Can't Appreciate the Unknown

For the discussion of math. Duh.

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Kitafra
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Can't Appreciate the Unknown

Postby Kitafra » Wed Feb 17, 2010 10:45 pm UTC

Hi, I'm a Canadian high-school student. I'm only 16, and our class just started on trigonometry.
Now this is completely new to me and before this class, I would have no idea what Sine or Tangent was.

This got me thinking, since I love math so much, what am I missing out on? (Assuming you think math is fun)
Or simply what things can I look forward to?

Thanks.

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Yakk
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Re: Can't Appreciate the Unknown

Postby Yakk » Wed Feb 17, 2010 11:03 pm UTC

You mean in the future, as in the years to come?

Calculus. Formal proofs. Induction. Computability. Graph theory. Topology. Algebraic Geometry. Entire forests of mathematical wonders that you can literally spend a lifetime wandering through and discovering new flowers.
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Rizzo
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Re: Can't Appreciate the Unknown

Postby Rizzo » Wed Feb 17, 2010 11:03 pm UTC

The higher up in math you get, the more weird and fun stuff appears. I'm taking a first semester college calculus course and I love it. Everything's new.

Besides, it's fun to figure things out as you go.

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Re: Can't Appreciate the Unknown

Postby kernelpanic » Wed Feb 17, 2010 11:13 pm UTC

Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration. Anyway, more advanced trig is fun, vectors are definitely not fun (long, exhausting, hard to set up, and the actual math, the fun part, is easy), matrices are interesting, binomials are very nice, game theory is great. It depends on what you're good at. If you're good at spacial reasoning, you'll like geometry, if you like mind puzzles, logic is for you, and so on...
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RogerMurdock
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Re: Can't Appreciate the Unknown

Postby RogerMurdock » Wed Feb 17, 2010 11:50 pm UTC

kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration. Anyway, more advanced trig is fun, vectors are definitely not fun (long, exhausting, hard to set up, and the actual math, the fun part, is easy), matrices are interesting, binomials are very nice, game theory is great. It depends on what you're good at. If you're good at spacial reasoning, you'll like geometry, if you like mind puzzles, logic is for you, and so on...


I don't know where you're from, but in most of the US 16 is quite a normal age to do trig at. In fact, I was doing trig at 16 and I was on the "fast track" so to speak for math classes at my school.

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Re: Can't Appreciate the Unknown

Postby Dason » Thu Feb 18, 2010 12:16 am UTC

I agree with RogerMurdock. 16 sounds about right. I knew one kid in the calc class when he was a sophomore but he was not a typical student. Also... Chaos Theory! It's a really interesting subject and you can do quite a bit of exploration in it without knowing too much higher level math.
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Re: Can't Appreciate the Unknown

Postby wsdenker » Thu Feb 18, 2010 12:19 am UTC

kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration. Anyway, more advanced trig is fun, vectors are definitely not fun (long, exhausting, hard to set up, and the actual math, the fun part, is easy), matrices are interesting, binomials are very nice, game theory is great. It depends on what you're good at. If you're good at spacial reasoning, you'll like geometry, if you like mind puzzles, logic is for you, and so on...


Vectors are indeed dull things. They do get to be more interesting in linear algebra, but you've got to have enough calculus under your belt to take a class on that. If you've played with any matrix mathematics in your classes you'll have already seen a little bit of the basics of linear algebra and didn't know it. Later on you'll find that vectors are easier to work with and in can be handled in greater numbers in matrix form.

Kitafra wrote:Hi, I'm a Canadian high-school student. I'm only 16, and our class just started on trigonometry.
Now this is completely new to me and before this class, I would have no idea what Sine or Tangent was.

This got me thinking, since I love math so much, what am I missing out on? (Assuming you think math is fun)
Or simply what things can I look forward to?


It gets way more interesting as you progress. Trig is actually not high on my list of favorite mathematics disciplines, but to each his own :D. Don't let people convince you that calculus is difficult, by the way. There are difficult concepts in calculus but, on the whole, it's actually rather easy. Derivation is amusingly simple and actually somewhat fun when you understand its application.

To imagine what calculus is all about, imagine some of the constructs you've already seen as they are graphed. Think of a parabola, for instance. You can compute all kinds of useful things about a parabola (or any curve) but without calculus you can't determine the rate at which the curve changes at any given point. Calculus derivatives are the mathematics of change and motion. If you took a parabola and inverted it and shifted it upward on the graph, you'd have a hard time calculating the area beneath that curve (between it and the x-axis). Integration gives you powerful tools that allow you to do that, which you later learn extends to calculating the areas of pretty much any shape imaginable in three dimensions.

