Mathematics
Faculty List
E.W.
Ellers, Ph.D. (Hamburg), Professor Emeritus
E.
Mendelsohn, B.Sc., M.Sc. (Manitoba), Ph.D. (McGill), Professor
Emeritus
R.W.
Sharpe, M.Sc., Ph.D. (Yale), Professor Emeritus
J.
Friedlander, M.A. (Waterloo), Ph.D. (Penn. State), F.R.S.C., University
Professor
R.-O.
Buchweitz, Ph.D. (Hanover), Professor
M.
Goldstein, Ph.D. (Tashkent), Professor
L.C.
Jeffrey, A.B. (Princeton), M.A. (Cambridge), D. Phil. (Oxford),
Professor
P.
Selick, B.Sc., M.Sc., Ph.D. (Princeton), Professor
J.
Scherk, D.Phil. (Oxford), Associate Professor
B.
Virag, Ph.D. (Berkeley), Associate Professor
G.
Pete, Ph.D. (Berkeley), Assistant Professor
B.
Szegedy, Ph.D. (Budapest), Assistant Professor
R. Young, B.A. (Simon's Rock), M.Sc., Ph.D. (Chicago), Assistant
Professor
N.
Cheredeko, M.Sc. (Kharkov), Ph.D. (Moscow), Senior Lecturer
S.
Chrysostomou, M.Sc. (Toronto), Senior Lecturer
R.
Grinnell, Ph.D. (Queen's), Senior Lecturer
X.
Jiang, B.Sc., M.Sc., Ph.D. (Glasgow), Senior Lecturer
E.
Moore, M.A. (Memorial), Ph.D. (Toronto), Senior Lecturer
Z.
Shahbazi, B.Sc. (Sharif), M.Sc., Ph.D. (Toronto), Lecturer
Associate Chair: L.C. Jeffrey (416-287-7265)
Our Mathematics began in the ancient Mesopotamian civilizations. The
Babylonians already knew much of the mathematics taught traditionally
in our schools. Their algebra and geometry was phrased in terms of
crops and fields and money. Since the Renaissance, much of mathematics
has come from problems in physics and astronomy; for example, calculus
arose from problems in mechanics. In turn mathematics has provided
the theoretical framework and tools in the Physical Sciences. In the
19th century some parts of mathematics appeared to develop away from
their origins in the physical world. To the great surprise of many
scientists and mathematicians, some of the "pure" mathematics has
turned out to be essential in many aspects of 20th century science.
Differential geometry provides the language for general relativity
and cosmology, and Hilbert space theory and group representations
are the tools for quantum mechanics. Similarly, graph theory, combinatorics
and number theory play a major role in computer science.
The Specialist and Major Programs in Mathematics and the Specialist
Program in Mathematics and Its Applications are eligible for inclusion
in the Co-operative Program in Physical Sciences and in the Concurrent
Teacher Education Program (CTEP). Please refer to the Physical Sciences
section, the Co operative Programs section and the Concurrent
Teacher Education section of this Calendar for
further information. The Supervisor of Studies for the Co-operative
programs is S. Chrysostomou (chrysostomou@utsc.utoronto.ca).
Science Engagement Courses
For science experiential learning through community outreach, classroom
in-reach and team research, please see the Science
Engagement section of this Calendar.
SPECIALIST PROGRAM IN MATHEMATICS (SCIENCE)
Supervisor of Studies: E. Moore (416-287-7267) Email:
emoore@utsc.utoronto.ca
The Specialist Program in Mathematics is designed to give students
a thorough grounding in the main areas of Mathematics, together with
an understanding of the close relationship between Mathematics and
other Sciences. It provides an excellent education for students who
may decide to pursue a career in research, or who wish to go on to
careers in non-mathematical fields.
Writing Requirement:
Students are required to take a course from the following list of
courses by the end of their second year.
