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Geometry of Complex Polynomials: On Sendov's Conjecture
(Stellenbosch : Stellenbosch University, 201612)ENGLISH ABSTRACT : Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a ... 
Ultraproducts and Los’s Theorem: A CategoryTheoretic Analysis
(Stellenbosch : Stellenbosch University, 201703)ENGLISH ABSTRACT : Ultraproducts are an important construction in model theory, especially as applied to algebra. Given some family of structures of a certain type, an ultraproduct of this family is a single structure ...