Let's discuss Mathematics

[Mise]

well it doesn't matter what the remainder is since it's always less than 1, so you don't need a function to compute it. You just need to know that it's less than 1.

 

[Perfection]

you don't need a function to compute it.

I don't need to huff model airplane glue, but it's still fun.

 

[ParadigmShifter]

You can use the sandwich theorem!

n(x-1)/n < floor(nx)/n <= nx/n

=> nx/n - 1/n < floor(nx)/n <= nx/n

=> x - 1/n < floor(nx)/n <= x

x - 1/n -> x - 0 as n->+inf

Dunno why Wolfram Alpha couldn't work that out.

 

[IdiotsOpposite]

You can use the sandwich theorem!

n(x-1)/n < floor(nx)/n <= nx/n

=> nx/n - 1/n < floor(nx)/n <= nx/n

=> x - 1/n < floor(nx)/n <= x

FIFY

And yeah, now I see multiple ways to prove it. Now I'm bored. I'm taking Linear Algebra. Is there some interesting problem there that I can use to be un-bored?

 

[ParadigmShifter]

Linear Algebra is pretty boring anyway Unless you like doing proofs. The examples tend to be dull.

 

[IdiotsOpposite]

Ugh, I liked my Calc III class much better... maybe i'll dig out the textbook and try my skills on a surface integral.

 

[ParadigmShifter]

At least Linear Algebra is easy!

It's also very useful if you want to be a 3D programmer

 

[IdiotsOpposite]

But I want to be a mathematician. When does math get to the interesting stuff again, Diffy Q's?

 

[ParadigmShifter]

I hated applied maths and calculus, so I didn't do diff equations. EDIT: Ok, I liked differentiation but didn't like integration

I liked metric spaces which is generalised analysis.

Combinatorics was good as well.

Complex Analysis was way hard. EDIT: So was topology.

I also liked Abstract Algebra (ring theory) which was quite similar to number theory, but not as hard.

 

[dutchfire]

Topology is really interesting, but also really hard. One of my textbooks literally required me to read every page 5 times to even get a clue of what it was saying.
The results of complex analysis are quite stunning.
Group theory is also quite interesting.

 

[pboily]

For me, Category Theory, Measure Theory, Dynamical Systems, Abstract Algebra were all very interesting. Algebraic Topology, Number Theory, Algebraic Geometry and Cryptography were rater boring.

 

[ParadigmShifter]

You can use the sandwich theorem!

n(x-1)/n < floor(nx)/n <= nx/n

=> nx/n - 1/n < floor(nx)/n <= nx/n

=> x - 1/n < floor(nx)/n <= x

x - 1/n -> x - 0 as n->+inf

Dunno why Wolfram Alpha couldn't work that out.

This is wrong

n(x-1)/n = x-1

So sandwich theorem doesn't work.

 

[Mise]

Yeah cos it should be (nx-1)/n ya numpty.

 

[ParadigmShifter]

Yeah

Was just about to correct that.

+1 numptiness.

 

[Atticus]

You just mistyped the first line, it should be (nx-1)/n, on the second line it's correct.

I didn't like topology that much. Functional analysis was my favourite course. Our course contained good deal of topology at the beginning, the best part of it, I'd say, Baire's category theorem and such. Maybe that's why the actual topology course felt boring. Plus I really never saw the idea of more general topologies than those induced by a metric. Sure, they are more general, and so on, but they felt very artificial. I think I've seen non-metric topology one or two times part from the classes.

EDIT: X-post. Adult content.

 

[ParadigmShifter]

We did a bit of knot theory first in topology - that was interesting, and doesn't use a metric.

 

[IdiotsOpposite]

We did a bit of knot theory first in topology - that was interesting, and doesn't use a metric.

Explain this "knot theory" to a poor college undergrad.

 

[ParadigmShifter]

Can a knot be untied?

We did the Jones polynomial which is an invariant for knots under the Reidermeister manoeuvres.

http://en.wikipedia.org/wiki/Reidemeister_move

 

[IdiotsOpposite]

A knot can always be untied. Just use the Gordian knot method.

 

[ParadigmShifter]

No cutting is allowed.

Some knots are not the same as the others. The Jones polynomial says which knots definitely aren't equivalent.