ANTA01H3, ANTA02H3,
(CLAA02H3), ENGA10H3,
ENGA11H3, ENGB06H3,
ENGB07H3, ENGB08H3,
ENGB09H3, ENGB17H3,
ENGB19H3, ENGB50H3,
ENGB51H3, GGRA02H3,
GGRA03H3, GGRB05H3,
(GGRB06H3), (HISA01H3),
HLTA01H3, LINA01H3,
(HUMA11H3), (HUMA17H3),
( HUMA19H3), (LGGA99H3),
PHLA10H3, PHLA11H3,
WSTA01H3.
Program Requirements
- (3.0 full credits):
CSCA48H3 Introduction
to Computer Science
MATA23H3 Linear Algebra
I
MATA31H3 Calculus I for
Mathematical Sciences
MATA37H3 Calculus II for
Mathematical Sciences
PHYA10H3 Introduction to Physics
IA
PHYA21H3 Introduction to Physics
IIA
- (2.5 credits):
[CSCB07H3 Software
Design or CSCB36H3
Introduction to the Theory of Computation]
MATB24H3 Linear Algebra
II
MATB41H3 Techniques of the
Calculus of Several Variables I
MATB42H3 Techniques of the
Calculus of Several Variables II
MATB43H3 Introduction to
Analysis
- (1.5 credits):
MATB44H3 Differential Equations
I
STAB52H3 An Introduction
to Probability
STAB57H3 An Introduction
to Statistics
- (1.5 credits):
MATC01H3 Groups and Symmetry
MATD01H3 Fields and Groups
[MATC15H3 Introduction to
Number Theory or MATD02H3
Classical Plane Geometries and their Transformations]
- (1.0 credit):
MATC34H3 Complex Variables
MATC46H3 Differential Equations
II
- (1.0 credit): Two of:
MATB61H3 Linear Programming
and Optimization
MATC27H3 Introduction to
Topology
MATC35H3 Chaos, Fractals
and Dynamics
MATC37H3 (MATC38H3)
Introduction to Real Analysis
MATD10H3 Topics in Mathematics
MATD11H3 Topics in Mathematics
MATD12H3 Topics in Mathematics
MATD34H3 Complex Variables
II
- (0.5 credit): One of:
CSCC50H3 Numerical
Algebra and Optimization
CSCC51H3 Numerical
Approximation, Integration and Ordinary Differential Equations
MATC09H3 Introduction to
Mathematical Logic
MATC16H3 Coding Theory and
Cryptography
MATC32H3 Graph Theory and
Algorithms for its Applications
MATC44H3 Introduction to
Combinatorics
- 1.0 credit from MAT at B-, C-, or D-level.
- (0.5 credit):
[CSCD03H3 Social Impact
of Information Technology or PSCD02H3
Current Questions in Mathematics and Science]
MAJOR PROGRAM IN MATHEMATICS (SCIENCE)
Supervisor of Studies: N. Cheredeko (416-287-7226) Email:
n.cheredeko@utoronto.ca
Recommended Writing Course: Students are urged to take a course
from the following list of courses by the end of their second year.
ANTA01H3, ANTA02H3,
(CLAA02H3), ENGA10H3,
ENGA11H3, ENGB06H3,
ENGB07H3, ENGB08H3,
ENGB09H3, ENGB17H3,
ENGB19H3, ENGB50H3,
ENGB51H3, GGRA02H3,
GGRA03H3, GGRB05H3,
(GGRB06H3), (HISA01H3),
HLTA01H3, (HUMA11H3),
(HUMA17H3), (HUMA19H3),
(LGGA99H3), LINA01H3,
PHLA10H3, PHLA11H3,
WSTA01H3.
Program Requirements
This program requires eight full credits.
- Core Courses:
[CSCA48H3 Introduction
to Computer Science
or
PSCB57H3] Introduction
to Scientific Computing
MATA23H3 Linear Algebra
I
[MATA30H3 Calculus I for
Biological and Physical Sciences or MATA31H3
Calculus I for Mathematical Sciences] and
[MATA36H3 Calculus II for
Physical Sciences or MATA37H3
Calculus II for Mathematical Sciences.] The sequence MATA31H3
and MATA37H3 is recommended.
MATA31H3 is the pre-requisite
for MATA37H3.
