrivial, abstract theorems along the way. Similarly, many new theorems, or indeed new areas of mathematics, arise through a mathematician motivated by, or trying to generalise, a particular problem.
Though I don't think it's insulting to say that VCE maths is biased towards problem-solving. In any case, the only "difference" between exercises and problems is the labelling - exercises may be simple because the path to solve them seems clearly laid out, but that's just personal perception. It just depends on how quickly you're able to make the leap from a problem to its solution.

[kamil9876]

Yeah I agree with all of that - except for me being biased to problem-solving . I do enjoy theory probably more as well, but I think certain problem solving can help with understanding theory a lot and in some way there isn't a big gulf between certain kinds of theory and certain kinds of problems. E.g: there is a bigger gulf between a VCE math problem and Riemann Hypothesis than there is between Riemann Hypothesis and Grothendieck-like maths, that's what I didn't like about the dichotomy. Also some IMO problems, although they aren't the biggest gems in mathematics, can help in developing an insightful mind and I believe the people who enjoy these sorts of problems would be more interested in theory than vce problem solving. And yes I agree that many top level mathematicians may be real mathematicians in soul without being concerned with Erdos-like problems, but I'm sure that when they were young(say mine or /0's age) they must've been curious about problem solving(on a level much lower than Erdos) and in some way inspired by it to be creative and excell in theory.

Also: finding the area under a parabola is an average methods problem; but Ancient Greeks, Cavallieri etc. finding it was a big thing.(Theory or problem solving? I can't really tell hence again my confusion/dislike of the dichotomy)

[shadowbane91]

I love maths, however I have a slight dislike of probability, however its pretty cool to see it applied to real life situations, in particular gambling, lol, facinating. Even so, this is all a tad intimidating seeing everyone's exceptionally high enter scores on this forum lol!