Program Overview

Doctorate in Philosophy Mathematics and Statistics

The University of Ottawa offers a rich academic environment to study mathematics and statistics under the supervision of professors who have gained an international reputation for their research. Most major fields of research in mathematics and statistics are represented within the Department of Mathematics and Statistics.

Program Description

The Doctorate in Philosophy Mathematics and Statistics is a research-based program that allows students to explore their interests in mathematics and statistics. The program is offered in English and is designed to provide students with a comprehensive education in mathematics and statistics, as well as the opportunity to conduct original research.

Admission Requirements

To be eligible for the program, candidates must:

• Have a master's degree in mathematics and statistics (or equivalent) with a minimum average of 75% (B+).
• Demonstrate a good academic performance in previous studies as shown by official transcripts, research reports, abstracts, or any other documents demonstrating research skills.
• Meet the funding requirements.
• Identify at least one professor who is willing to supervise their research and thesis.

Program Requirements

The program requires students to complete:

• 18 optional course units in mathematics at the graduate level.
• Two options from the following: Real Analysis, Algebra, Topology, Differential Equations, Discrete Mathematics, Probability Theory, or Mathematical Statistics.
• A comprehensive examination.
• A thesis based on original research carried out under the direct supervision of a faculty member of the Institute.

Research Areas

The Faculty of Science has become a true centre of excellence in research through its world-class professors as well as its programs and infrastructure in Biology, Chemistry, Earth Sciences, Mathematics and Statistics, and Physics. The research accomplished by its 140 internationally recognized professors, its approximately 400 graduate students, and its dozens of postdoctoral researchers and visiting scientists has positioned the Faculty of Science as one of the most research-intensive science faculties in Canada.

Courses

A wide range of courses is available, including:

• Discrete Applied Mathematics I: Graph Theory
• Combinatorial Optimization
• Discrete Applied Mathematics II: Combinatorial Enumeration
• Introduction to Hilbert Space
• Banach Algebras
• Real Analysis I
• Real Analysis II
• Complex Analysis
• Ordinary Differential Equations I
• Partial Differential Equations I
• Topics in Differential Equations
• Algebra I: Rings and Modules
• Algebra II: Groups and Galois Theory
• Lie Algebras
• Commutative Algebra
• Group Theory
• Rings and Modules
• Homological Algebra and Category Theory
• Group Representations and Applications
• Algebraic Geometry
• Topology I
• Topology II
• Differentiable Manifolds
• Lie Groups
• Mathematical Cryptography
• Mathematical Logic
• Mathematical Foundations of Computer Science
• Analytic Number Theory
• Algebraic Number Theory
• Theory of Automata
• Formal Language and Syntax Analysis
• Homology Theory
• Foundations of Geometry
• Probability Theory I
• Probability Theory II
• Topics in Stochastic Processes
• Stochastic Analysis
• Network Performance
• Robust Statistical Inference
• Advanced Statistical Inference
• Multivariate Normal Theory
• Numerical Analysis for Differential Equations
• Data Mining I
• Modern Applied and Computational Statistics
• Asymptotic Methods of Applied Mathematics
• Topics in Applied Mathematics
• Mathematical Statistics I
• Mathematical Statistics II
• Sampling Theory and Methods
• Linear Models
• Stochastic Processes and Time Series Analysis
• Design of Experiments
• Multivariate Analysis
• Stochastic Optimization
• Stochastic Models

Comprehensive Exams

Students must pass comprehensive exams in their area of specialization, including:

• Real Analysis
• Algebra
• Topology
• Differential Equations
• Discrete Mathematics
• Probability Theory
• Mathematical Statistics

Thesis

Students must complete a thesis based on original research carried out under the direct supervision of a faculty member of the Institute. The thesis must be presented and successfully defended.