MATB24H3 Linear Algebra
II
MATB41H3 Calculus of Several
Variables I
MATB42H3 Calculus of Several
Variables II
STAB52H3 Introduction to
Probability
[MATC01H3 Groups and Symmetry
or MATC15H3 Introduction
to Number Theory]
- Analysis: 1.5 credits from:
MATB43H3, MATB44H3,
MATC27H3, MATC46H3,
MATC35H3, MATC37H3,
MATC34H3, MATD34H3
- Algebra and Geometry: 1.0 credit from
MATB61H3, MATC01H3,
MATC09H3, MATC15H3,
MATC32H3, MATC44H3,
MATC63H3, MATD01H3,
MATD02H3
- Applications: 1.0 credit from
CSC C-level, CSC D-level, MATC16H3,
MATC32H3, MATC44H3,
MATC58H3, MATC82H3,
MATC90H3, MATD61H3,
STAB57H3, any STA C-level
or D-level course, any STA-300, STA-400 level course on the St.
George campus
SPECIALIST PROGRAM IN MATHEMATICS AND ITS APPLICATIONS (SCIENCE)
Supervisor of Studies: E. Moore (416-287-7267) Email:
emoore@utsc.utoronto.ca
The Specialist program in Mathematics and its Applications is recommended
to students with strong interests in mathematics and with career goals
in areas such as teaching, computer science, the physical sciences
and statistics. The program is flexible; there is a core of courses
in mathematics and related disciplines, but you can choose among several
areas of concentration.
Writing Requirement:
Students are required to take a course from the following list of
courses by the end of their second year. ANTA01H3,
ANTA02H3, (CLAA02H3),
ENGA10H3, ENGA11H3,
ENGB06H3, ENGB07H3,
ENGB08H3, ENGB09H3,
ENGB17H3, ENGB19H3,
ENGB50H3, ENGB51H3,
GGRA02H3, GGRA03H3,
GGRB05H3, (GGRB06H3),
(HISA01H3), HLTA01H3,
(HUMA11H3), (HUMA17H3),
(HUMA19H3), (LGGA99H3),
LINA01H3, PHLA10H3,
PHLA11H3, WSTA01H3.
Program Requirements
In selecting courses, students must ensure that they include 4.0 credits
at the C- or D-level of which 1.0 must be at the D-level.
Core for all program streams:
- (2.0 full credits):
[CSCA48H3 Introduction
to Computer Science or PSCB57H3
Introduction to Scientific Computing] (if PSCB57H3
is selected it should be taken in second year)*
MATA23H3 Linear Algebra
I
[MATA30H3 Calculus I for
Biological and Physical Sciences or MATA31H3
Calculus I for Mathematical Sciences] and
[MATA36H3 Calculus II for
Physical Sciences or MATA37H3
Calculus II for Mathematical Sciences.] The sequence MATA31H3
and MATA37H3 is recommended.
MATA31H3 is the pre-requisite
for MATA37H3.
- (2.5 credits):
MATB24H3 Linear Algebra
II
MATB41H3 Techniques of the
Calculus of Several Variables I
MATB42H3 Techniques of the
Calculus of Several Variables II
MATB43H3 Introduction to
Analysis
MATB44H3 Differential Equations
I
- (1.0 credit):
STAB52H3 An Introduction
to Probability**
STAB57H3 An Introduction
to Statistics**
- (0.5 credit):
MATC01H3 Groups and Symmetry
- (0.5 credit):
MATC34H3 Complex Variables
* PSCB57H3 is required
for the Computational Physical Sciences stream
** STAB52H3 and STAB57H3
must be taken in second year for the Statistics stream
AREAS OF CONCENTRATION:
Teaching Stream:
Students following this stream require a total of 13.0 credits.
