
Department of Mathematics, University of Toronto
STA 261 (UTM), Winter, 2012
Probability and Statistics II
The introduction to current statistical theory and methodology.
Topics include: estimation, testing, and confidence intervals; unbiasedness,
sufficiency, likelihood; simple linear and generalized linear models.
MAT 235, Fall 2011 /Winter 2012
Calculus Science II
One year multivariable calculus course: differential and integral calculus of functions of several variables,
line and surface integrals, the divergence theorem, Stokes theorem.
MAT 232 (UTM), Fall, 2011
Calculus of Several Variables
One term multivariable calculus course: partial differentiation,
chain rule, optimization problems, Lagrange multipliers, classification of critical points.
Introduction to multiple integrals.
MAT 235, Summer, 2011
Calculus Science II
One year multivariable calculus course: differential and integral calculus of functions of several variables,
line and surface integrals, the divergence theorem, Stokes theorem.
MAT 337, Winter, 20102011
Introduction to Real Analysis
Metric spaces; compactness and connectedness. Sequences and series of functions, power series;
modes of convergence. Interchange of limiting processes; differentiation of integrals.
Function spaces; Weierstrass approximation; Fourier series. Contraction mappings;
existence and uniqueness of solutions of ordinary differential equations.
Countability; Cantor set; Hausdorff dimension.
MAT 1508, Winter, 20102011
Techniques of Applied Math: Introductory Numerical Methods for Differential Equations
The course will focus on finite difference and spectral methods (Galerkin method, the tau method,
the collocation method) for ordinary and partial differential equations (parabolic, hyperbolic and elliptic)
with partial emphasis on theoretical aspects, such as error and stability analysis.
APM 384, Fall, 20102011
Partial Differential Equations
Boundary value problems and SturmLiouville theory for ordinary differential equations.
Partial differential equations of first order, characteristics, HamiltonJacobi theory.
Diffusion equations; Laplace transform methods. Harmonic functions, Green’s functions for
Laplace’s equation, surface and volume distributions; Fourier transforms. Wave equation,
characteristics; Green’s functions for the wave equation; Huygens principle.
MAT 234, Winter, 20092010
Differential Equations
Ordinary differential equations. Linear and nonlinear equations of first and second orders.
Bessel’s equation. Legendre’s equation. Series solutions. Partial differential equations.
The diffusion equation. Laplace’s equation. The wave equation. Solution by separation of variables.
APM 346, Fall, 20092010
Applied Partial Differential Equations
Partial differential equations of second order, separation of variables, integral equations,
Fourier transform, SturmLiouville problems, Green’s functions.
MAT 234, Winter, 20082009
Differential Equations
Ordinary differential equations. Linear and nonlinear equations of first and second orders.
Bessel’s equation. Legendre’s equation. Series solutions. Partial differential equations.
The diffusion equation. Laplace’s equation. The wave equation. Solution by separation of variables.
APM 346, Fall, 20082009
Applied Partial Differential Equations
Partial differential equations of second order, separation of variables, integral equations,
Fourier transform, SturmLiouville problems, Green’s functions.
Department of Mathematics and Statistics, McMaster University
Mathematics 2M03, Fall, 20072008
Engineering Mathematics II
Ordinary differential equations, Laplace transforms, Fourier series, with engineering applications.
Mathematics 2T03, Winter, 20062007
Numerical Linear Algebra
Introduction to MatLab; matrix and vector norms; sensitivity, conditioning, convergence and complexity; direct and iterative methods for linear systems; eigenvalues and eigenvectors; least squares.
Mathematics 3DC3, Fall, 20062007
Discrete Dynamical Systems and Chaos
Iteration of functions: orbits, graphical analysis, fixed and periodic points, stability, bifurcations, chaos, fractals.
Mathematics 3D03, Winter, 20052006
Mathematical Physics II
Methods of mathematical physics, with emphasis on integral calculus in functions of complex variables, probability and statistics, and variational problems.
Mathematics 3C03, Fall, 2004 2005
Mathematical Physics I
Methods of mathematical physics, with emphasis on linear systems of algebraic, differential, and partial differential equations.
Mathematics 2C03, Summer 2004
Differential Equations
Ordinary differential equations, Laplace transforms, series solutions, partial differential equations, separation of variables, Fourier series.
Statistics 2D03, Spring 2004
Probability Theory
Combinatorics, independence, conditioning; Poissonprocess; discrete and continuous distributions with statistical applications; expectation, transformations, order statistics. Distribution of sample mean and variance, momentgenerating functions, central limit theorem.
Statistics 3Y03, Winter 2004
Statistical Analysis for Engineering Introduction to probability, univariate and multivariate random
variables and their distributions, statistical estimation and nference,
regression and correlation, decision making, applications.
Academy for Mathematics & Science
TUTORING K12 MATHEMATICS AND SCIENCE
 Preparation to Pascal Contest for Grade 9 Mathematics
 Principles of Mathematics, Grade 9, Academic (MPM1D)
 Science, Grade 9, Academic (SNC1D)
 Principles of Mathematics, Grade 10, Academic (MPM2D)

Science, Grade 10, Academic (SNC2D)

Functions and Relations, Grade 11, University Preparation (MCR3U)

Functions, Grade 11, University/College Preparation (MCF3M)

Mathematics of Personal Finance, Grade 11, College Preparation (MBF3C)

Advanced Functions and Introductory Calculus, Grade 12, University Preparation (MCB4U)

Geometry and Discrete Mathematics, Grade 12, University Preparation (MGA4U)

Mathematics of Data Management, Grade 12, University Preparation (MDM4U)

