Institute of Mathematical Sciences, Claremont Graduate University
MATH 251, Fall, 2013
Applied Probability
One term course covers the main elements of probability theory at an intermediate level. Topics include: combinatorial analysis, conditional probabilities, discrete and continuous random variables, probability distributions, central limit theorem, utility functions, Markov Chains and numerous applications.
MATH 368, Fall, 2013
Advanced Numerical Analysis
One term course of numerical linear algebra including LU decomposition, Jacobi, Gauss-Seidel and SOR iterations, Krylov subspace methods (Conjugate Gradient, GMRES), QR and SVD factorization of matrices, eigenvalue problems via power, inverse, QR and Arnoldi iterations, error analysis, forward and backward stability; numerical integration of ODEs including Runge-Kutta and Adams formulas, predictor-corrector methods, stiff equation solvers and shooting method for BVPs; other numerical methods including interpolation via Lagrange and Chebyshev polynomials and cubic splines, integration and quadrature with trapezoidal and Simpson rules, Newton-Cotes formulae, Gaussian quadrature, and singular integrals, root-finding via one-point iteration, bisection, Newton and secant methods, numerical differentiation using finite differences, spectral and pseudo-spectral methods.
MATH 362, Spring, 2013
Numerical Methods for Partial Differential Equations
Finite difference and finite element methods for elliptic, parabolic and hyperbolic partial differential equations. Free and moving boundary problems. Error and stability analysis of algorithms.
MATH 388, Spring, 2013
Continuous Mathematical Modeling
A course aimed at the construction, simplification, analysis, interpretation and evaluation of mathematical models that shed light on problems arising in the physical and social sciences. Derivation and methods for solution of model equations, heat conduction problems, simple random walk processes, simplification of model equations, dimensional analysis and scaling, perturbation theory, and a discussion of self-contained modular units that illustrate the principle modeling ideas. Students will normally be expected to develop a modeling project as part of the course requirements.
MATH 251, Fall, 2012
Applied Probability
One term course covers the main elements of probability theory at an intermediate level. Topics include: combinatorial analysis, conditional probabilities, discrete and continuous random variables, probability distributions, central limit theorem, utility functions, Markov Chains and numerous applications.
MATH 368, Fall, 2012
Advanced Numerical Analysis
One term course of numerical linear algebra including LU decomposition, Jacobi, Gauss-Seidel and SOR iterations, Krylov subspace methods (Conjugate Gradient, GMRES), QR and SVD factorization of matrices, eigenvalue problems via power, inverse, QR and Arnoldi iterations, error analysis, forward and backward stability; numerical integration of ODEs including Runge-Kutta and Adams formulas, predictor-corrector methods, stiff equation solvers and shooting method for BVPs; other numerical methods including interpolation via Lagrange and Chebyshev polynomials and cubic splines, integration and quadrature with trapezoidal and Simpson rules, Newton-Cotes formulae, Gaussian quadrature, and singular integrals, root-finding via one-point iteration, bisection, Newton and secant methods, numerical differentiation using finite differences, spectral and pseudo-spectral methods.
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, 2010-2011
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, 2010-2011
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, 2010-2011
Partial Differential Equations
Boundary value problems and Sturm-Liouville theory for ordinary differential equations. Partial differential equations of first order, characteristics, Hamilton-Jacobi 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, 2009-2010
Differential Equations
Ordinary differential equations. Linear and non-linear 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, 2009-2010
Applied Partial Differential Equations
Partial differential equations of second order, separation of variables, integral equations, Fourier transform, Sturm-Liouville problems, Green’s functions.
MAT 234, Winter, 2008-2009
Differential Equations
Ordinary differential equations. Linear and non-linear 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, 2008-2009
Applied Partial Differential Equations
Partial differential equations of second order, separation of variables, integral equations, Fourier transform, Sturm-Liouville problems, Green’s functions.
Department of Mathematics and Statistics, McMaster University
Mathematics 2M03, Fall, 2007-2008
Engineering Mathematics II
Ordinary differential equations, Laplace transforms, Fourier series, with engineering applications.
Mathematics 2T03, Winter, 2006-2007
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, 2006-2007
Discrete Dynamical Systems and Chaos
Iteration of functions: orbits, graphical analysis, fixed and periodic points, stability, bifurcations, chaos, fractals.
Mathematics 3D03, Winter, 2005-2006
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; Poisson-process; discrete and continuous distributions with statistical applications; expectation, transformations, order statistics. Distribution of sample mean and variance, moment-generating 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 K-12 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)