Department of Mathematics and Statistics Graduate Projects
Recent Submissions

Empirical Study on Bayesian and Frequentist Model Calibration of Computer Models
(201801)Computational modelling and simulation are used to study many complex phenomena where physical experiments are not feasible or too expensive. Examples include climate models, weather forecasting models, earth simulator ... 
A review of a model for imperfect vaccination, honeymoon periods and methods to characterize transient dynamics
(201808)Vaccination is a common method for protecting newborns from some childhood diseases like measles, mumps, and rubella. This control measure has proven to be very successful as evidenced by large decreases in the incidence ... 
Nonholonomic and Variational Equations of Motion for Mechanical Systems
(201808)In this project, we use two approaches for writing the equations of motion of a mechanical system subject to nonholonomic velocity constraints: nonholonomic mechanics and constrained variational mechanics. We introduce the ... 
ON STOCHASTIC TEAMS WITH COUNTABLY MANY DECISION MAKERS
(20171121)This report is concerned with the connections between team optimal and personbyperson optimal solutions for static teams with countably infinite decision makers. The average cost problem for static teams is studied and ... 
On the BorelWeil Theorem for SL_n
(2017) 
Evaluation and Application of a Test for TreatmentBiomarker Interaction Effects Using Probabilistic Indices
(201708)A predictive biomarker is a patient characteristic which associates with different effects of the treatment on the patient. In clinical trials, it is often of interest to assess whether the effects of the treatment differ ... 
Working with sophisticated problems in a grade 10 math classroom: The exploration of new experiences on selfefficacy
(201709)Studies show that selfefficacy is a strong indicator of student math achievement (Kitsantas et al., 2011). It has also been seen that selfefficacy changes based on the situation that one has to face (Bandura, 1997). This ... 
Experimenting with low threshold, high ceiling mathematics tasks in a Grade 10 mathematics class: a mixed method study on student engagement
(20170922)The experiment. In collaboration with the Mathematical Knowledge Network and the Fields institute, Professor Peter Taylor and his team created Math912, a new approach to curricular instruction following inquirybased ... 
Ensemble Controllability of Linear Control Systems
(2017)This thesis is concerned about ensemble controllability. We give an overview of the notions of ensemble controllability, in particular, $L_{2}$ensemble controllability, and uniform ensemble controllability. We review the ... 
Representation of numbers by quaternary quadratic forms
(20160927) 
An Rpackage for the Estimation and Testing of Multiple Covariates and Biomarker Interactions for Survival Data Based on Local Partial Likelihood
(20160927)When we study the variables that a ffect survival time, we usually estimate their eff ects by the Cox regression model. In biomedical research, e ffects of the covariates are often modi ed by a biomarker variable. This ... 
On The Dirichlet Distribution
(20160927)The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution ... 
Degeneracy of velocity constraints in rigid body systems
(20160927)The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the ... 
Elliptic Functions and Elliptic Interpolation
(20160921) 
Estimation of Sample Size and Power For Quantile Regression
(20160824)Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of ... 
A Review on Repeated Games and Reputations with Incomplete Information
(20160720)In this project we review the effects of reputation within the context of game theory. This is done through a study of two key papers. First, we examine a paper from Fudenberg and Levine: Reputation and Equilibrium ... 
The Chowla Problem and its generalizations
(20150915)In this thesis, we study the vanishing of certain $L$series attached to periodic arithmetical functions. Throughout the writeup, we let $f$ be an algebraicvalued (at times even rationalvalued) arithmetical function, ... 
The Saddle Point Method and its Applications to Number Theory
(20150915)In this thesis, we study the classical procedures useful in obtaining asymptotic expansions of functions defined by integrals and their applications to number theory. The final chapter in the thesis reports on a recent ...