Degree and Diploma Programs by Graduate Unit
2014-15 SGS Calendar
Mathematics
Faculty Affiliation
Arts and Science
Degree Programs Offered
satisfy the Department of Mathematics' additional
admission requirements stated below.
 Evidence of an excellent academic background and
mathematical ability.
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.utoronto.ca
Email: 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
 Applicants are admitted under the General Regulations
of the School of Graduate Studies. Applicants must also
2014-2015 School of Graduate Studies Calendar
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Program Requirements
 Full-time students are accepted into a 12-month, 16month, 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 (FCEs) and a supervised research project
(MAT 4000Y), or its equivalent, or (b) successfully
complete 2.0 approved FCEs 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 16month 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 the12-month
program.
Program Length
3 sessions full-time 1-year MSc (typical registration
sequence: F/W/S);
4 sessions full-time 16-month MSc (typical registration
sequence: F/W/S/F);
6 sessions full-time 2-year MSc (typical registration
sequence: F/W/S/F/W/S);
6 sessions part-time
Time Limit
3 years full-time;
6 years part-time
Doctor of Philosophy
Minimum Admission Requirements
 Applicants are admitted under the General Regulations
of the School of Graduate Studies. Applicants must also
Mathematics
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Degree and Diploma Programs by Graduate Unit
satisfy the Department of Mathematics' additional
admission requirements stated below.
 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.
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
 At least 6.0 half courses or 3.0 full-course equivalents
MAT 1008H
Functions of a Complex Variable
 Students must pass a comprehensive examination in
MAT 1010H
Functional Analysis
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.
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
Program Requirements
(FCEs).
Program Length
4 years full-time; 5 years direct-entry
Time Limit
6 years full-time; 7 years direct-entry
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, and 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 1075H
Differential Analysis
MAT 1001H
Real Analysis II
MAT 1100H
Algebra I
MAT 1002H
Complex Analysis
MAT 1101H
Algebra II
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Mathematics
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Degree and Diploma Programs by Graduate Unit
MAT 1102H
Topics in the Theory of Groups
MAT 1304H
Topics in Combinatorics
MAT 1103H
Topics in Algebra I
MAT 1305H
Topics in Geometric Topology
MAT 1104H
Topics in Algebra II
MAT 1309H
Geometrical Inequalities
MAT 1109H
Classical Groups
MAT 1312H
Topics in Geometry
MAT 1110H
Algebraic Groups
MAT 1313Y
Seminar in Geometry
MAT 1120H
Lie Groups and Lie Algebras I
MAT 1314H
Introduction to Noncommutative
Geometry
MAT 1121H
Lie Groups and Lie Algebras II
MAT 1340H
Differential Topology
MAT 1122H
Lie Groups and Representations I
MAT 1341H
Topics in Differential Geometry
MAT 1124H
Topics in Matrix Theory
MAT 1342H
Introduction to Differential Geometry
MAT 1126H
Lie Groups and Fluid Dynamics
MAT 1343H
Riemannian Manifolds
MAT 1128H
Topics in Probability
MAT 1344H
Symplectic Geometry
MAT 1155H
Commutative Algebra
MAT 1345H
Symplectic Geometry and Topology
MAT 1190H
Algebraic Geometry
MAT 1346H
Homotopy Theory
MAT 1191H
Topics in Algebraic Geometry
MAT 1347H
MAT 1194H
Algebraic Curves
Topics in Symplectic Geometry and
Topology
MAT 1195H
Elliptic Curves and Cryptography
MAT 1350H
Topics in Algebraic Topology I
MAT 1196H
Representation Theory
MAT 1351H
Topics in Homotopy Theory
MAT 1197H
Automorphic Forms and
Representation Theory I
MAT 1352H
Topics in Algebraic Topology II
MAT 1355H
Singularity Theory
MAT 1198H
Automorphic Forms and
Representation Theory II
MAT 1359H
Moduli Spaces of Flat Connections
MAT 1199H
Automorphic Forms
MAT 1360H
Complex Manifolds
MAT 1200H
Algebraic Number Theory
MAT 1392H
Algebra Seminar
MAT 1202H
Analytic Number Theory
MAT 1399H
Advanced Point Set Topology
MAT 1203H
Computational Aspects of Number
Theory
MAT 1403H
Model Theory
MAT 1404H
MAT 1210H
Topics in Number Theory
Introduction to Model Theory and
Set Theory
MAT 1299H
General Topology
MAT 1430H
Set Theory
MAT 1300H
Topology I
MAT 1435H
Topics in Set Theory
MAT 1301H
Topology II
MAT 1436H
Large Cardinals, Structure Theory of
Ideals and Applications
MAT 1302H
Combinatorial Theory
MAT 1448H
Topics in Set Theoretic Topology
MAT 1303H
Combinatorial Designs
2014-2015 School of Graduate Studies Calendar
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Mathematics
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Degree and Diploma Programs by Graduate Unit
MAT 1449H
Seminar in Foundations
MAT 1760H
Computer Algebra
MAT 1450H
Topics in Foundations
MAT 1761H
Algorithms in Algebraic Geometry
MAT 1499H
Teaching Large Mathematics
Courses (Credit/No Credit)
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
Applied Mathematics
MAT 1500Y
Applied Analysis
MAT 1501H
Applied Analysis I
MAT 1502H
Topics in Geometric 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
Individual Reading Courses
MAT 1638H
Fluid Mechanics
MAT 1639Y
Topics in Fluid Mechanics
MAT 1900Y
Readings in Pure Mathematics
MAT 1700H
General Relativity
MAT 1901H
Readings in Pure Mathematics
MAT 1705H
Foundations of Classical Mechanics
MAT 1902H
Readings in Pure Mathematics
MAT 1710H
Group Theory and Quantum Mechanics
MAT 1950Y
Readings in Applied Mathematics
MAT 1711H
Topics in Quantum Mechanics
MAT 1951H
Readings in Applied Mathematics
MAT 1722H
C* Algebras and Quantum Mechanics
MAT 1952H
Readings in Applied Mathematics
MAT 1723H
Foundations of Quantum Mechanics
MAT 2000Y
Readings in Theoretical Mathematics
MAT 1724H
Functional Analysis in Quantum
Mechanics
MAT 2001H
Readings in Theoretical Mathematics I
MAT 2002H
Readings in Theoretical Mathematics II
MAT 1725Y
Scattering Theory
MAT 1739H
Topics in Mathematical Physics
MAT 1750H
Computational Mathematics
MAT 1751H
Topics in Computational Mathematics
2014-2015 School of Graduate Studies Calendar
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MSc Project
MAT 4000Y+
Supervised Research Project
Extended course. For academic reasons, coursework is
extended into session following academic session in which
course is offered.
+
Mathematics
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