Skip to Content

Mathematics

Courses | Faculty | Overview | Programs: Collaborative, Degree

Faculty Affiliation

Arts and Science

Degree Programs Offered

Mathematics – MSc, PhD

Overview

The Department of Mathematics offers opportunities for research – leading to the Master of Science and Doctor of Philosophy degrees - in 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 cooperation with the Department of Statistics), combinatorics, optimization, control theory, dynamical systems, computer algebra, cryptography, and mathematical finance.

More information about this program and courses may be found in the brochure Graduate Studies in Mathematics at the University of Toronto.

Contact and Address

Web: www.math.toronto.edu/graduate
E-mail: grad-info@math.toronto.edu
Telephone: (416) 978-7894
Fax: (416) 978-4107

Department of Mathematics
University of Toronto
Room 6290, 40 St. George Street
Toronto, Ontario M5S 2E4
Canada

Degree Programs

Mathematics

Master of Science

Minimum Admission Requirements

  • SGS general regulations and evidence of an excellent academic background and mathematical ability.

Program Requirements 

  • Full-time students are accepted into a 12-month, 16-month, or 24-month program. The program may be completed on a part-time basis.
  • Students in the 12-month program are required either (a) to successfully complete 3.0 approved full-course equivalents (FCE) and a supervised research project (MAT 4000Y), or its equivalent, or (b) successfully complete 2.0 approved FCE and submit an acceptable thesis. Two approved half-year courses are considered the equivalent of a full-year course. Two prerequisite courses may, with approval, be substituted for one program course. Students may, with approval, take courses outside the department as part of a coherent program.
  • Students who do not have a complete undergraduate background in mathematics may be accepted into a 16-month or 24-month program which includes an approved selection of prerequisite and other courses in addition to the requirements of the 12-month program. This possibility may interest students who have some background in a subject in which mathematics is applied and/or who are interested in industrial applications of mathematics.
  • Students who undertake the MSc part-time must, at a minimum, satisfy the requirements of the 12-month program.

Normal Program Length

  • 3 sessions (full-time 1-year MSc); 4 sessions (full-time 16-month MSc); 6 sessions (full-time 2-year MSc); 6 sessions (part-time)

Doctor of Philosophy

Minimum Admission Requirements 

  • Normally a master's degree from a recognized university. However, exceptionally strong BSc students may apply for direct admission to the PhD program. In all cases students must satisfy the department of their ability to do independent research at an advanced level. They must show evidence of an excellent academic background and mathematical ability.

Program Requirements 

  • At least 6.0 half-courses or 3.0 full-course equivalents (FCE).
  • Students must pass a comprehensive examination in basic mathematics before beginning an area of specialization. This examination should be taken as soon as possible, and not later than the beginning of the third session of PhD study. The usual examination covers the three general areas of analysis, algebra, and topology, at the level of the first-year graduate courses offered by the department in these subjects. Students planning to specialize in applied mathematics must take the analysis and/or algebra portion of the comprehensive examination, but may substitute from several areas of applied mathematics for the remaining portions.
  • Students must pass a specialist oral examination or give a seminar presentation in their particular field of study before embarking on serious thesis research.
  • The main requirement of the degree is an acceptable thesis embodying original research of a standard that warrants publication in the research literature.

Normal Program Length

  • 4 years (full-time PhD); 5 years (direct-entry PhD)

Course List

Each year the department offers a selection of courses chosen from the following list, with the possibility of further additions. The courses, MAT 1000H, 1001H, 1100H, 1101H, 1300H, 1301H, will be offered each year; the complete list of courses will be available from the department in May. In addition, it may be possible for a student to arrange to take one of the listed courses as an individual reading course. Students should consult the office of the Coordinator at the beginning of the academic year.

PhD students are expected to attend and contribute to seminars in the research areas.

