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See announcement (PDF).

Notice of the Final Oral Examination for the Degree
of Master of Science
of

FELICIA HALLIDAY
BSc (Dalhousie University, 2017)

Cops, Robbers and Pre-Calculus Skills

Department of Mathematics and Statistics
Friday, December 13, 2019 10:30 A.M.
David Strong Building Room C114

Supervisory Committee:
Dr. Jane Butterfield, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Gary MacGillivray, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner:
Dr. Celina Berg, Department of Computer Science, UVic

Chair of Oral Examination:
Dr. Michael Masson, Department of Psychology, UVic

Abstract

This thesis is partitioned into three parts: improving pre-calculus skills of students in an introductory calculus course, the game of Cops and Robber on oriented graphs, and the generalized game of Cops and Robber. In the first part, we study the effect of review modules on student performance using an Educational Action Research framework. In addition to the study, we report what instructors at various institutions say they were doing to improve pre-calculus skills. In the second part, we introduce the game of Cops and Robber on oriented graphs using a two-part article that will appear in the problem-solving journal for high school students and undergraduates, Crux Mathematicorum. Next, we present a survey of previous results and provide family of counter examples to a conjecture that was recently shown to be false. In the last part of the thesis, we consider general Cops and Robber games. We give a survey of previous results and conclude with a new characterization of graphs in which the Cops have a winning strategy.

Notice of the Final Oral Examination for the Degree of Master of Science of

FLORA BOWDITCH
BSc (University of Victoria, 2017)

“Localized Structure in Graph Decompositions”

Department of Mathematics and Statistics
Friday, November 22, 2019 11:00 A.M.
David Strong Building Room C130

Supervisory Committee:
Dr. Peter Dukes, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Gary MacGillivray, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Esther Lamken, Mathematics and Statistics, Caltech

Chair of Oral Examination:
Dr. Daniela Constantinescu, Department of Mechanical Engineering, UVic

See abstract(pdf)

Notice of the Final Oral Examination for the Degree of Master of Science of

MACKENZIE WHEELER

BSc (University of Victoria, 2017)

“Chromatic Polynomials of Mixed Graphs”

Department of Mathematics and Statistics

Wednesday, August 21, 2019 11:00 A.M.
Clearihue Building Room B007

Supervisory Committee:
Dr. Gary MacGillivray, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Peter Dukes, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Danielle Cox, Department of Mathematics, Mount Saint Vincent University

Chair of Oral Examination:
Dr. Michel Lefebvre, Department of Physics and Astronomy, UVic

Abstract (PDF)

Notice of the Final Oral Examination for the

Degree of Master of Science of

YING YING YE

MSc (University of Victoria, 2008)
BSc (University of Victoria, 2007)

“On Chordal Digraphs and Semi-Strict Chordal Digraphs”

Department of Mathematics and Statistics

Wednesday, August 14, 2019 10:30 A.M.

David Strong Building Room C126

Supervisory Committee:
Dr. Jing Huang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Venkatesh Srinivasan, Department of Computer Science, UVic (Outside Member)

External Examiner:
Dr. César Hernández Cruz, Departamento de Computación, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional

Chair of Oral Examination:
Dr. Colin Bradley, Department of Mechanical Engineering, UVic

Abstract

Chordal graphs are an important class of perfect graphs. The beautiful theory surrounding their study varies from natural applications to elegant characterizations in terms of forbidden subgraphs, subtree representations, vertex orderings, and to linear time recognition algorithms. Haskins and Rose introduced the class of chordal digraphs as a digraph analogue of chordal graphs. Chordal digraphs can be defined in terms of vertex orderings and several results about chordal graphs can be extended to chordal digraphs. However, a forbidden subdigraph characterization of chordal digraphs is not known and finding such a characterization seems to be a difficult problem. Meister studied semi-complete chordal digraphs and gave a forbidden subdigraph characterization of this class of digraphs.

In this thesis, we study chordal digraphs within the classes of quasi-transitive, extended semi- complete, and locally semi-complete digraphs. For each of these classes we obtain a forbidden subdigraph characterization of digraphs which are chordal. We also introduce in this thesis a new variant of chordal digraphs called semi-strict chordal digraphs. We obtain a forbidden subdigraph characterization of semi-strict chordal digraphs for each of the classes of semi- complete, quasi-transitive, extended semi-complete, and locally semi-complete digraphs.

