Victoria Math Forum: Analysis or Algebra? Let's Discuss!

fourier jr
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I've been looking for a math forum for a while, I guess I just found one! I'm a 4th-yr student at the University of Victoria, BC & I can't decide whether I like analysis or algebra better. Right now I'm trying to work through the rest of the 1st part of Munkres' Topology text, the stuff on metrization theorems, function spaces, local finiteness, etc that we didn't get to in the course I just finished.
 
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There is no question. Algebra is definately beautiful and fun. Analysis is always about finding an upper bound, or guessing a magic trick. I am just a bit provocative (^_^)
 
humanino:
Algebra is definitely unfunny and ugly.
Analysis is beautiful and fun.
 
if you say so...
but in my opinion, any valuable mathematician is on my side... at least the ones I met.

I would really like to have statistics on that matter. By the way : I am NOT a mathematician, I am a physicist. So maybe my opinion is worthless.

The reason why I love algebra, is because it deals with structure of objects. It is neat as geometry is neat : powerful and simple.
 
Well, jokes aside, isn't it primarily a matter of personal taste whether one is drawn to either analysis or algebra ?
From my point of view, at least, they represent equally important and "valuable" branches of mathematics; I don't think there exist an "objective" manner of assigning
different values to them.
 
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Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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