## Course Requirements

All courses listed here are one-term courses (i.e. half courses). Not all courses listed are available every year. Degree requirements vary for the different degree options.

For the **Thesis** stream, students are normally required to take AMOD 5210H, 5310H, 5320H, and one of 5220H, 5230H or 5240H, in addition to the two seminar courses AMOD 5901H and 5902H.

The course-based option for** Financial Analytics** requires two courses from the following: Foundations of Modelling, Statistical Aspects of Modelling, Mathematical Aspects of Modelling, Computational Aspects of Modelling, four courses from the following: Mathematical Finance, Portfolio Theory and Risk Management, Financial Econometrics, Linear Programming, Numerical Methods, Financial Management; a seminar presentation and completion of a research paper.

The course-based option for **Big Data Analytics** requires three courses from the following selection: Foundations of Modelling, Statistical Aspects of Modelling, Mathematical Aspects of Modelling, Computational Aspects of Modelling, Introduction to Data Analytics with R; four courses from the following selection: Data Visualization, High Performance Computing, Data Mining, Introduction to Databases, Big Data; a seminar presentation and completion of a research paper.

## Recommended Schedule - 2017/2018

**Thesis **

For Fall 2017, thesis students are required to register in the following course:

AMOD 5210H: Foundations of Modelling

Option to register in the following courses:

AMOD 5240H: Statistical Aspects of Modelling

AMOD 5310H: Reading Course 1

For Winter 2017, thesis students are required to register for:

AMOD 5901H: First Seminar on Applications of Modelling

Option to Register in the following courses:

AMOD 5220H: Mathematical Aspects of Modelling

AMOD 5310H: Reading Course 1

AMOD 5320H: Reading Course 2

**Financial Analytics**

For Fall 2017, Financial Analytics students are required to register in one of the following courses:

AMOD 5210H: Foundations of Modelling

AMOD 5240H: Statistical Aspects of Modelling

Must also choose two of the following courses:

AMOD 5310H: Numerical Methods

AMOD 5320H: Financial Econometrics

AMOD 5530H: Portfolio Theory and Risk Management

For Winter 2018, Financial Analytics students are required to register in the following two courses:

AMOD 5220H: Mathematical Aspects of Modelling

AMOD 5520H: Mathematical Finance

Must also choose one of the following courses:

AMOD 5510H: Linear Programming

AMOD 5310H: Financial Management

**Big Data Analytics**

For Fall 2017, Big Data Analytics students are required to register in the following three courses:

AMOD 5210H: Foundations of Modelling

AMOD 5240H: Statistical Aspects of Modelling

AMOD 5440H: Data Mining

For Winter 2018, Big Data Analytics students are required to register in the following two courses;

AMOD 5410H: Big Data

AMOD 5430H: Data Visualization

Option to register in the following course:

AMOD 5220H: Mathematical Aspects of Modelling

## Course Descriptions

**AMOD 5210H:
The Foundations of Modelling**

This course will introduce modelling process and basic types of models adopted in natural and social
sciences. Models from a range of disciplines will be discussed. Prerequisite: one university course in
either of calculus or statistics.

**AMOD 5220H: Mathematical Aspects of Modelling**

Mathematical approaches to modelling are illustrated, with the emphasis on the methods rather
than on the mathematical details. The topics include analytical modelling and computer simulation
of dynamic processes, decision making, forecasting, probabilistic analysis, based on case studies
from biology, geography, physics, economics, and social sciences.

**AMOD 5230H: Computational Aspects of Modelling **

This course will introduce fundamental principles and concepts in the general area of system
modelling and simulation. Topics to be covered include the basics of discrete-event system
simulation, mathematical and statistical models, simulation design, experiment design, and
analysis of simulation output.

**AMOD 5240H: Statistical Aspects of Modelling**

Various statistical approaches to modelling are illustrated, with an emphasis on the applications of
statistics within the social and natural sciences. The course discusses both univariate and multivariate procedures, with particular attention to the latter (e.g., multiple regression, multi-analysis of
variance, exploratory factor analysis, confirmatory factor analysis, and path analysis).

**AMOD 5250H: Data Analytics with R**

This course will introduce the student to the statistical programming language R. A wide range of topics will be covered, from data frames and functions to regression and statistical analysis. Emphasis is on visualization and statistical modelling to provide relevant applications for students to graduate research.

**AMOD 5310H, 5320H: Reading Course**

Discipline-specific courses in your home department. These may be given by the research supervisor in
a reading/project course format.

