Professional Degree courses in Dentistry, Education, Law, Medicine and Theology (MTS, MDiv)
Courses offered by Continuing Studies
Graduate Studies courses
* These courses are equivalent to pre-university introductory courses and may be counted for credit in the student's record, unless these courses were taken in a preliminary year. They may not be counted toward essay or breadth requirements, or used to meet modular admission requirements unless it is explicitly stated in the Senate-approved outline of the module.
1.0 course not designated as an essay course
0.5 course offered in first term
0.5 course offered in second term
0.5 course offered in first and/or second term
1.0 essay course
0.5 essay course offered in first term
0.5 essay course offered in second term
0.5 essay course offered in first and/or second term
1.0 accelerated course (8 weeks)
1.0 accelerated course (6 weeks)
0.5 graduate course offered in summer term (May - August)
0.25 course offered within a regular session
0.25 course offered in other than a regular session
1.0 accelerated course (full course offered in one term)
0.5 course offered in other than a regular session
0.5 essay course offered in other than a regular session
A course that must be successfully completed prior to registration for credit in the desired course.
A course that must be taken concurrently with (or prior to registration in) the desired course.
Courses that overlap sufficiently in course content that both cannot be taken for credit.
Many courses at Western have a significant writing component. To recognize student achievement, a number of such courses have been designated as essay courses and will be identified on the student's record (E essay full course; F/G/Z essay half-course).
A first year course that is listed by a department offering a module as a requirement for admission to the module. For admission to an Honours Specialization module or Double Major modules in an Honours Bachelor degree, at least 3.0 courses will be considered principal courses.
Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predator-prey dynamics, age-structured populations.
Introduction to first order differential equations, linear second and higher order differential equations with applications, complex numbers including Euler's formula, series solutions, Bessel and Legendre equations, existence and uniqueness, introduction to systems of linear differential equations.
Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.
Introduction to numerical analysis; polynomial interpolation, numerical integration, matrix computations, linear systems, nonlinear equations and optimization, the initial value problem. Assignments using a computer and the software package, Matlab, are an important component of this course.
An introduction to mathematical biology. Case studies from neuroscience,immunology, medical imaging, cell biology, molecular evolution and ecology will give an overview of this diverse field, illustrating standard mathematical approaches such as compartmental analysis and evolutionary game theory.
Functions of a complex variable, analytic functions, integration in the complex plane, Taylor and Laurent series, analytic continuation, Cauchy's theorem, evaluation of integrals using residue theory, applications to Laplace transforms, conformal mapping and its applications.
Existence and uniqueness of solutions, phase space, singular points, stability, periodic attractors, Poincaré-Bendixson theorem, examples from physics, biology and engineering, frequency (phase) locking, parametric resonance, Floquet theory, stability of periodic solutions, strange attractors and chaos, Lyapunov exponents, chaos in nature, fractals.
Boundary value problems for Laplace, heat, and wave equations; derivation of equations; separation of variables; Fourier series; Sturm-Liouville Theory; eigenfunction expansions; cylindrical and spherical problems; Legendre and Bessel functions; spherical harmonics; Fourier and Laplace transforms.
An introduction to neural networks, covering the fundamentals of neural computation and how networks of neurons support information processing in the brain. Coursework will introduce techniques in computational modeling, programming and data science, focusing on recent developments in deep learning as applied to the context of explaining the brain.
Strengths and limitations of computer algebra systems (CAS); complexity of exact computations versus possible instability of numerical computations; selecta from Groebner bases, resultants, fractional derivatives, Risch integration algorithm, special functions including the Lambert W function. The emphasis is on preparing the student to use CAS in mathematics, science, and engineering.
Boundary value problems for Laplace and Helmholtz equations, initial value problems for heat and wave equations, in one to three dimensions; Green's functions in bounded and unbounded domains; Method of Images.
The student will work on a project under faculty supervision. The project may involve an extension, or more detailed coverage, of material presented in other courses. Credit for the course will involve a written as well as oral presentation.
Prerequisite(s): Registration in the fourth year of a program in Applied Mathematics.