There are many, many branches of mathematics nowadays, mentioned above by other posters. They're used to solve all kinds of real problems, but interestingly there's quite a lot of mathematics which have no application whatsoever (that we know of) and there are a lot of problems in both pure mathematics and applied mathematics which have not yet been solved. Then there's mathematics which were initially invented without having had a purpose, and later a purpose was discovered for them. Math is full of useful things, but it's also full of bizarre and interesting things.

You may never have thought about it but every time you play a 3D video game there's an incredible amount of mathematics going on to display them. A lot of the mathematics that goes into displaying 3D worlds and characters is trigonometry (almost everything is drawn with millions of tiny triangles) and the graphics cards can calculate billions of triangles per second to animate all those little triangles around on the screen. I bet your teacher didn't tell you that. ;)

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Re: Can't Appreciate the Unknown

Postby student_t_w » Thu Feb 18, 2010 12:33 am UTC

In math, like many other disciplines, I think that the more you know the more you realize how much more there is out there that you have yet to learn. As for cool things to look forward to -- I really liked my introductory discrete math course freshman year of college, introduced me to branches of math that are often not touched on in high school.

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Re: Can't Appreciate the Unknown

Postby kernelpanic » Thu Feb 18, 2010 1:42 am UTC

kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration.

Oh, sorry, just read that again and it sounded very smug and asshole-ish. It's just that at my school you do trig at 7th grade (I was 12), and while I am in an advanced program, everybody did trig at roughly the same time.
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Re: Can't Appreciate the Unknown

Postby lu6cifer » Thu Feb 18, 2010 1:58 am UTC

kernelpanic wrote:
kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration.

Oh, sorry, just read that again and it sounded very smug and asshole-ish. It's just that at my school you do trig at 7th grade (I was 12), and while I am in an advanced program, everybody did trig at roughly the same time.


trig @ 7th grade? To my knowledge of school curriculums,trig is standard at senior year, junior year if you're advanced, and sophomore year if you're doubly advanced. And after trig, it's on to calculus. So, if you don't mind me asking, what does your school's math curriculum look like?
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Re: Can't Appreciate the Unknown

Postby kernelpanic » Thu Feb 18, 2010 2:55 am UTC

lu6cifer wrote:
kernelpanic wrote:
kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration.

Oh, sorry, just read that again and it sounded very smug and asshole-ish. It's just that at my school you do trig at 7th grade (I was 12), and while I am in an advanced program, everybody did trig at roughly the same time.


trig @ 7th grade? To my knowledge of school curriculums,trig is standard at senior year, junior year if you're advanced, and sophomore year if you're doubly advanced. And after trig, it's on to calculus. So, if you don't mind me asking, what does your school's math curriculum look like?

We start IGCSE Extended on 7th, on 8th some people drop to the core class, on 9th the advanced class do the actual exam, everybody else on 10th. right now (10th for me) we (the advanced class) do a course that is called Advanced maths, additional maths, or mathematic techniques, depending on whether you ask the timetable, the school, or the exam board, and that changes every few weeks. That is something that I also don't know, who is the exam board, if the IGCSE, or someone else. I hear it's been referred to as an O-level by some teachers, but I choose to ignore those comments because I don't have any idea whatsoever what an O-level is.
Note: I'm using US grades here.
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Re: Can't Appreciate the Unknown

Postby the tree » Thu Feb 18, 2010 11:21 am UTC

I'd say I was somewhere between 14 and 16 when I learned trig in the geometric sense (just bare definitions), but then learned it all again around 16 in the algebraic sense (identities and stuff).

But bearing in mind that American schools seem to teach like, other stuff, I don't see much wrong with starting trig at any age.

More to the point, there's kind of lots of maths and there's no saying what order you'll be exposed to it.

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Re: Can't Appreciate the Unknown

Postby WarDaft » Thu Feb 18, 2010 1:34 pm UTC

student_t_w wrote:In math, like many other disciplines, I think that the more you know the more you realize how much more there is out there that you have yet to learn. As for cool things to look forward to -- I really liked my introductory discrete math course freshman year of college, introduced me to branches of math that are often not touched on in high school.
The awesome thing about math is there is quite literally an infinite pool of potential knowledge.
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Re: Can't Appreciate the Unknown

Postby DavCrav » Thu Feb 18, 2010 1:55 pm UTC

kernelpanic wrote:I hear it's been referred to as an O-level by some teachers, but I choose to ignore those comments because I don't have any idea whatsoever what an O-level is.


