Favourite Mathematical Concept/trick? (1 Viewer)

[RealiseNothing]

So if we take the kth number from the kth line then add 1, then put it in the kth digit of the exact same number, it wouldn't be the same number anymore, hence a contradiction? Is that right or did I misinterpret it?

 

[largarithmic]

So if we take the kth number from the kth line then add 1, then put it in the kth digit of the exact same number, it wouldn't be the same number anymore, hence a contradiction? Is that right or did I misinterpret it?

Yup thats exactly right. You construct a number that has at least one digit different from every number on the list (precisely, it differs from the kth number on the list in the kth digit), giving a contradiction coz then it couldn't be on the list.

 

[kaz1]

Laplace Transformations and adding dem diagonals for dat determinant

 

[RealiseNothing]

Yup thats exactly right. You construct a number that has at least one digit different from every number on the list (precisely, it differs from the kth number on the list in the kth digit), giving a contradiction coz then it couldn't be on the list.

That's a pretty awesome proof.

Another one I found cool was the proof that nCk = n!/(n-k)!k! by differentiation and binomial expansion. Although I think it's just an elementary proof as I got it from the extension section of Cambridge 3U.

 

[Carrotsticks]

That's a pretty awesome proof.

Another one I found cool was the proof that nCk = n!/(n-k)!k! by differentiation and binomial expansion. Although I think it's just an elementary proof as I got it from the extension section of Cambridge 3U.

Gotta love that Extension section.

 

[largarithmic]

Another one I found cool was the proof that nCk = n!/(n-k)!k! by differentiation and binomial expansion. Although I think it's just an elementary proof as I got it from the extension section of Cambridge 3U.

Have you seen the counting argument version?

 

[hayabusaboston]

Have you seen the counting argument version?

Elaborate, Sir Largarithmic?

 

[RealiseNothing]

Have you seen the counting argument version?

Are you talking about the one that involves induction or is this a different one? I know the induction method, but if it's another way I haven't seen it.

This method uses the fact that (k+1)C(r) = kCr + (k)C(r-1), just to save confusion in case there was another approach to using induction.

 

[Peeik]

Partial Differential Equations (PDEs).....best topic ever..

 

[hayabusaboston]

Partial Differential Equations (PDEs).....best topic ever..

true dat!

 

[math man]

Yeh de's in general, but I also love chi square distributions, there applications like determining whether data follows binomial model or symmetry between data etc suits me, also don't forget Taylor series

 

[seanieg89]

A favourite concept: The study of the distribution of primes using the analytic structure of Riemann's Zeta function. It is surprising that the "continuous" methods of analysis have any bearing on the "discrete" questions one may pose in number theory.

Favourite techniques: Interchanging order of integration, differentiating inside the integral sign...etc

 

[hayabusaboston]

A favourite concept: The study of the distribution of primes using the analytic structure of Riemann's Zeta function. It is surprising that the "continuous" methods of analysis have any bearing on the "discrete" questions one may pose in number theory.

Favourite techniques: Interchanging order of integration, differentiating inside the integral sign...etc

Yea that's very fun eh? hehe.

 

[IamBread]

Anything to do with calculus. Wooo calculus

 

[Carrotsticks]

Partial Differential Equations (PDEs).....best topic ever..

Doing that Second Semester this year lol.

Is it as the name suggests, just Differential Equations... but including Partial Derivatives? Is there much more to it than that?

 

[study-freak]

Doing that Second Semester this year lol.

Is it as the name suggests, just Differential Equations... but including Partial Derivatives? Is there much more to it than that?

You're kinda right. DEs with partial derivatives (and no total derivatives, I think?)
But you can't solve them directly in most cases. What we mostly do is that we reduce them down to ODEs to solve them.

It'll involve lots of tedious algebra (not in the sense of linear algebra but tedious working outs!).

 

[Peeik]

Doing that Second Semester this year lol.

Is it as the name suggests, just Differential Equations... but including Partial Derivatives? Is there much more to it than that?

yer sort of but it goes into applied mathematics and its very interesting! Are you doing linear algebra and vector calc in sem 1?

 

[Carrotsticks]

You're kinda right. DEs with partial derivatives (and no total derivatives, I think?)
But you can't solve them directly in most cases. What we mostly do is that we reduce them down to ODEs to solve them.

It'll involve lots of tedious algebra (not in the sense of linear algebra but tedious working outs!).

Oh dear, I've never really been a big fan of tedious working out. I found Integral Calculus in First Year to be relatively simple. They basically gave you everything as in...

- If you get this linear DE, use this integrating factor

- If you get this type of DE, use this formula etc etc.

Perhaps because it's First Year, and they didn't want to scare away everybody?

yer sort of but it goes into applied mathematics and its very interesting! Are you doing linear algebra and vector calc in sem 1?

Of course =)

 

[study-freak]

Oh dear, I've never really been a big fan of tedious working out. I found Integral Calculus in First Year to be relatively simple. They basically gave you everything as in...

- If you get this linear DE, use this integrating factor

- If you get this type of DE, use this formula etc etc.

Perhaps because it's First Year, and they didn't want to scare away everybody?



Of course =)

Yep, 1st year maths is, in general, much easier than later ones. Esp true for MATH1903 lol, the 2nd easiest course ever with the 1st being discrete maths (MATH1004).

EDIT: but I've been learning a bit of vector calc in these holidays and it doesn't seem much harder than MATH1901 - though generalised to higher dimensions. 1901 was the hardest 1st yr maths course imo anyway.
(I'm gonna do linear alg/vector calc (adv) too!)

 

[Carrotsticks]

Yep, 1st year maths is, in general, much easier than later ones. Esp true for MATH1903 lol, the 2nd easiest course ever with the 1st being discrete maths (MATH1004).

EDIT: but I've been learning a bit of vector calc in these holidays and it doesn't seem much harder than MATH1901 - though generalised to higher dimensions. 1901 was the hardest 1st yr maths course imo anyway.
(I'm gonna do linear alg/vector calc (adv) too!)

I was under the impression that you already did Second Year maths. Unless you are referring to 3rd Year vector calc equivalent?

IMO order of difficulty MATH1903 --> MATH1901 --> MATH1905 --> MATH1004 --> MATH1902, where Linear Algebra was the hardest.

I started on a bit of Vector Calculus, and it seems quite interesting. You're right about it not being much different from MATH1901 and 1902 combined.

Plus, it has double/triple integrals to evaluate surface areas and volumes of non-revolutionary solids.

I think it also has polar and spherical co-ordinates. Not quite sure, I've just been going through my massive blue Calculus: Early Transcendentals textbook (the fat $150 one from the Co-op bookshop).