Math 459, Senior Seminar
10/13/2011
Name: Katie Geiser
Title: A Proof of Rouché’s Theorem
Source: Michael Filaseta, Rouché’s Theorem for Polynomials, The American Mathematical
Monthly, 107, No. 9, (Nov., 1990), pp. 834-835.
Senior Project Ideas
1. The paper discusses Perron’s Theorem in its relation to Rouché’s Theorem. Find the
relationship between the two theorems and write a paper on the uses of the theorem and
the correlation.
2. Rouché’s Theorem is also used to prove the Fundamental Theorem of Algebra.
Complete this proof and explore the other methods used to prove the Fundamental
Theorem of Algebra. Write a paper in which you explore a number of the proofs for this
theorem.
3. Explore the Rouché-Capelli Theorem, which is the extension of Rouché’s theorem into
linear algebra. Write a paper discussing Rouché’s theorem, and ````
how it
can be branched into linear algebra and the Rouché-Capelli Theorem.