- (2.0 full credits):
MATC15H3 Introduction to
Number Theory
MATD01H3 Fields and Groups
MATD02H3 Classical Plane
Geometries and their Transformations
[MATC32H3 Graph Theory and
Algorithms for its Applications or MATC44H3
Introduction to Combinatorics]
- (1.5 credit): Three of:
MATB61H3 Linear Programming
and Optimization
MATC09H3 Introduction to
Mathematical Logic
MATC16H3 Coding Theory and
Cryptography
MATC35H3 Chaos, Fractals
and Dynamics
MATC37H3 (MATC38H3)
Introduction to Real Analysis
MATC46H3 Differential Equations
II
MATC63H3 Differential Geometry
MATC90H3 Beginnings of Mathematics
MATD34H3 Complex Variables
II
- (2.0 full credits):
MATC82H3 Mathematics for
Teachers
Three C- or D-level CSC, MAT or STA half-credit courses
- (0.5 credit):
[PSCD02H3 Current
Questions in Mathematics and Science or CSCD03H3
Social Impact of Information Technology]
Statistics Stream:
Students following this stream require a total of 13.0 credits.
- (2.5 credits):
MATB61H3 Linear Programming
and Optimization
MATC46H3 Differential Equations
II
MATD01H3 Fields and Groups
MATD02H3 Classical Plane
Geometries and their Transformations
STAC67H3 Regression Analysis
- (1.0 credit): Two of:
MATC35H3 Chaos, Fractals
and Dynamics
MATC37H3 (MATC38H3)
Introduction to Real Analysis
MATC58H3 An Introduction
to Mathematical Biology
MATD34H3 Complex Analysis
II
- 2.0 credits from ACTB47H3, C-level &
D-level STA courses and 300- & 400-level STA courses on the
St. George campus.
- (0.5 credit):
[PSCD02H3 Current
Questions in Mathematics and Science or CSCD03H3
Social Impact of Information Technology]
Computational Physical Sciences Stream:
Students following this stream require a total of 14.0 credits.
- (5.0 full credits):
ASTA01H3 Introduction to Astronomy
and Astrophysics I: The Sun and Planets
ASTA02H3 Introduction to Astronomy
and Astrophysics II: Beyond the Sun and Planets
CSCC50H3 Numerical
Algebra and Optimization
CSCC51H3 Numerical
Approximation, Integration and Ordinary Differential Equations
MATB61H3 Linear Programming
and Optimization
MATC35H3 Chaos, Fractals
and Dynamics
MATC44H3 Introduction to
Combinatorics
MATC46H3 Differential Equations
II
PHYA10H3 Introduction to Physics
IA
PHYA21H3 Introduction to Physics
IIA
- (1.5 credits): Three of:
ASTB23H3 Astrophysics of Stars,
Galaxies and the Universe
ASTC25H3 Astrophysics of Planetary
Systems
PHYB54H3 Mechanics: From Oscillations
to Chaos
PHYB56H3 Introduction to Quantum
Physics
(PHYC24H3) Quantum Physics
I
- (0.5 credit): One of:
CSCD18H3 Computer Graphics
MATD34H3 Complex Variables
II
MATD94H3 Readings in Mathematics
MATD95H3 Readings in Mathematics
PSCD02H3 Current Questions
in Mathematics and Science
CSCD03H3 Social Impact
of Information Technology
Computer Science Stream:
See Joint Mathematics stream in the Computer Science Specialist Program.
Design Your Own Stream:
Students following this stream require a total of 13.0 credits.
- (6.0 full credits): 12 half-credit courses chosen with the approval
of the program supervisor for Mathematics and Its Applications.
- (0.5 credit): [PSCD02H3
Current Questions in Mathematics and Science or CSCD03H3
Social Impact of Information Technology]
SPECIALIST PROGRAM IN QUANTITATIVE ANALYSIS (SCIENCE)
See the Statistics
section of this Calendar for program requirements.
SPECIALIST PROGRAM IN NATURAL SCIENCES (SCIENCE)
See the Physical Sciences
section of this Calendar for program requirements.
MATA02H3
The Magic of Numbers
A selection from the following topics: the number sense (neuroscience
of numbers); numerical notation in different cultures; what is a number;
Zeno’s paradox; divisibility, the fascination of prime numbers;
prime numbers and encryption; perspective in art and geometry; Kepler
and platonic solids; golden mean, Fibonacci sequence; elementary probability.
