Login

Welcome, Guest. Please login or register.

March 19, 2024, 07:34:26 pm

Author Topic: Resources/Guides: For advanced students  (Read 29567 times)  Share 

0 Members and 1 Guest are viewing this topic.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Resources/Guides: For advanced students
« on: July 21, 2011, 02:53:54 am »
+4
So here I'll post some guides on some topics that are above VCE level for those keen students, however you can grasp these concepts to a sufficient degree with VCE knowledge. However some topics actually aren't necessarily "harder" than your VCE maths, rather they emphasize rigour and solid proofs.

To get started, here's a nice guide on epsilon-delta proofs. Used quite a lot in real analysis.

Before you get into it, here's a bit of background on what these are.

I'm sure most of you guys have done differentiation by first principles, you know, where you limit the h to 0 and etc. Yes, that stuff. Now remember the last step? Where you guys just thought "hmm just means I can sub h = 0 in, after canceling out the h's" Well a really basic way of extending that limit stuff to a more rigorous approach is using epsilon delta proofs. What you will find is that you are actually not "substituting h = 0 everytime you see h", rather you are using a very intuitive approach formalised by using an epsilon-delta proof.

Now go read.



Also I attached them as pics because VN won't let me attach as a rar file o.O


Vic Mod edit: re-added attachments
« Last Edit: June 20, 2012, 04:54:19 pm by VegemitePi »
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

taiga

  • Honorary Moderator
  • ATAR Notes Legend
  • *******
  • Posts: 4085
  • Respect: +588
Re: Resources/Guides: For advanced students
« Reply #1 on: July 21, 2011, 03:01:59 am »
+2
Finally some of your maths I can understand :P
vce: english, methods, spesh, chemistry, physics, geography.

ex admin/mod/partner

2010: Melbourne High School (VCE)
2011 - 2016: Monash University BComm/BEng (Hons)


If you guys have any concerns/suggestions for making ATARNotes a better place, don't hesitate to PM me.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #2 on: July 21, 2011, 03:08:52 am »
+1
haha :P

Anyways, for those who are quite keen, here's a challenge question, the method to prove this one is a bit different from the examples that you've read above, however the general jist is the same, if you understood the overall concept, have a good at this one, post a solution even if you think it's not right! Have a shot!

Show that
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

xZero

  • Victorian
  • Forum Leader
  • ****
  • Posts: 898
  • Respect: +68
Re: Resources/Guides: For advanced students
« Reply #3 on: July 21, 2011, 02:40:15 pm »
+1
if then , since , we have to adjust the epsilon part of the proof, let M=any positive number, f(x)>M (this means that as you approach the point a, f(x) becomes larger than any finite number)


                 
                 

let
, a=0
           
           
           
This completes the proof, hence


Think this is correct :S
2009: Chinese SLA
2010: English, Maths method[45,A+ A+ A+], Specialist maths[44,A+,A,A+], Physics[40,A,A+,A+], Psychology Atar:94.75
2011-2015: Bachelor of Aerospace Engineering/Science @ Monash

Methods/Spesh/Physics tuition

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #4 on: July 22, 2011, 02:05:02 am »
0
Nice :]
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #5 on: July 22, 2011, 11:59:00 pm »
0
wdf? why is this thread "doubled"
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

Hutchoo

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2356
  • Mate.
  • Respect: +218
Re: Resources/Guides: For advanced students
« Reply #6 on: July 23, 2011, 12:09:47 am »
+2
wdf? why is this thread "doubled"
Two times the fun.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #7 on: July 23, 2011, 12:11:24 am »
0
wdf? why is this thread "doubled"
Two times the fun.
loving ur dp brah, makes it triple the fun
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #8 on: July 23, 2011, 12:12:24 am »
0
also wat the shit, where did xZero's post go.

WDF, why are so many threads are all screwed up on vn
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Re: Resources/Guides: For advanced students
« Reply #9 on: July 23, 2011, 12:13:38 am »
+2
wait, where did all the attachments go?

years of collection of useful things. GONE!

Thank god for agora. Not all is lost.
http://vce.atarnotes.com/agora/index.php
« Last Edit: July 23, 2011, 12:16:19 am by Mao »
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

xZero

  • Victorian
  • Forum Leader
  • ****
  • Posts: 898
  • Respect: +68
Re: Resources/Guides: For advanced students
« Reply #10 on: July 23, 2011, 12:51:13 am »
0
wdf? why is this thread "doubled"
Two times the fun.
Is your dp yoona? And wtf how come my post didn't get doubled?
2009: Chinese SLA
2010: English, Maths method[45,A+ A+ A+], Specialist maths[44,A+,A,A+], Physics[40,A,A+,A+], Psychology Atar:94.75
2011-2015: Bachelor of Aerospace Engineering/Science @ Monash

Methods/Spesh/Physics tuition

Lasercookie

  • Honorary Moderator
  • ATAR Notes Legend
  • *******
  • Posts: 3168
  • Respect: +326
Re: Resources/Guides: For advanced students
« Reply #11 on: August 30, 2011, 10:09:11 pm »
+2
I found where the notes that were attached to the first post went:
Re: Chat.

Forum must have glitched lol.

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: Resources/Guides: For advanced students
« Reply #12 on: August 30, 2011, 11:29:03 pm »
+1
I found where the notes that were attached to the first post went:
Re: Chat.

Forum must have glitched lol.
LOOOOOOOOOOOOOL NICE FIND
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Re: Resources/Guides: For advanced students
« Reply #13 on: August 30, 2011, 11:58:57 pm »
0
I found where the notes that were attached to the first post went:
Re: Chat.

Forum must have glitched lol.

WUT.

So what you mean is, there is a whole heap of practice exams littered in random threads all over the forum? Lawl'd.
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

Lasercookie

  • Honorary Moderator
  • ATAR Notes Legend
  • *******
  • Posts: 3168
  • Respect: +326
Re: Resources/Guides: For advanced students
« Reply #14 on: August 31, 2011, 08:01:02 am »
0
I found where the notes that were attached to the first post went:
Re: Chat.

Forum must have glitched lol.

WUT.

So what you mean is, there is a whole heap of practice exams littered in random threads all over the forum? Lawl'd.
Lol, nah I think it's just stuff that was uploaded after the upgrade. I remember I did upload some stuff that did go missing - that's probably attached to some random threads now lol.