The main goal of this course is to present the first part of some fundamental notions and results of modern mathematical analysis, necessary for applied analysis. This course is necessary for anyone who intends to follow advanced courses in fields such as Optimization, Game Theory, Dynamical Systems, Partial Differential Equations, Integral Equations, etc. The content of this course forms a good background for many courses in Masters and PhD programs. The topics presented include:  necessary notions related to real numbers, topological spaces, metric spaces, Lebesgue integral, and convex analysis.

The main goal of this course is to present the second part of some fundamental notions and results of modern mathematical analysis, necessary for applied analysis. Part I of this course is a prerequisite. This course is necessary for anyone who intends to follow advanced courses in fields such as Optimization, Game Theory, Dynamical Systems, Partial Differential Equations, Integral Equations, etc. The content of this course forms a good background for many courses in Masters and PhD programs. The material presented is as follows: Banach and Hilbert Spaces, Linear operators between Hilbert Spaces, Fixed Point theorems, and Variational Inequalities.

Solutions of partial differential equations using implicit difference methods for parabolic, elliptic and hyperbolic equations, and methods for gradient boundary conditions; introduction to finite element methods; root finding and optimisation; modern simulation techniques including Monte Carlo, pseudo-random number generation, and simplex applications; other advanced topics as appropriate.

Integral representation of functions. Green's functions in one and higher dimensions. Solutions of integral equations. Additional topics in mathematical physics as time permits. Software packages for symbolic and numerical computation will be used wherever possible.

Geometry is the basis for our present understanding of nature's fundamental laws at all scales from the very large (the whole Universe) to the very small (elementary particles). The goal of this course is to serve as an introduction to this unifying tool. The topics covered include: Review of the lagrangian formalism. Differentiable manifolds. Global and local groups of transformations and examples of their tensor representations. Fiber bundles. Connexions and curvatures. Metrics and metric connexions. Construction of lagrangians. Geodesics. Applications will correspond to the students' interest in topics in General Relativity (e.g. black holes and cosmic strings) and models of fundamental particles. Examples and exercises will be given where the use of Maple's differential geometry tools is required.

The purpose of this course is to offer the possibility of doing an in-depth study of a scientific topic in which the student is particularly interested. The format is flexible and depends on the topic area. At one end of the spectrum, the student could be associated with a research group in  Mathematics and be given responsibility for part of a research project. At the other end, the student may choose a programme of independent study under the supervision of a member of the faculty. In all cases, the student's progress would be regularly monitored and an interim report would be submitted by the student at the end of the Fall term. The final mark would be based on a combination of assessment by the faculty supervisor(s) and an oral presentation to the Honours Science students and a faculty assessment committee.

Rings, polynomial rings, homomorphisms. Euclidean and principal ideal domains. Unique factorization domains. Fields, extensions of fields, finite fields and applications.

The objective of this course is to allow members of the department to share their expertise with students in areas of mathematics not covered in other courses. Students will present seminars and written reports, as appropriate.

Conditional distributions; probability generating functions; Poisson processes; the role of exponential and Poisson distributions in applications. Introduction to stochastic processes; birth-and-death processes; renewal processes. Markov chains and their properties. Use of computer software programs to solve problems in various stochastic processes.

This course involves a study of the principles of mathematical modelling. Continuous models based on ordinary differential equations, systems of ordinary differential equations, partial differential equations and integral equations. Models based on optimization and variational calculus. Each model type will be illustrated by concrete examples and numerical methods appropriate to these equations will be investigated. The latter part of the course will be dedicated to a qualitative study of mathematical models. Mathematical models for military problems will be considered.

Concurrency and recovery. Decision support . Object databases. Distributed databases and client-server architecture. Active databases and temporal databases. Deductive databases. Data warehousing and data mining. Study of applications such as GIS, genome database, bioinformatics, digital library and multimedia databases.

The purpose of this course is to offer the possibility of doing an in-depth study of a scientific topic in which the student is particularly interested. The format is flexible and depends on the topic area. At one end of the spectrum, the student could be associated with a research group in Computer Science and be given responsibility for part of a research project. At the other end, the student may choose a programme of independent study under the supervision of a member of the faculty. In all cases, the student's progress would be regularly monitored and an interim report would be submitted by the student at the end of the Fall term. The final mark would be based on a combination of assessment by the faculty supervisor(s) and an oral presentation to the Honours Science students and a faculty assessment committee.

Laboratory exercises designed to introduce the students to the basic concepts of multiprocessing, multithreading, interprocess communication, distributed programming, parallel computing, socket connection, client/server model, networking, UDP and TCP protocols, routing information protocols, web security, fundamentals of cryptography, firewalls.

The objective of this course is to allow members of the department to share their expertise with students in areas of computer science not covered in other courses. Students may be expected to work on software projects, and will present seminars and written reports as appropriate.

After the course, students will be able to solve problems using computer simulations. More specifically, students will be able to describe the procedures involved in modeling and simulation; they will know how to structure and then verify models for complex systems, how to conduct designs of experiment on models, i.e., simulation, and how to measure and evaluate these experiments (simulation analysis). Advanced applications will be shown and students will be able to solve problems by using various skills of modeling and simulation. Finally, they will be able to apply their knowledge of modeling and simulation to solve defence related applications.

This course gives a comprehensive introduction to the foundations of Artificial Intelligence (AI). It starts with an introduction to intelligent agents. Secondly, it reviews the methods of solving problems by searching and game playing. Then, it explores knowledge, knowledge representations and reasoning with the help of propositional and first order logics. Furthermore, AI programming languages such as Prolog/Clips/JESS and their usages in building expert systems are studied. Afterwards, knowledge and reasoning with uncertainty are discussed. It also explains some concepts of machine learning from the aspects of statistics and mathematics. In addition, computer vision,dealing with sound, and robotics are introduced. Finally, it highlights major applications of AI for military defence.

Genetic information processing. Natural mechanisms of optimization of species. Molecular computers. Algorithm of artificial genetics. Neural networks. Elements of functioning of natural networks and of learning. Artificial networks: the most important models, including the perceptron, the adaline, the associative memories, error back-propagation, Kohonen's SOM, the radial basis functions networks, and many of their practical applications.