Exclusion: (MATA20H3),
MATA23H3, MATA30H3,
MATA31H3, MATA32H3,
MAT102H, MAT123H, MAT125H, MAT133Y, MAT134Y, MAT135Y, MAT137Y, MAT157Y
Breadth Requirement: Quantitative Reasoning
MATA23H3
Linear Algebra I
Systems of linear equations, matrices, Gaussian elimination; basis,
dimension; dot products; geometry to Rn; linear transformations; determinants,
Cramer's rule; eigenvalues and eigenvectors, diagonalization.
Prerequisite: Grade 12 Calculus and Vectors or [Grade 12 Advanced
Functions and Introductory Calculus & Geometry and Discrete Mathematics]
Exclusion: MAT223H
Breadth Requirement: Quantitative Reasoning
MATA30H3
Calculus I for Biological and Physical Sciences
An introduction to the basic techniques of Calculus. Elementary functions:
rational, trigonometric, root, exponential and logarithmic functions
and their graphs. Basic calculus: limits, continuity, derivatives,
derivatives of higher order, analysis of graphs, use of derivatives;
integrals and their applications, techniques of integration.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3),
(MATA27H3), MATA31H3,
MATA32H3, MAT123H, MAT124H,
MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning
MATA31H3
Calculus I for Mathematical Sciences
A theoretical course in calculus emphasizing proofs and techniques,
as well as the intuition behind them. Axioms and basic properties
of real numbers. Functions, including transcendentals. Limits and
continuity. Least upper bounds, extreme and intermediate value theorems.
Derivatives and applications. Integrals and the fundamental theorem
of calculus.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3),
(MATA27H3), MATA30H3,
MATA32H3, MAT123H, MAT124H,
MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning
MATA32H3
Calculus for Management I
This is a calculus course with most examples and applications of an
economic nature. Topics to be covered: linear programming (geometric);
introduction to financial mathematics; continuous functions including
exponential and logarithmic functions with applications to finance;
differential calculus of one variable; marginal analysis; optimization
of single variable functions; techniques of integration.
Prerequisite: Grade 12 Calculus and Vectors
Exclusion: (MATA20H3),
(MATA27H3), MATA30H3,
MAT123H, MAT125H, MAT133Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y,JMB170Y
Breadth Requirement: Quantitative Reasoning
MATA33H3
Calculus for Management II
This course will introduce the students to multivariable calculus
and linear algebra. Topics will include: matrix algebra; multi-variable
functions; contour maps; partial and total differentiation; optimization
of multi-variable functions; optimization of constrained multi-variable
functions; Lagrange multipliers.
Prerequisite: MATA32H3
Exclusion: (MATA21H3),
(MATA27H3), MATA35H3,
MATA36H3, MATA37H3,
MAT124H, MAT126H, MAT133Y, MAT134Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y,
JMB170Y
Breadth Requirement: Quantitative Reasoning
MATA35H3
Calculus II for Biological Sciences
A calculus course emphasizing examples and applications in the biological
and environmental sciences. Discrete probability; basic statistics:
hypothesis testing, distribution analysis. Basic calculus: extrema,
growth rates, diffusion rates; differential equations; population
dynamics; vectors and matrices in 2 and 3 dimensions; genetics applications.
Note: This course will not satisfy the Mathematics requirements for
any Program in Computer and Mathematical Sciences, nor will it normally
serve as a prerequisite for further courses in Mathematics. Students
who are not sure which Calculus II course they should choose are encouraged
to consult with the supervisor(s) of Programs in their area(s) of
interest.
Prerequisite: MATA30H3 or
MATA31H3
Exclusion: (MATA21H3),
MATA33H3, MATA36H3,
MATA37H3, MAT123H, MAT124H,
MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y, (MATA27H3)
Breadth Requirement: Quantitative Reasoning
MATA36H3
Calculus II for Physical Sciences
This course is intended to prepare students for the physical sciences.
Topics to be covered include: Newton's method, approximation of functions
by Taylor polynomials, numerical methods of integration, complex numbers,
sequences, series, Taylor series, differential equations.
