Once I read an answer to question posted by a user named Chinamath .... that started with something like "My proof is also very Chinese. I will infact use the Chinese Remainder Theorem .... " .. :D
don't get me wrong, i love going to church. but when you're doing poorly in a class you'd already taken back in high school, study time comes above everything
@Mike. Thx a million for today. I did a lot of maths today and wouldn't have progressed as well or learn't as much if it wasn't for your assistance ! I think I've got a good grasp on this now !
@r9m Prove that for any triangle ABC and point P inside ABC, the sum of the distances from P to the sides is less than or equal to half of the sum of the distances from P to the vertices.
I'm sure if you really try your best you could beat most of the people in your class that he is grading you against @user127001 they must have some background information that you didn't :-)
However, I think there is kind of an omission of a class of book on that list, namely a basic historical-ish overview of modern math.
He does have Dieudonne, A Panorama of Pure Mathematics on there, but that's kind of too advanced for what I'm looking for.
So I'm curious if anyone has like a... popsci-ish sort of book to get a good feel on how all the different bits and piece of math fit together.
To be clear, I'm not looking for a book on math history, but rather a book which uses the history to help motivate why the different fields are important.
@Darius That's correct, but it's definitely pretty easy to get into with minimal background (more is better, but all that's truly required is calculus). But as you approach new topics you may enjoy looking at them in the PTM.
My main worry is getting confused by a single proof or single idea in some book and then spinning wheels and burning out on it, so having alternate references is definitely very important to me.
@Daniel $L^\infty (\Bbb N)$ is a unital commutative $\Bbb C^*$ algebra. So it's isomorphic to $C(X)$ for some compact space $X$. I've been told but haven't proved that $X$ is the one-point compactification of $\Bbb N$ (at least, it's easy to see that $\Bbb N$ is a subspace.)
@Daniel So the question is: hat is the multiplicative linear functional corresponding to $\infty$? My first guess was the Cesaro mean, but I found a bounded sequence for which the means didn't converge.
Whoever wrote these tasks have a really hard time with arithematics. Last task had overall 124 points. This task has 100 points, but this question of supposedly 25 points have 18, and another of 35 has 27...
