CSE is a rapidly growing multidisciplinary area with connections to the sciences, engineering, mathematics, and computer science. CSE focuses on the development of problem-solving methodologies and robust tools for the solution of scientific and engineering problems. The Department offers a course of studies leading to the Ph. The thesis topic is chosen by the student in consultation with the research supervisor.
The thesis must be examined and approved by an internal examiner normally the research supervisor , an external examiner, and the Oral Examination Committee. The student must present an oral defence of the thesis before that Committee. To submit a thesis for examination, the student must first pass comprehensive examinations. Students successfully completing the Bioinformatics option at the Ph.
Mathematics and Statistics Admission Requirements and Application Procedures Admission Requirements In addition to the general Graduate and Postdoctoral Studies requirements, the Department requirements are as follows:. The normal entrance requirement for the master's programs is a Canadian honours degree or its equivalent, with high standing, in mathematics or a closely related discipline in the case of applicants intending to concentrate in statistics or applied mathematics.
Applicants wishing to concentrate in pure mathematics should have a strong background in linear algebra, abstract algebra, and real and complex analysis. Applicants wishing to concentrate in statistics should have a strong background in linear algebra and basic real analysis. A calculus-based course in probability and one in statistics are required, as well as some knowledge of computer programming. Some knowledge of numerical analysis and optimization is desirable. Applicants wishing to concentrate in applied mathematics should have a strong background in most of the areas of linear algebra, analysis, differential equations, discrete mathematics, and numerical analysis.
Some knowledge of computer programming is also desirable. Students whose preparation is insufficient for the program they wish to enter may, exceptionally, be admitted to a Qualifying year. Students without a master's degree, but with exceptionally strong undergraduate training, may be admitted directly to Ph.
Our faculty members are leading experts in a wide variety of mathematical fields, including Discrete Mathematics, Scientific Computing, Pure Mathematics, Theoretical Computer Science, as well as Probability and Statistics. Click here for a selection of recent research highlights. Most PhD students are supported by scholarships , which cover tuition fees and provide a stipend and other forms of support.
Scholarships typically include teaching and service requirements; the exact terms and conditions are explained upon the offering of the scholarship. For information about the available terms of support, please contact us. To apply for the PhD programme, please go to our Admission Requirements page , and read the instructions carefully. Cohomology and K-theory of aperiodic tilings. Enumerative combinatorics of posets. Tree-based decompositions of graphs on surfaces and applications to the traveling salesman problem. Algorithmic and topological aspects of semi-algebraic sets defined by quadratic polynomials.
Validated Continuation for Infinite Dimensional Problems. An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems. Maximum Codes with the Identifiable Parent Property. Nodal sets and contact structures. Bifurcations, Normal Forms and their Applications. Topological Analysis of Patterns.
Conley-Morse Chain Maps. Matching structure and Pfaffian orientations of graphs.
Mathematics and Statistics
Pricing of Game Options in a market with stochastic interest rates. Extremal Functions for Contractions of Graphs. Nonparametric estimation of Levy processes with a view towards mathematical finance. Lorentz Lattice Gases on Graphs. Numerical Methods for the Continuation of Invariant Tori. Independent Tress in 4-Connected Graphs. Disjoint Paths in Planar Graphs. Dynamics of Billiards. Applications of the Monge-Kantorovich Theory.
PhD Thesis Defenses
Paths, Samping and Markov Chain Decomposition. Curvature, Isoperimetry, and Discrete Spin Systems. Generating Random Absolutely Continuous Distributions. Multiwavelets in Higher Dimensions. On Properties of Completely Flexible Loops. Time-Frequency Analysis of Pseudodifferential Operators. Random Sampling of Combinatorial Structures. Diamagnetic Behavior of Sums of Dirichlet Eigenvalues. Independent Sets in Bounded Degree Graphs. Planar Covers of Graphs Negami's Conjecture.
Coloring Girth Restricted Graphs on Surfaces. Existence of Traveling Waves and Applications. Unique Coloring of Planar Graphs. Computation of Homology and an Application to the Conley Index. Estimates for the St.
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Petersburg Game. Ranges of Vector Measures and Valulations. Controllability of Cellular Neural Networks. Conley Index and Chaos.
PhD Dissertations | School of Mathematical and Statistical Sciences
Dilation Equations with Matrix Dilations. Compactifications and Function Spaces. An Analysis of the Oregonator. Skew-product semiflows and time dependent dynamical systems. Hyperbolic Iterated Function Systems and Applications.
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Fractal Functions, Splines and Wavelets. Saddle-Node Bifurcations with Homoclinic Orbits. Cyclic Feedback Systems. Cases of Equality in the Riesz Rearrangement Inequality. Eigenvalue Gaps for Self-Adjoint Operators. Structural Stability of Periodic Systems.
Infinite dimensional dynamics described by ordinary differential equations. Stability and Bifurcation of Traveling Wave Solutions. On Cahn-Hilliard Type Equation. Spectral Theory of Laplace-Beltrami Operators.