Prerequisite: MATA30H3 or
MATA31H3
Exclusion: (MATA21H3),
MATA33H3, MATA35H3,
MATA37H3, MAT123H, MAT124H,
MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning
MATA37H3
Calculus II for Mathematical Sciences
A continuation of MATA31H3,
emphasizing proofs and techniques, as well as the intuition behind
them. Transcendental functions revisited. Techniques and applications
of integration. Taylor polynomials and remainder term. Sequences and
series. Uniform convergence and power series.
Prerequisite: MATA31H3
Exclusion: (MATA21H3),
MATA33H3, MATA35H3,
MATA36H3, MAT123H, MAT124H,
MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Breadth Requirement: Quantitative Reasoning
MATB24H3
Linear Algebra II
Fields, vector spaces over a field, linear transformations; inner
product spaces, coordinatization and change of basis; diagonalizability,
orthogonal transformations, invariant subspaces, Cayley-Hamilton theorem;
hermitian inner product, normal, self-adjoint and unitary operations.
Some applications such as the method of least squares and introduction
to coding theory.
Prerequisite: MATA23H3 or
MAT223H
Exclusion: MAT224H
Breadth Requirement: Quantitative Reasoning
MATB41H3
Techniques of the Calculus of Several Variables I
Partial derivatives, gradient, tangent plane, Jacobian matrix and
chain rule, Taylor series; extremal problems, extremal problems with
constraints and Lagrange multipliers, multiple integrals, spherical
and cylindrical coordinates, law of transformation of variables.
Prerequisite: [MATA23H3 or
MAT223H] & [[MATA36H3
or MATA37H3] or MAT137Y or
MAT157Y]]
Exclusion: MAT232H, MAT235Y, MAT237Y, MAT257Y
Breadth Requirement: Quantitative Reasoning
MATB42H3
Techniques of the Calculus of Several Variables II
Fourier series. Vector fields in Rn, Divergence and curl, curves,
parametric representation of curves, path and line integrals, surfaces,
parametric representations of surfaces, surface integrals. Green's,
Gauss', and Stokes' theorems will also be covered. An introduction
to differential forms, total derivative.
Prerequisite: MATB41H3
Exclusion: MAT235Y, MAT237Y, MAT257Y, MAT368H
Breadth Requirement: Quantitative Reasoning
MATB43H3
Introduction to Analysis
Generalities of sets and functions, countability. Topology and analysis
on the real line: sequences, compactness, completeness, continuity,
uniform continuity. Topics from topology and analysis in metric and
Euclidean spaces. Sequences and series of functions, uniform convergence.
Prerequisite: [MATA37H3 or
MAT137Y] & MATB24H3
Corequisite: MATB42H3
Exclusion: MAT246Y
Breadth Requirement: Quantitative Reasoning
MATB44H3
Differential Equations I
Ordinary differential equations of the first and second order, existence
and uniqueness; solutions by series and integrals; linear systems
of first order; non-linear equations; difference equations.
Prerequisite: [MATA36H3 or
MATA37H3] & MATA23H3
Corequisite: MATB41H3
Exclusion: MAT244H, MAT267H
Breadth Requirement: Quantitative Reasoning
MATB61H3
Linear Programming and Optimization
Linear programming, simplex algorithm, duality theory, interior point
method; quadratic and convex optimization, stochastic programming;
applications to portfolio optimization and operations research.
Prerequisite: MATA23H3
Corequisite: MATB42H3
Exclusion: APM236H
Breadth Requirement: Quantitative Reasoning
MATC01H3
Groups and Symmetry
Congruences and fields. Permutations and permutation groups. Linear
groups. Abstract groups, homomorphisms, subgroups. Symmetry groups
of regular polygons and Platonic solids, wallpaper groups. Group actions,
class formula. Cosets, Lagrange's theorem. Normal subgroups, quotient
groups. Emphasis on examples and calculations.
Prerequisite: MATA37H3 &
[MATB24H3 or MAT224H]
Exclusion: MAT301H, MAT347Y
Breadth Requirement: Quantitative Reasoning
MATC09H3
Introduction to Mathematical Logic
Predicate calculus. Relationship between truth and provability; Gödel's
completeness theorem. First order arithmetic as an example of a first-order
system. Gödel's incompleteness theorem; outline of its proof. Introduction
to recursive functions.
