Doctor of Philosophy in Mathematics

The Department of Mathematics offers opportunities for researchleading to the Master of Science and Doctor of Philosophy degreesin the fields of pure mathematics and applied mathematics. Faculty areas of research include, but are not limited to, real and complex analysis, ordinary and partial differential equations, harmonic analysis, nonlinear analysis, several complex variables, functional analysis, operator theory, C-algebras, ergodic theory, group theory, analytic and algebraic number theory, Lie groups and Lie algebras, automorphic forms, commutative algebra, algebraic geometry, singularity theory, differential geometry, symplectic geometry, classical synthetic geometry, algebraic topology, set theory, set-theoretic topology, mathematical physics, fluid mechanics, probability (in co-operation with the Department of Statistics), combinatorics, optimization, control theory, dynamical systems, computer algebra, cryptography, and mathematical finance.

Applicants to the PhD program must have an appropriate University of Toronto master's degree, or its equivalent, with an average of at least A-, or demonstrated comparable research competence. (Direct entry from the bachelor's to the PhD is possible for some eminently qualified applicants - optional). All applicants must satisfy the admission requirements of the department, which will take into account the background and accomplishments of the student as well as their academic achievements.
Official transcripts of your academic record from each university attended are required for admission: you will not be required to submit official paper copies of your transcripts until after the admissions committee makes its decision. If admitted, you will be required to submit an official transcript, verification of your paper transcript will be a condition that must be met prior to registration.
At least THREE supporting letters of reference are required. Referees are automatically contacted via e-mail when you submit their name and contact info on the on-line application form. Letters of reference will be part of the official student academic record, they are confidential and applicants/students will not have access to them. Please note there are no reference forms and that your referee's email must be an official institutional email address (personal email addresses not accepted).
A letter of intent or personal statement to be up-loaded on the online application form.
A curriculum vitae to be uploaded on the on-line application form.

IELTS - Minimum required score 7.0 (Academic) with at least 6.5 for each component.
TOEFL IBT - Overall Score - 93, Writing and Speaking- 22, TOEFL Paper-based Test - Overall Score 580, TWE 5