MAT 1000H Real Analysis I
MAT 1001H Real Analysis II
MAT 1002H Complex Analysis
MAT 1003H Theory of Several Complex Variables
MAT 1004H Theory of Approximation
MAT 1005H Fourier Analysis
MAT 1006H Topics in Real Analysis
MAT 1007H Topics in Complex Variables
MAT 1008H Functions of a Complex Variable
MAT 1010H Functional Analysis
MAT 1011H Introduction to Linear Operators
MAT 1012H Real Analysis II
MAT 1013H Theory of Several Complex Variables II
MAT 1015H Topics in Operator Theory
MAT 1016Y Topics in Operator Algebras
MAT 1017H Introduction to K-theory for Operator Algebras
MAT 1034H Topics in Harmonic Analysis
MAT 1035H C* Algebras
MAT 1037H Von Neumann Algebras
MAT 1044H Potential Theory
MAT 1045H Topics in Ergodic Theory
MAT 1051H Introduction to Ordinary Differential Equations
MAT 1052H Topics in Ordinary Differential Equations
MAT 1060H Partial Differential Equations I
MAT 1061H Partial Differential Equations II
MAT 1062H Topics in Partial Differential Equations I
MAT 1063H Topics in Partial Differential Equations II
MAT 1075H Differential Analysis
MAT 1100H Algebra I
MAT 1101H Algebra II
MAT 1102H Topics in the Theory of Groups
MAT 1103H Topics in Algebra I
MAT 1104H Topics in Algebra II
MAT 1109H Classical Groups
MAT 1110H Algebraic Groups
MAT 1120H Lie Groups and Lie Algebras I
MAT 1121H Lie Groups and Lie Algebras II
MAT 1122H Lie Groups and Representations I
MAT 1124H Topics in Matrix Theory
MAT 1126H Lie Groups and Fluid Dynamics
MAT 1155H Commutative Algebra
MAT 1190H Algebraic Geometry
MAT 1191H Topics in Algebraic Geometry
MAT 1194H Algebraic Curves
MAT 1195H Elliptic Curves and Cryptography
MAT 1196H Representation Theory
MAT 1197H Automorphic Forms and Representation Theory I
MAT 1198H Automorphic Forms and Representation Theory II
MAT 1199H Automorphic Forms
MAT 1200H Algebraic Number Theory
MAT 1202H Analytic Number Theory
MAT 1203H Computational Aspects of Number Theory
MAT 1210H Topics in Number Theory
MAT 1299H Point Set Topology
MAT 1300H Topology I
MAT 1301H Topology II
MAT 1302H Combinatorial Theory
MAT 1303H Combinatorial Designs
MAT 1309H Geometrical Inequalities
MAT 1312H Topics in Geometry
MAT 1313Y Seminar in Geometry
MAT 1314H Introduction to Noncommutative Geometry
MAT 1340H Differential Topology
MAT 1341H Differentiable Manifolds and Applications
MAT 1342H Introduction to Differential Geometry
MAT 1343H Riemannian Manifolds
MAT 1344H Symplectic Geometry
MAT 1345H Basic Algebraic Topology
MAT 1346H Homotopy Theory
MAT 1347H Topics in Symplectic Geometry and Topology
MAT 1350H Topics in Algebraic Topology I
MAT 1351H Topics in Homotopy Theory
MAT 1352H Topics in Algebraic Topology II
MAT 1355H Singularity Theory
MAT 1359H Moduli Spaces of Flat Connections
MAT 1360H Complex Manifolds
MAT 1392H Algebra Seminar
MAT 1399H Advanced Point Set Topology
MAT 1403H Model Theory
MAT 1404H Introduction to Model Theory and Set Theory
MAT 1430H Set Theory
MAT 1435H Infinitary Combinatorics
MAT 1436H Large Cardinals, Structure Theory of Ideals and Applications
MAT 1448H Topics in Set Theoretic Topology
MAT 1449H Seminar in Foundations
MAT 1450H Topics in Foundations
MAT 1499H Teaching Large Mathematics Courses (Credit/No Credit)

Applied Mathematics
MAT 1500Y Applied Analysis
MAT 1501H Equations and Variational Calculus
MAT 1502H Dynamical Systems and Stochastic Analysis
MAT 1507H Asymptotic and Perturbation Methods
MAT 1508H Techniques of Applied Mathematics
MAT 1520H Wave Propagation
MAT 1525Y Inverse Problems of X-Ray and Radar Imaging
MAT 1638H Fluid Mechanics
MAT 1639Y Topics in Fluid Mechanics
MAT 1700H General Relativity
MAT 1705H Foundations of Classical Mechanics
MAT 1710H Group Theory and Quantum Mechanics
MAT 1711H Topics in Quantum Mechanics
MAT 1722H C* Algebras and Quantum Mechanics
MAT 1723H Foundations of Quantum Mechanics
MAT 1724H Functional Analysis in Quantum Mechanics
MAT 1725Y Scattering Theory
MAT 1739H Topics in Mathematical Physics
MAT 1750H Computational Mathematics
MAT 1751H Topics in Computational Mathematics
MAT 1760H Computer Algebra
MAT 1761H Algorithms in Algebraic Geometry
MAT 1839H Optimization and Control
MAT 1840H Control Theory
MAT 1843H Mathematics of Pattern Recognition
MAT 1844H Nonlinear Dynamical Systems
MAT 1845H Dynamical Systems
MAT 1846H Topics in Dynamical Systems
MAT 1847H Holomorphic Dynamics
MAT 1855H Mathematical Economics
MAT 1856H Mathematical Finance
MAT 1880H Case Studies in Applied Mathematics

Individual Reading Courses
MAT 1900Y Readings in Pure Mathematics
MAT 1901H Readings in Pure Mathematics
MAT 1902H Readings in Pure Mathematics
MAT 1950Y Readings in Applied Mathematics
MAT 1951H Readings in Applied Mathematics
MAT 1952H Readings in Applied Mathematics
MAT 2000Y Readings in Theoretical Mathematics
MAT 2001H Readings in Theoretical Mathematics I
MAT 2002H Readings in Theoretical Mathematics II

MSc Project
MAT 4000Y+ Supervised Research Project

+Extended course. For academic reasons, course work is extended into session following academic session in which course is offered.

