M.Sc. Mathematics and Statistics
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Prime Rational Functions and Integral Polynomials
(Brock University, 20150105)Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. ... 
A gametheoretic network formation model
(Brock University, 20140723)We study the dynamics of a gametheoretic network formation model that yields largescale smallworld networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the ... 
Edgechoosability of Planar Graphs
(Brock University, 20130926)According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge(∆ + 1)choosable as by Vizing’s ... 
Rings, Group Rings, and Their Graphs
(Brock University, 20130905)We associate some graphs to a ring R and we investigate the interplay between the ringtheoretic properties of R and the graphtheoretic properties of the graphs associated to R. Let Z(R) be the set of zerodivisors of R. ... 
Acyclic 5Choosability of Planar Graphs Without Adjacent Short Cycles
(Brock University, 20130905)The conjecture claiming that every planar graph is acyclic 5choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph ... 
Square Root Finding In Graphs
(Brock University, 20130124)Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of ... 
Response curves of deterministic and probabilistic cellular automata in one and two dimensions
(20120402)One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in ... 
The von Neumann Minimax Theorem and its relatives and a study of externality in online auctions
(20120330)This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships ... 
Zerosum problems in finite cyclic groups
(Brock University, 20090128)The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zerosum theory. A zerosequence in a finite cyclic group G is said to have the basic property if ...