# Courses Offered

AM9000 – PhD Seminar Course |

This course features presentations by guest speakers and PhD students. All students are required to attend and actively participate in seminars every semester. Students will present one seminar on a topic relevant to their dissertation and one seminar on their dissertation, normally in their final year. Students will also participate on panels which will introduce and question the speakers. This course aims to improve the communication skills of students. To facilitate this goal, student presentations will be assessed by attending faculty and the student panel. Pass/Fail |

Electives |
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AM9AAA – Advanced topics in Discrete Mathematics |

A selection of topics from: algorithms and their complexity, random graph models such as binomial random graphs and random regular graphs; models of complex networks such as preferential attachment, ranking, geometric, and copying models; graph searching such as Cops and Robbers games, graph cleaning, and firefighting; designs, coverings, arrays, and their applications; homomorphisms and constraint satisfaction. 1 Credit. |

AM9BBB – Advanced Topics in Financial Mathematics |

A selection from the following topics in Financial Mathematics: Arbitrage pricing. Completness and Hedging. The Martingale Approach to Arbitrage. Incomplete Markets. Exotic Derivatives. Interest Rate Models. Stochastic calculus for general semi-martingales. Levy processes. Advanced portfolio risk management. Dynamic risk measures. Advanced Credit Risk Models. 1 Credit. |

AM9CCC – Advanced Topics in Biomathematics and Fluids |

A selection of topics from Mathematical Biology and Fluid Dynamics: Review of basic fluid dynamics; hydrodynamic stability theory; mathematical modeling of blood flow and thin-film flows; biochemical networks; probability models; stochastic simulation; Markov processes; chemical and biochemical kinetics; The fixed point index, nonlinear eigenvalue problems, bifurcation, nonlinear elliptic boundary value problems; population models. 1 Credit. |

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 |

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 |

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, 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 |