• Geometry of Complex Polynomials: On Sendov's Conjecture 

      Chalebgwa, Taboka Prince (Stellenbosch : Stellenbosch University, 2016-12)
      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 Category-Theoretic Analysis 

      Chimes, Mark Jonathan (Stellenbosch : Stellenbosch University, 2017-03)
      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 ...