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October 21, 2025, 08:18:40 pm
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Author Topic: Mao's Bound Notes  (Read 21330 times)  Share 

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TrueTears

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Re: Mao's Bound Notes
« Reply #30 on: April 17, 2010, 01:12:36 am »
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its just a personal thing, some people find it useful some dont, ive never ever found making maths notes useful, id just remember the concepts behind everything and do the questions, or try remember clever ways of deriving, like geometric ways of deriving compound angle formulas etc, or the general concept behind double integrals using riemann sums or things like prime product factorisation one can prove by remembering how to prove uniqueness using contradiction etc.
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tram

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Re: Mao's Bound Notes
« Reply #31 on: April 17, 2010, 09:57:50 am »
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hey tt, how do you prove the double angle formulas geometrically? i would be very interested to see that. i've given it a go, can't seem to make it work. i just keep going around in circles
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tram

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Re: Mao's Bound Notes
« Reply #32 on: April 17, 2010, 09:58:20 am »
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no pun intended;)
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brightsky

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Re: Mao's Bound Notes
« Reply #33 on: April 17, 2010, 10:29:58 am »
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Perhaps this could help.

http://vcenotes.com/forum/index.php/topic,21004.msg249937.html#msg249937

EDIT: Just change the to an and you get your double angle formula. :)
« Last Edit: April 17, 2010, 10:33:15 am by brightsky »
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tram

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Re: Mao's Bound Notes
« Reply #34 on: April 17, 2010, 10:53:48 am »
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lol, i reackon the complex exponential is the best way to prove the double angle formulae. The most elegant way in my view
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kyzoo

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Re: Mao's Bound Notes
« Reply #35 on: April 17, 2010, 12:56:12 pm »
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Quote from: tram on April 17, 2010, 10:53:48 am
lol, i reackon the complex exponential is the best way to prove the double angle formulae. The most elegant way in my view

You only learned that last Wednesday LOL
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TrueTears

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Re: Mao's Bound Notes
« Reply #36 on: April 17, 2010, 02:31:29 pm »
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ok.

consider

Let AC = 1 = AB

= MC = BM







Now how about

You can also prove it using that diagram. Can you of how? I leave u as an exercise

hint: you might have to leave out the x's, define some new angles, and THINK ABOUT AREA!!


another favorite of mine which i never forget about is proving the uniqueness of a natural number's PFF (left out many parts but thats the main meat ^.^)



Clearly for all ,



for any .



This means that for all and all there are values of which equals to those of . For example, could equal to , or etc. This also means we have created a bijection between and such that .

Therefore if the number has PPF's then the prime number 'base' will be exactly the same, the only different would be in the powers, namely and .

Now since each has a corespondent equivalent we can rewrite as:





however can not be divided by unless for some such that

But since we have a contradiction!

« Last Edit: April 17, 2010, 02:40:15 pm by TrueTears »
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TyErd

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Re: Mao's Bound Notes
« Reply #37 on: April 17, 2010, 06:14:10 pm »
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wow that is impressive Mao. Any chance you have bound notes for Methods? or physics, further...
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Re: Mao's Bound Notes
« Reply #38 on: April 17, 2010, 06:22:09 pm »
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Quote from: TyErd on April 17, 2010, 06:14:10 pm
wow that is impressive Mao. Any chance you have bound notes for Methods?

+1
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superflya

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Re: Mao's Bound Notes
« Reply #39 on: April 17, 2010, 06:29:20 pm »
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^^ i dont think anyone could be bothered compiling such notes for methods.
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kyzoo

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Re: Mao's Bound Notes
« Reply #40 on: April 17, 2010, 08:15:36 pm »
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0.o Lol I made 100 pages or so of notes for Methods
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superflya

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Re: Mao's Bound Notes
« Reply #41 on: April 17, 2010, 08:21:10 pm »
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Quote from: kyzoo on April 17, 2010, 08:15:36 pm
0.o Lol I made 100 pages or so of notes for Methods

ha, i take back wat i said :P
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Yitzi_K

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Re: Mao's Bound Notes
« Reply #42 on: April 17, 2010, 08:29:06 pm »
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Quote from: kyzoo on April 17, 2010, 08:15:36 pm
0.o Lol I made 100 pages or so of notes for Methods

Care to share?  ;)
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Blakhitman

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Re: Mao's Bound Notes
« Reply #43 on: April 17, 2010, 08:41:49 pm »
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Quote from: Yitzi_K on April 17, 2010, 08:29:06 pm
Quote from: kyzoo on April 17, 2010, 08:15:36 pm
0.o Lol I made 100 pages or so of notes for Methods

Care to share?  ;)

Because sharing is caring!
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TyErd

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Re: Mao's Bound Notes
« Reply #44 on: April 17, 2010, 09:00:35 pm »
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pleaseee?
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