Prerequisite: MATB24H3 &
[MATB43H3 or CSCB36H3]
Exclusion: MAT309H, CSC438H
Breadth Requirement: Quantitative Reasoning
MATC15H3
Introduction to Number Theory
Elementary topics in number theory; arithmetic functions; polynomials
over the residue classes modulo m, characters on the residue classes
modulo m; quadratic reciprocity law, representation of numbers as
sums of squares.
Prerequisite: [MATA36H3 or
MATA37H3] & MATB24H3
Exclusion: MAT315H
Breadth Requirement: Quantitative Reasoning
MATC16H3
Coding Theory and Cryptography
The main problems of coding theory and cryptography are defined. Classic
linear and non-linear codes. Error correcting and decoding properties.
Cryptanalysis of classical ciphers from substitution to DES and various
public key systems [e.g. RSA] and discrete logarithm based systems.
Needed mathematical results from number theory, finite fields, and
complexity theory are stated.
Prerequisite: MATB24H3 &
STAB52H3
Corequisite: MATC15H3 recommended
Breadth Requirement: Quantitative Reasoning
MATC27H3
Introduction to Topology
Fundamentals of set theory, topological spaces and continuous functions,
connectedness, compactness, countability, separatability, metric spaces
and normed spaces, function spaces, completeness, homotopy.
Prerequisite: MATB24H3 &
MATB43H3
Exclusion: MAT327H
Breadth Requirement: Quantitative Reasoning
MATC32H3
Graph Theory and Algorithms for its Applications
Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian
properties, matchings, vertex and edge colourings, planarity, network
flows and strongly regular graphs; applications to such problems as
timetabling, personnel assignment, tank form scheduling, traveling
salesmen, tournament scheduling, experimental design and finite geometries.
Prerequisite: [MATB24H3 or
CSCB36H3] & at least
one other B-level course in Mathematics or Computer Science
Breadth Requirement: Quantitative Reasoning
MATC34H3
Complex Variables
Theory of functions of one complex variable, analytic and meromorphic
functions. Cauchy's theorem, residue calculus, conformal mappings,
introduction to analytic continuation and harmonic functions.
Prerequisite: MATB42H3
Exclusion: MAT334H
Breadth Requirement: Quantitative Reasoning
MATC35H3
Chaos, Fractals and Dynamics
Topics covered include: metric spaces, dynamics on the real line,
fixed points, periodic points, attractors, repellers, Sharkovski's
theorem parametrized families of functions and bifurcations, period
doubling, dynamics of the logistic map, symbolic dynamics, chaos,
topological equivalence of the logistic map and the shift map, Newton's
method; dynamics on the complex line, iterations of rational functions,
Julia sets, Mandelbrot set.
Prerequisite: MATB43H3
Exclusion: MAT335H
Breadth Requirement: Quantitative Reasoning
MATC37H3
Introduction to Real Analysis
Topics in measure theory: the Lebesgue integral, Riemann-Stieltjes
integral, Lp spaces, Hilbert and Banach spaces, Fourier series.
Prerequisite: MATB43H3
Exclusion: MAT337H, (MATC38H3)
Breadth Requirement: Quantitative Reasoning
MATC44H3
Introduction to Combinatorics
Basic counting principles, generating functions, permutations with
restrictions. Fundamentals of graph theory with algorithms; applications
(including network flows). Combinatorial structures including block
designs and finite geometries.
Prerequisite: MATB24H3
Exclusion: MAT344H
Breadth Requirement: Quantitative Reasoning
MATC46H3
Differential Equations II
Sturm-Liouville problems, Green's functions, special functions (Bessel,
Legendre), partial differential equations of second order, separation
of variables, integral equations, Fourier transform, stationary phase
method.
Prerequisite: MATB44H3 &
MATB24H3
Corequisite: MATB42H3
Exclusion: APM346H
Breadth Requirement: Quantitative Reasoning
MATC58H3
An Introduction to Mathematical Biology
Mathematical analysis of problems associated with biology, including
models of population growth, cell biology, molecular evolution, infectious
diseases, and other biological and medical disciplines. A review of
mathematical topics: linear algebra (matrices, eigenvalues and eigenvectors),
properties of ordinary differential equations and difference equations.