Graduate Faculty

Full Members

Alexakis, Spyridon - BA, PhD
Angel, Omer - PhD
Arkhipov, Sergey - PhD
Arthur, James - BSc, MSc, PhD
Bar-Natan, Dror - BSc, PhD (Coordinator of Graduate Studies)
Bierstone, Edward - BSc, MA, PhD
Binder, Ilia - PhD
Bland, John - BSc, MSc, PhD
Blomer, Valentin - PhD
Bloom, Thomas - BSc, MA, PhD
Buchweitz, Ragnar-Olaf - ScD, DRHAB
Burchard, Almut - MS, PhD
Choi, Man-Duen - BSc, MSc, PhD
Colliander, James - BA, MS, PhD
Cook, Stephen - BS, AM, PhD
Del Junco, Andres - BSc, MSc, PhD
Derzko, Nicholas - BSc, PhD
Elliott, George - BSc, MSc, PhD
Friedlander, John - BSc, BS, MA, PhD
Goldstein, Michael - BA, MMath, ScD, PhD
Graham, Ian - BSc, ScD
Gualtieri, Marco - BSc, DPhil
Guth, Lawrence - BS, PhD
Ivrii, Victor - MA, PhD, DSc
Jeffrey, Lisa - BA, MA, PhD
Jerrard, Robert - AB, PhD
Kamnitzer, Joel - BMath, PhD
Kapovitch, Vitali - BS, PhD
Karshon, Yael - PhD
Khanin, Konstantin - PhD
Khesin, Boris - MS, PhD
Khovanskii, Askold - PhD, DSc
Kim, Henry - BSc, PhD
Kudla, Stephen - BA, MA, PhD
Lorimer, Joseph - BSc, MSc, PhD
McCann, Robert - BS, PhD
Meinrenken, Eckhard - PhD
Mendelsohn, Eric - BSc, MSc, PhD
Milman, Pierre - MA, PhD
Murnaghan, Fiona - BSc, MSc, PhD
Murty, Vijayakumar - BSc, PhD (Chair & Graduate Chair)
Nabutovsky, Alexander - MSc, PhD
Nachman, Adrian - BSc, MA, PhD
Pugh, Charles - PhD
Pugh, Mary - BA, MS, PhD
Quastel, Jeremy - BSc, MS, PhD
Repka, Joseph - BSc, PhD
Rosenthal, Jeffrey - PhD
Rosenthal, Peter - BS, MA, PhD
Rotman, Regina - BA, PhD
Scherk, John - BSc, MSc, DPhil
Seco, Luis - PhD
Selick, Paul - BSc, MSc, PhD
Shub, Michael - AB, MA, PhD
Sigal, Israel Michael - BA, PhD
Sulem, Catherine - MMath, PhD
Szegedy, Balazs - MS, PhD
Tall, Franklin - AB, PhD
Tanny, Stephen - BSc, PhD
Todorcevic, Stevo - PhD
Virag, Balint - BA, MA, PhD
Weiss, William - BSc, MSc, PhD
Yampolsky, Michael - DPhil

Members Emeriti

Akcoglu, Mustafa - MSc, PhD
Andrews, David - BSc, MSc, PhD
Barbeau, Edward - BA, MA, PhD
Davis, H Chandler - BS, MA, PhD
Ellers, Erich - DrRerNat, DrRerNat
Fraser, Donald AS - BA, MA, PhD, Fell Royal Society Canada
Greiner, Peter - BSc, MA, PhD
Halperin, J Stephen - BSc, MSc, PhD, Fell Royal Society Canada
Haque, Wahidul - MA, MS, PhD
Jurdjevic, Velimir - BS, MS, PhD
Kupka, Ivan - BSc, PhD, PhD
Masson, David - BSc, MSc, PhD
McCool, James - BSc, PhD
Murasugi, Kunio - BSc, DSc
Rooney, Paul - BSc, PhD
Sen, Dipak - MSc, DSc
Sharpe, Richard - BSc, MA, PhD
Sherk, F Arthur - BA, MSc, PhD
Smith, Stuart - BSc, PhD

Associate Members

Pete, Gabor Zoltan - PhD


-Back to Top-