Sheil-Small T. Complex polynomials 2002 torrent

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Complex Polynomials explores the geometric theory of polynomials and rational functions in the plane. Early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology, and analysis. Throughout the book, the author introduces a variety of ideas and constructs theories around them, incorporating much of the classical theory of polynomials as he proceeds. These ideas are used to study a number of unsolved problems. Several solutions to problems are given, including a comprehensive account of the geometric convolution theory.
The algebra of polynomials
The degree principle and the fundamental theorem of algebra
The Jacobian problem
Analytic and harmonic functions in the unit disc
Circular regions and Grace’s theorem
The Ilieff–Sendov conjecture
Self-inversive polynomials
Duality and an extension of Grace’s theorem to rational functions
Real polynomials
Level curves
Miscellaneous topics