Prerequisite: MATB44H3
Breadth Requirement: Quantitative Reasoning
MATC63H3
Differential Geometry
Curves and surfaces in Euclidean 3-space. Serret-Frenet frames and
the associated equations, the first and second fundamental forms and
their integrability conditions, intrinsic geometry and parallelism,
the Gauss-Bonnet theorem.
Prerequisite: MATB43H3
Exclusion: MAT363H
Breadth Requirement: Quantitative Reasoning
MATC82H3
Mathematics for Teachers
The course discusses the Mathematics curriculum (K-12) from the following
aspects: the strands of the curriculum and their place in the world
of Mathematics, the nature of proofs, the applications of Mathematics,
and its connection to other subjects.
Prerequisite: [MATA23H3 &
MATA37H3] or [MATA23H3
& MATA36H3 & [CSCA65H3
or MATB24H3]
Exclusion: MAT382H
Breadth Requirement: Quantitative Reasoning
MATC90H3
Beginnings of Mathematics
Mathematical problems which have arisen repeatedly in different cultures,
e.g. solution of quadratic equations, Pythagorean theorem; transmission
of mathematics between civilizations; high points of ancient mathematics,
e.g. study of incommensurability in Greece, Pell's equation in India.
Prerequisite: One Grade 12 Mathematics course & 5.0 full university
courses
Exclusion: MAT390H
Breadth Requirement: Quantitative Reasoning
MATD01H3
Fields and Groups
Abstract group theory: Sylow theorems, groups of small order, simple
groups, classification of finite abelian groups. Fields and Galois
theory: polynomials over a field, field extensions, constructibility;
Galois groups of polynomials, in particular cubics; insolvability
of quintics by radicals.
Prerequisite: MATC01H3
Exclusion: (MAT302H), MAT347Y, (MATC02H3)
Recommended Preparation: MATC34H3
Breadth Requirement: Quantitative Reasoning
MATD02H3
Classical Plane Geometries and their Transformations
An introduction to geometry with a selection of topics from the following:
symmetry and symmetry groups, finite geometries and applications,
non-Euclidean geometry.
Prerequisite: MATA23H3
Corequisite: MATC01H3
Exclusion: MAT402H, (MAT365H), (MATC25H3)
Breadth Requirement: Quantitative Reasoning
MATD10H3
MATD11H3
MATD12H3
Topics in Mathematics
A variety of topics from geometry, analysis, combinatorics, number
theory and algebra, to be chosen by the instructor.
Prerequisite: MATC01H3 &
[MATC35H3 or MATC37H3]
& [MATC15H3 or MATD02H3]
MATD34H3
Complex Variables II
Applications of complex analysis to geometry, physics and number theory.
Fractional linear transformations and the Lorentz group. Solution
to the Dirichlet problem by conformal mapping and the Poisson kernel.
The Riemann mapping theorem. The prime number theorem.
Prerequisite: MATC34H3
Exclusion: MAT354H, (MATC65H3)
Breadth Requirement: Quantitative Reasoning
MATD61H3
Introduction to Industrial Mathematics
Monte Carlo Method (mean time between failures, servicing requests),
Data Manipulation (z-transform, filters, Bode Plots), Discrete Fourier
Transform (real time processing , FFT, image processing), Regression
(best fit to discrete data, Hilbert Space, Gram's theorem), Frequency-Domain
Methods, Numerical Models for PDE, Galerkin's methods, Cubic Splines.
The course provides extensions of mathematics useful in industrial
problems, interweaving analytic and computing methods during problem
solving.
Prerequisite: MATB42H3 &
MATB44H3 & STAB52H3
Recommended Preparation: MATB61H3
& MATC46H3
Breadth Requirement: Quantitative Reasoning
MATD94H3
MATD95H3
Readings in Mathematics
Independent study under direction of a faculty member.
Prerequisite: MATC01H3 &
[MATC35H3 or MATC37H3]
& [MATC15H3 or MATD02H3