Is my life now anything like I thought it would be when I was younger? Not even close.. I fucked up one too many times and made one too many dumb mistakes in life. I'm also incredibly lazy now so I honestly don't give a fuck anymore.
too bad for me I guess...
Optimization in calc basically refers to finding the min or max of something, the stuff burky and everyone else is talking about is completely different.
http://en.wikipedia.org/wiki/Optimization_(mathematics)
IronPlant = Wrong.
I'm not wrong about this. If he wants to have a complete understanding of the subject he needs to take calc. Period.Quote:
Originally Posted by OmniGear
Aight.
Ok, I'll straighten things out for you guys.
Joust is right; decision maths is mostly an idiot subject, that's why I took it as it is supposably easy, although it is very pendantic about the answers you give, hence I fucked up.
A lot of decision maths can be solved by simultaneous equations, for example with linear programming. A 12-year old could do most of that.
Then you have the algorithms, to find shortest routes across a network, where each line has a set value, for example time or money, in which you optimize in order to minimise the time/money spent. If you can model that using calculus IP, I will be impressed.
I think the optimisations which would require calculus would be things like what should the angles be inside a triangle, with a set perimeter in order for the area to be maximised and things like that. (We have only done optimising area/perimeter in shapes so far, nothing more, but what my class have officially covered is idiot material)
As for the fact that I have never done calculus, most of the maths course I take is pure maths, focussed heavily on calculus, but also on sums of series, proof, imaginary numbers, eigenvalues and vectors, etc. Officially I have been taught only basical calculus and application, which again a 12 year old could do; e.g: int(2x) = x^2 + C, and of course differentiation too.
Then because I am trying for Cambridge, I have taught myself most of this years work already, which is way more strongly focussed on calculus. Includes the calculus of functions and hyperbolic functions, applications to find the volume of a curve rotated x degrees round the y/x axis, length of a curve (hence the surface area of a 3-d shape after being rotated), to solve first and second order differential equations (with real and imaginary solutions) and then also the Maclaurin and Taylor series.
So I have done a bit of calculus.
What else do you do in calculus in university, as I hope to study that (applied and analysis) in more detail in my second year?
Thanks for trying to make me feel better IP, but I just fucked up that paper for no apparent reason. There is no calculus in that paper, nor could it possibly be used. I just had a bad day I guess.
(I'm pretty good at maths in general; there was a competition for 18s and under this year held across English speaking schools in Europe, in which I came 23rd, at which point I was 16. Next year I aim for top 10)
short answer, drive yourself insane and eat time.Quote:
Originally Posted by burky
To be honest I haven't thought about it a lot this summer. Last semester I got done with calc 2 ~ 5 hour, which means I had calc 2 and 3 over one semester, everyday, for an hour +/- 30 minutes. I've tried to not think about calc at all after the final.
I do however remember that physics relies heavily on it. The motion equations are all derivatives/integrals of each other. I forget the order, but position, speed, and think acceleration maybe, are related in that way. Another thing, off the top of my head, is some problems that you can solve with matrixes, can also be solved with calc. No one solves them with calc though, its easier to just type the numbers into a TI-89 and run a matrix on it.
You brought up modeling. I may be wrong about this, but I think one of the uses of calc is to get out of modeling crap.
Ok, I just found an online syllabus for decision maths
See if you think you can apply calc to any of that, but I can't see it myself.
I got a TI 84-plus which is the best calculator which I can take into an exam. It too does matrices (but not eigenvalues and vectors, but will do inverses), in which I only have to play with 3x3 matrices. It also applies calculus, but it will not tell you the derivitive/intergral of a function, only the result of an application, which is great for checking answers.
As for physics, I have covered the relationships between the motion equations, which wasn't so bad, as it pretty much makes sense (you learn in school the area under a speed time graph equals distance covered, so you just integrate the f(time) equals the distance covered)
I guess it gets more complicated though.
I fucking suck at math.
Yea, there's no Calculus there. IronPlant just thinks he knows everything.
If you want to be an Optimization expert, by all means, take Calculus. But there's not a lot of "change" in Optimization since you're mostly dealing with a discrete network and a discrete number of steps you're trying to limit. I took a course called Stochastic Processes, which deals with risk and probabilty
And yea, Calculus isn't the be-all end-all. You'll use a little bit of it in most of your courses but Linear Algebra is just as important, easily, especially in Applied Math courses.
And Calculus isn't tough, either. There's a lot of trial-and-error, and its time-consuming, but the entry-level courses are fundamentally similar to what you did in high school: no rigorous proofs and a lot of plug-and-chug. It isn't until you take an Analysis course that you study the nuts-and-bolts of Calculus and rigorously prove and apply its ideas (and arrive interesting conclusions). Analysis was very difficult for me because I was poor at proof-writing, I didnt settle in until halfway through my 2nd course.
But a lot of people end their math career at Calculus and as such come to the conclusion that its the pinnacle or something.
Yeh, that sounds good. I get one year of general maths in which I study all the various branches which I could focus on in the second year onward. That will help me decide for sure, as I have no idea what analysis is like (apart from like you say, it is the "nuts and bolts" of calculus).
Right now what I enjoy the most is just the calculus I'm doing right now, but that's only applied. (It proves all the points you need to know in the textbook, but you don't study them properly nor are you asked to quote them at all)