# Courses Offered

AM8000 – Master's Seminar |

The course consists of regular research seminars in the general area of applied mathematics, given by graduate students, faculty members, visiting scholars, and guest speakers. In order to pass this course, each student is normally expected to attend seminars during each term in the program, for a maximum of four terms, and to give one presentation. Pass/Fail. |

Group A: Foundation Courses |
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AM8001 – Analysis and Probability |

Topics to be covered will be taken from the following list: metric spaces, Banach and Hilbert Spaces, measure spaces, integration, functional spaces and operators, random variables and conditional expectation; modes of convergence, discrete time martingales and filtrations; Brownian motion, continuous time stochastic processes and martingales; stochastic calculus. 1 Credit |

AM8002 – Discrete Mathematics and its Applications |

Selected topics from discrete mathematics: graph isomorphisms and homomorphisms; Ramsey theory, random graphs; infinite graphs; automorphism groups; graph searching games (such as Cops and Robbers); Steiner triple systems; graph decompositions; Latin squares; finite fields; polynomial rings; finite projective and affine planes.1 Credit |

Group B: Core Courses |

AM8101 – Principles and Techniques in Applied Mathematics |

Asymptotic Expansions; Perturbation Methods; Eigenfunction Expansions; Integral Transforms; Discrete Fourier Transforms. 1 Credit |

AM8102 – Advanced Numerical Analysis |

Numerical methods; numerical linear algebra; numerical methods for ODEs; numerical methods for PDEs. 1 Credit |

Group C: Elective Courses |

AM8201 – Financial Mathematics |

This course covers the fundamentals of mathematical methods in finance. After providing a background in Stochastic Calculus, it considers the study of financial derivatives. Fixed income instruments, derivative pricing in discrete and continuous time, including Black-Scholes formulation, American and Exotic options are considered. Elements of Portfolio Management and Capital Asset Pricing Model are also taken into account. 1 Credit |

AM8204 – Topics in Discrete Mathematics |

Selected advanced topics from discrete mathematics: random graphs; models of complex networks; homomorphisms and constraint satisfaction; adjacency properties; Ramsey theory; graph searching games; Latin squares; designs, coverings, arrays, and their applications. 1 Credit |

AM8205 – Applied Statistical Methods |

This course covers a wide variety of statistical methods with application in medicine, engineering, and economics. Exploratory data analysis. Parametric probability distributions. Sampling and experimental designs. Estimation, confidence intervals and tests of hypothesis. Analysis of variance. Multiple regression analysis, tests for normality. Nonparametric statistics. Statistical analysis of time series; ARMA and GARCH processes. Practical techniques for the analysis of multivariate data; principal components, factor analysis. 1 Credit |

AM8206 – Partial Differential Equations |

Topics to be covered will be taken from the following list: Derivation of equations from conservation laws; First-order Equations and the Method of Characteristics; Weak Solutions; Hyperbolic Systems; Diffusion and Reaction-Diffusion Equations; Traveling Wave Solutions; Elliptic Equations. 1 Credit |

AM8207 – Topics in Biomathematics |

Discrete and continuous time processes applied to biology and chemistry. Deterministic and stochastic descriptions for birth/death processes in chemical kinetics. Numerical methods for spatially distributed systems including multi-species reaction-diffusion equations. Applications will include some or all of: chemical waves, traveling wave fronts in excitable media, spiral waves, pattern formation, blood flow and flow in chemical reactors. 1 Credit |

AM8208 – Topics in Mathematics |

The topics in this course will vary each time it is offered as it will depend on the professor teaching it and the topics that interest the students. 1 Credit |

AM8209 – Directed Studies in Math |

This course is for students who wish to gain knowledge in a specific area for which no graduate level classes are available. Students who are approved to take the course are assigned a suitable class advisor most familiar with the proposed content. Students are required to present the work of one term (not less than 90 hours in the form of directed research, tutorials and individual study) in an organized format. 1 Credit |

AM8210 – Mathematical Biology |

Linear and nonlinear differential equations, Routh-Hurwitz criteria, local stability, phase-plane analysis, bifurcations and global stability. Applications including some of predator-prey models, epidemic models, competition models and spruce budworm models. New journal research papers related to these models. 1 Credit |

AM82111 - Operations Research |

Nonlinear Programming, Decision Making, Inventory Models, Markov Chains, Queuing Theory, Dynamic Programming, Simulation. Antirequisite: MTH603 1 Credit |

AM8212 - Introduction to Fluid Dynamics |

We derive equations governing fluid flows from the basic physical conservation laws. Exact analytic solutions to various elementary flow problems are obtained. We consider viscous flow, irrotational flow, boundary layers and water waves. Flow instability will also be examined. Mathematical results are related to phenomena observed in aerodynamics, flow through conduits and geophysical flows. Antirequisite: MTH732 1 Credit |

AM8213 - Financial Mathematics II |

The course covers fixed income derivatives and the quantitative aspects of risk and portfolio management in modern finance. It introduces single factor interest rate models and pricing and covers analysis of risk measures and their properties, market, credit risk and an overview of other types of risks. The course also develops portfolio optimization techniques. Case studies and preparation for financial certification programs (FRM and PRM) are also included. Antirequisite: MTH800 1 Credit |

AM8214 - Computational Complexity |

Order of Growth notation, time and space complexities of DTMs and NDTMs, intractability, basic complexity classes, P=NP?, reducibility and completeness, NP-completeness, Cook's theorem, hierarchy results, circuit complexity, probabilistic algorithms, models for parallel computation. Anti requisite: MTH814 1 Credit |

AM8215 - Stochastic Processes |

This course provides a brief and broad introduction to various important stochastic processes that lie at the heart of stochastic analysis and modelling. Topics to be covered include Bernoulli processes, random walks, Poisson processes, Markov processes, Martingales, Brownian motions. 1 credit |

Note: Students will also be able to use other "approved graduate courses" offered at Ryerson as electives and would require the approval from the Graduate Program Director.