bounds on zeroes theorem? requires calc proof?

[Curd]

I've come across the bounds on zeros theorem in my algebra book, but they don't seem to try to offer proof for it. Does this proof require calculus?

[micromass]

What IS the zeros theorem??

[Curd]

here

[micromass]

Yes, they are based on Rouche's theorem. This is a classical theorem in complex analysis. Here is some information on it: http://en.wikipedia.org/wiki/Properties_of_polynomial_roots

[Curd]

Yes, they are based on Rouche's theorem. This is a classical theorem in complex analysis. Here is some information on it: http://en.wikipedia.org/wiki/Properties_of_polynomial_roots

So I do need more than algebra to understand it and this is why they didn't show proof of it?

[mtayab1994]

So I do need more than algebra to understand it and this is why they didn't show proof of it?

Yes to understand that you'll need to learn so set theory and logic i believe.

[micromass]

So I do need more than algebra to understand it and this is why they didn't show proof of it?

Yes.


There might be proofs with only algebra, but I do not know them.

[Curd]

Yes to understand that you'll need to learn so set theory and logic i believe.

what are good books on this?

[micromass]

Read "Complex Analysis" by Freitag and Busam. But in order to be able to read that, you'll need some familiarity with calculus I-III and real analysis.

[Curd]

Read "Complex Analysis" by Freitag and Busam. But in order to be able to read that, you'll need some familiarity with calculus I-III and real analysis.


What book would be good for real analysis?

[micromass]

What book would be good for real analysis?

I'd say "principles of real analysis" by Aliprantis and Burkinshaw/