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Adam
04-18-02, 03:04 AM
A little educational background. I quit school in year 11 to join the navy. In the last couple of years of high school I did barely any maths at all. After the navy I completed year 12 at a community college, passed everything, but did not study maths in that course either. So now I'm doing this computer engineering degree, no maths background whatsoever.

Lucky me, our maths lecturer is the best maths teacher I have ever encountered. The dude explains everything very well, and I'm having no real problems with any of it. Even the calculus is making sense.

A funny thing happened in today's lecture. He was covering limits today, explaining why and how and so on. You know, explaining that the slope at P gets more accurate as Q approaches it and all, and that it can't ever actually reach P. Fair enough, limits don't hit the number they approach. Now, the entire class was having trouble grasping the reason why Q never actually reaches P. Then I, with far less background in maths than anyone else there, realised why and spoke up. If Q = P, there can be no angle, as it's a single point. This was all new to me, but it seemed very bloody obvious.

So, there does indeed seem quite a difference between learning by rote to pass an exam and understanding the reasons and concepts behind it all.

Given my inexperience with maths, I just thought I'd brag about how well I'm doing.

sjmarsha
04-18-02, 03:22 AM
I hate maths. I am doing a Computing course (CRTS) in England.

Please pass some of your knowledge this way :)

Adam
04-18-02, 09:29 AM
Hell no, I don't know enough amths to teach anyone. I'm just getting started.

sjmarsha
04-18-02, 12:45 PM
Actually I meant pass me the piece of your brain that has your poor maths knowledge in... not teach me. I have too many teachers as it is...

thed
04-18-02, 03:19 PM
Originally posted by Adam
So, there does indeed seem quite a difference between learning by rote to pass an exam and understanding the reasons and concepts behind it all.

Given my inexperience with maths, I just thought I'd brag about how well I'm doing.

Good for you Adam. A good maths teacher makes all the difference.

I normally learn by rote then start to see how it all fits together as time goes by. The penny normally drops the day <u>after</u> the exam.

OK, here's a good one for you. If f(x) = ln(x) what is the lim x-> 0; f(x), hint, expand ln(x) as a power series. Hope I got that right.

Adam
04-18-02, 07:38 PM
Originally posted by thed

OK, here's a good one for you. If f(x) = ln(x) what is the lim x-> 0; f(x), hint, expand ln(x) as a power series. Hope I got that right.

If f(x) =ln(x), what is lim x->0?

ln(x) = (LOGe10).(LOGX) = LOGX/LOGe.

Nah, you've got me. This is new to me, I'm stuck.

rick1138
04-18-02, 08:10 PM
Actually the problem you are dealing with is one of the deepest in mathematics,and at present there is still no reasonable explanation.In the eighteenth and nineteenth century the problemm of limits was explained in terms of infinitesimals,which are smlaller than the smallest number but stil larger than zero.Needless to say infinitesimals generate all kinds of logical difficulties so during the movement in modern mathematics to place all math on rigorous logical ground they were abandoned,in fact one of the main motivations behind modern math was to get rid of infinitesimals.

ImaHamster2
04-18-02, 09:37 PM
Huh?

orthogonal
04-28-02, 11:26 AM
Hey Adam,

Great story. When a mathematical truth finally sinks in with me, I often have the same reaction as I do when I hear a good joke. There must be some unique pleasure center in our brain that's triggered when we finally "get it".

Your story reminded me of a pleasant evening last week. I'd been trying for some weeks to find a proof for a problem that I'd taken from the archives of Japanese Temple Geometry. As I was tired, I put on a Mozart Piano Concerto and sat down to doodle on the problem. The proverbial "flash of insight" appeared soon after, and the next very happy hour was spent cleaning up the proof. My answer matched exactly with one given from 1835, probably obtained by some unknown Japanese peasant rice farmer. Surely a case of great peasant minds thinking alike ;)

I recently came across a nice quote by Ethan Bloch in his book, Proofs and Fundamentals:

"Mathematics is not 'about' proofs and logic anymore than literature is 'about' grammar, or music is 'about' notes. Mathematics is the study of some fascinating ideas..."

I do mathematics simply because I enjoy it. Why do I enjoy it? I might as well ask why I enjoy the curves of a woman's body. In the words of Arthur Cayley:

"As for for everything else, so for a mathematical theory: beauty can be perceived but not explained."

I overheard two guys at the gym recently talking about cars. They spoke so reverently about them that I was feeling sorry for myself that for me, a car body is just bent sheet metal. Then again, perhaps they don't share my pleasure in re-discovering mathematical proofs? Beauty is where we each find it, eh?

Hope you continue to enjoy your maths,
Michael

thed
04-28-02, 12:20 PM
Sorry, I forgot about what I posted.

Have a read of this page (http://www.phys.virginia.edu/classes/152.mf1i.spring02/Exponential_Function.htm) for an answer to what I asked. Enjoy.

Adam
04-28-02, 02:42 PM
What does the "!" mean after certain numbers there?

Oh, and thanks.

thed
04-29-02, 08:43 AM
as in 2! = 2*1
3! = 3*2*1
4!=4*3*2*1 and so on.

Basically as e can be expressed as a power series, you can express ln as a power series, they are inverse functions to each other. You then look at the behaviour of the power series to see how the limit behaves. You use the same trick with trig functions and a variety of other functions.

Lots of fun to be had finding limits, and hence differentials, of non-continuous functions such as Tan(x).

Rick
04-30-02, 10:51 PM
Understand this with Thomas and Finney Book,it"ll clarify everything.
BTW.take a peep at this:

There's a curve like a parabola.ok,so now i set a point at the end of the parabola where i have to reach.i start moving.from a point on another end.do this:
i draw a secant from the point where i first was to the point where i have to reach.now i shift the point a little closer,the point where i stood.again i draw a secant,notice that this secant will become smaller this time...continue...

what do you thing will happen when i reach the point.that is the point at which i was standing coincides with the point wher i had to go.the secant that i intend to draw will become a tangent.

the problem that scientists faced was finding the slope of graphs in earlier times,they would see a graph,but they wouldnt be able to tell charracterstics of graph accurately...and thats how this stuff came into existance.

if you happen to have any problems regarding calculus feel free to ask.
okay do you know the history of the calculus's birth?its certainly interesting.

bye!