**AMOD 5410H: Big Data**

Big Data applications are pervading more and more aspects of our life, encompassing commercial and scientific uses at increasing rates as we move towards exascale analytics. Examples of Big Data applications include storing and accessing user data in commercial clouds, mining of social data, and analysis of large-scale simulations and experiments such as the Large Hadron Collider. In this course, students from a variety of disciplines will be introduced to the challenges and opportunities in this field, with the goal of providing them with theoretical and hands-on experience in the area of Big Data Analytics.

**AMOD 5420H: High Performance Computing**

High Performance Computing is the use of advanced computer architectures to solve problems which require significant processing power, memory access, or storage. Core topics include advanced computer architectures, programming for shared and distributed memory machines, networking issues, caching, performance evaluation and parallel algorithms. Topics are supplemented with algorithms.

**AMOD 5430H: Data Visualization**

Data visualization is the main step in the analysis of data in a wide range of scientific research areas as well as business applications. We will discuss general approaches and tools, and techniques for the visualization of various types of data, including spatial data, graph data, and time series data.

**AMOD 5440H: Data Mining**

An introduction to the principles of data mining. Topics to be covered include an overview of existing work in data mining with a special focus on applications in astronomy, sampling mechanisms, the statistical foundations of data mining, the problem of missing data, and outlier detection. We will discuss classification techniques such as Support Vector Machines, Neural Networks, and Decision Trees, as well as clustering techniques including k-means, self-organizing maps, and the Expectation Maximization algorithm. Furthermore, the course includes a practical component using open source software.

**Introduction to Databases**

This course introduces database systems and their use in the management of large quantities of data. The objectives are to gain an understanding of the information modelling and representation, the essential concepts, principles, techniques, and mechanisms for the design, analysis, use, and implementation of computerized database systems, and to gain experience in implementing and accessing relational databases using MySQL. At the end of this course, students will be able to understand and apply the fundamental concepts required for the design, use and optimization of database management systems.

**AMOD 5510H: Linear Programming**

Introduction to the concepts, techniques and applications of linear programming and discrete optimization. Topics include the simplex method, duality, game theory and integer programming.

**AMOD 5520H: Mathematical Finance**

This course covers the basic mathematical theory and computational techniques used to price a variety of stock and interest rate options using both discrete-time models, such as binomial probability trees, and continuous time models, such as the Black-Scholes model. Elementary concepts from stochastic calculus will be introduced. Computational techniques will be emphasized with implementation of models in Maple and Excel.

**AMOD 5530H: Portfolio and Risk Management**

Basic mathematical theory and computational techniques for how financial institutions can quantify and manage risks in portfolios of assets. Topics include: mean-variance portfolio analysis, the capital asset pricing model and Value at Risk (VaR).

**Financial Econometrics**

This course will integrate economic and financial market theory, applied mathematics, and probability and statistics to study econometric methods that are designed to deal with the unique features and characteristics of financial market data. Topics will include multiple regression, time-series analysis, time-varying volatility models, switching models, and limited dependent variable models.

**Numerical Methods**

This course covers commonly used numerical techniques for solving differential equations including adaptive, multi-step and finite difference methods. Numerical stability, convergence and the issue of solution consistency would also be covered. Computational implementation will be emphasized with Matlab/Octave.

**AMOD 5901H: First Seminar on Applications of Modelling**

Each student makes one presentation per year on his/her research, with emphasis on the
assumptions, methodology and analysis of the models used. These presentations are attended and
graded by her/his supervisory Committee. Attendance is compulsory. The course will be given a
pass/fail grade based on the presentations, attendance and participation by the student. This course
represents the first of two presentations and is expected to be about 10 – 15 minutes in length.

**AMOD 5902H: Second Seminar on Applications of Modelling**

As with AMOD 5901H, this course represents the second of two presentations required by each
student in the program on his/her research. The length of this presentation is expected to be about
25 minutes. As with the first presentation, it will be attended and graded by her/his Supervisory
Committee. Attendance is compulsory. The course will be given a pass/fail grade based on the
presentations, attendance and participation by the student.

**AMOD 5903H: Project Seminar on Applications of Modelling**

Each student in a course-based stream will present his or her work on the research project, with emphasis on the assumptions, methodology, and analysis of the models used. Attendance is compulsory. The course will be given a pass/fail grade based on the presentations, attendance, and participation by the student. The presentation is expected to be about 10-15 minutes in length.