- #1
Curd
- 78
- 1
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?
Bounds on zeroes theorem? requires calc proof?
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Homework Help Overview
The discussion revolves around the bounds on zeros theorem, its proof requirements, and its relationship to calculus and complex analysis. Participants explore whether algebra alone suffices for understanding the theorem.
Discussion Character
- Conceptual clarification, Assumption checking, Mixed
Approaches and Questions Raised
- Participants question the necessity of calculus for proving the bounds on zeros theorem and discuss its connection to Rouche's theorem. There are inquiries about the level of mathematical background needed to understand the theorem and its proof.
Discussion Status
The conversation includes suggestions for further reading and the types of mathematical knowledge required, such as calculus and real analysis. Some participants express uncertainty about whether algebraic proofs exist, indicating a lack of consensus on the proof's requirements.
Contextual Notes
Participants mention the need for familiarity with set theory, logic, and specific textbooks to grasp the concepts related to the theorem.
- #2
- 22,170
- 3,326
What IS the zeros theorem??
- #3
- #4
- 22,170
- 3,326
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
- #5
Curd
- 78
- 1
micromass said:
So I do need more than algebra to understand it and this is why they didn't show proof of it?
- #6
mtayab1994
- 584
- 0
Curd said:
Yes to understand that you'll need to learn so set theory and logic i believe.
- #7
- 22,170
- 3,326
Curd said:
Yes.
There might be proofs with only algebra, but I do not know them.
- #8
Curd
- 78
- 1
mtayab1994 said:
what are good books on this?
- #9
- 22,170
- 3,326
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.
- #10
Curd
- 78
- 1
micromass said:
What book would be good for real analysis?
- #11
- 22,170
- 3,326
Curd said:
I'd say "principles of real analysis" by Aliprantis and Burkinshaw/
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