Back in a mists of time the British system had Ordinary and Advanced qualification levels, O-levels and A-levels. Then the O-levels were replaced by the General Certificate of Secondary Education, or GCSE. The IGCSE is the international version of it. People still refer to the GCSE as O-levels, even though in the main they are much weaker qualifications.

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Re: Can't Appreciate the Unknown

Postby Shokk » Fri Feb 19, 2010 11:22 pm UTC

kernelpanic wrote:
lu6cifer wrote:
kernelpanic wrote:
kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration.

Oh, sorry, just read that again and it sounded very smug and asshole-ish. It's just that at my school you do trig at 7th grade (I was 12), and while I am in an advanced program, everybody did trig at roughly the same time.


trig @ 7th grade? To my knowledge of school curriculums,trig is standard at senior year, junior year if you're advanced, and sophomore year if you're doubly advanced. And after trig, it's on to calculus. So, if you don't mind me asking, what does your school's math curriculum look like?

We start IGCSE Extended on 7th, on 8th some people drop to the core class, on 9th the advanced class do the actual exam, everybody else on 10th. right now (10th for me) we (the advanced class) do a course that is called Advanced maths, additional maths, or mathematic techniques, depending on whether you ask the timetable, the school, or the exam board, and that changes every few weeks. That is something that I also don't know, who is the exam board, if the IGCSE, or someone else. I hear it's been referred to as an O-level by some teachers, but I choose to ignore those comments because I don't have any idea whatsoever what an O-level is.
Note: I'm using US grades here.

Christ almighty, I am immensely envious of you and the education system into which you have been placed.
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Re: Can't Appreciate the Unknown

Postby kernelpanic » Sat Feb 20, 2010 1:26 am UTC

Shokk wrote:
kernelpanic wrote:
lu6cifer wrote:
kernelpanic wrote:
kernelpanic wrote:Well, 16 certainly sounds quite old to begin trig - I'm 15 and doing integration.

Oh, sorry, just read that again and it sounded very smug and asshole-ish. It's just that at my school you do trig at 7th grade (I was 12), and while I am in an advanced program, everybody did trig at roughly the same time.


trig @ 7th grade? To my knowledge of school curriculums,trig is standard at senior year, junior year if you're advanced, and sophomore year if you're doubly advanced. And after trig, it's on to calculus. So, if you don't mind me asking, what does your school's math curriculum look like?

We start IGCSE Extended on 7th, on 8th some people drop to the core class, on 9th the advanced class do the actual exam, everybody else on 10th. right now (10th for me) we (the advanced class) do a course that is called Advanced maths, additional maths, or mathematic techniques, depending on whether you ask the timetable, the school, or the exam board, and that changes every few weeks. That is something that I also don't know, who is the exam board, if the IGCSE, or someone else. I hear it's been referred to as an O-level by some teachers, but I choose to ignore those comments because I don't have any idea whatsoever what an O-level is.
Note: I'm using US grades here.

Christ almighty, I am immensely envious of you and the education system into which you have been placed.

Thank you, but let's return to the original topic. I think the best part about math is applying it to the real world, such as exponential decay and the like.
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Re: Can't Appreciate the Unknown

Postby hawkmp4 » Sat Feb 20, 2010 7:06 am UTC

I think that really, truly understanding calculus is the most mind-blowing experience I have ever had. Nothing has compared to that.
Finally having the gradient and directional derivatives click today in class was pretty ridiculous too. I get chills.
But there's also game theory...I find that fascinating.
Oh, and probability and statistics have some very insightful statements...
I guess my point is, go forth and learn! There's so much in so many subjects. The more you learn the more you'll want to learn. It'll never stop. Expose yourself to the basics of as many different topics as you can and dive into any and all that interest you.
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Re: Can't Appreciate the Unknown

Postby Robstickle » Sat Feb 20, 2010 2:34 pm UTC

kernelpanic wrote:Thank you, but let's return to the original topic. I think the best part about math is applying it to the real world, such as exponential decay and the like.


Nah the best bit is when you're stuck on a problem for days and all of a sudden you realize A. How to do it with ease and B. That you're an idiot for not seeing it before. :)

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Re: Can't Appreciate the Unknown

Postby DavCrav » Sat Feb 20, 2010 6:06 pm UTC

Robstickle wrote:Nah the best bit is when you're stuck on a problem for days and all of a sudden you realize A. How to do it with ease and B. That you're an idiot for not seeing it before. :)


Well, I was stuck on a problem for a few days, but now I know how to do it. I wouldn't say it was easy, but the proof is only a couple of pages. My first version was ten pages long, wrong, and not as general...


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