Notice of the Final Oral Examination for the Degree of Master of Science of

HYUNGEUN SHIN
MSc (Kyungpook National University, 2014)
BSc (Kumoh National Institute of Technology, 2009)

“Effect of Equatorially Trapped Waves on the Tropical Cyclone Drift”

Department of Mathematics and Statistics

Wednesday, August 7, 2019 10:00 A.M.
David Strong Building Room C128

Supervisory Committee: Dr. Boualem Khouider, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Slim Ibrahim, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Jody Klymak, School of Earth and Ocean Sciences, UVic

Chair of Oral Examination:
Dr. Viviene Temple, School of Exercise, Science, Physical and Health Education, UVic

Abstract

The movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model, using a previously developed non-oscillatory balanced scheme. The model of TC used here takes an exponential form, and its size and strength are selected to be of a middle scale. Without a background flow, TCs move in the northwest direction due to the beta effect. In addition, the amplitudes of high wavenumber modes of the asymmetric flow, that are believed to be responsible for the TC drift, are computed using Fourier analysis. The amplitude of wavenumber one and two modes are dominant, so they are indicators of beta conversion of energy. Also, the effect of the monsoon trough on the TC movement is investigated. The results show a sudden change of the TC propagation path, consistent with earlier work. These two studies correspond to previous works. Here, the effect of equatorially trapped waves such as Kelvin, Rossby, and Mixed Rossby Gravity, on the TC path is newly studied by varying the wavenumber and wavespeed of the underlying waves. The effect of the waves is considered because they are believed to contribute to cyclogenesis. For studying the effect, the barotropic flow induced by these waves via momentum transport and its variation were simulated for 50 days, and some patterns are found in the change of maximum wind speed. At a given time during the simulation, a TC is injected and the effect of the background wave is obtained and analyzed. Using the wavefield of 11 cases from 10 days to 30 days, the trajectories are calculated, and their patterns appear to be stochastic. So, the patterns are identified by calculating the mean path and its spread. The trajectories of TCs are different for different developed time of the waves. Kelvin waves make small variations on the length and direction of trajectory of TC. On the contrary, Rossby waves cause a dramatic change in the TC path and yield longer trajectories. Meanwhile, TCs in MRG waves keep fairly the same direction and usually have longer traveling distance. These changes vary by wave conditions. Therefore, the three kinds of waves have different effects on the trajectories of the TC. For some peculiar cases, the movements are explained based on wavefields.

Notice of the Final Oral Examination for the Degree of Master of Science of

MEIXIN LIU
BSc (University of Victoria, 2017)

“Graph Decompositions and Variance Balanced Block Designs of Experiments”

Department of Mathematics and Statistics

Tuesday, August 6, 2019 10:00 A.M.

David Strong Building Room C128

Supervisory Committee:
Dr. Peter Dukes, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Julie Zhou, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner:
Dr. Hong-Chuan Yang, Department of Electrical and Computer Engineering, UVic

Chair of Oral Examination:
Dr. Charles Curry, School of Earth and Ocean Sciences, UVic

Abstract

We study construction methods for variance balanced design (VBD) with both uncorrelated and correlated errors, where block designs are used to investigate several treatment effects. We begin with a review for the development of VBDs when the errors in the linear effects model are uncorrelated. There are several construction methods of VBDs for equal and unequal block sizes. When the errors are correlated, we introduce graph theory to study construction methods of VBDs. We develop new methods via graph decomposition. In addition, we construct block designs such that the covariance matrix of the least squares estimator of treatment effects is completely symmetric. Various applications are presented for certain specific error covariance matrices.

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy of

LINDA NEILSON
B.ASc (University of British Columbia, 1989)
B.Ed (University of British Columbia, 1994)

“Broadcast Independence in Graphs”

Department of Mathematics and Statistics

Thursday, July 25, 2019 10:00 A.M.
Clearihue Building Room B021

Supervisory Committee:
Dr. Kieka Mynhardt, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Rick Brewster, Department of Mathematics and Statistics, UVic (Member)
Dr. Aaron Gulliver, Department of Electrical and Computer Engineering, UVic (Outside Member)

External Examiner:
Dr. David Erwin, Mathematics and Applied Mathematics, University of Cape Town

Chair of Oral Examination:
Dr. Tim Pelton, Department of Curriculum and Instruction, UVic

Abstract
The usual graph quantifiers related to independent and dominating sets can be adapted to broadcasts on graphs. We examine some possible definitions for an independent broadcast. We determine the minimum maximal and the maximum broadcast weight for all our independence parameters on both paths and grids. For graphs in general, we examine the relationships between these broadcast independence parameters and the existing minimum and maximum minimal broadcast domination weight (or cost). We also determine upper and lower bounds for maximum boundary independent broadcasts and a new upper bound for hearing independent broadcasts.