### Winter 2022 Term

The purpose of the AARMS Advanced Course program is to give graduate students and upper year undergraduates from AARMS Member Universities an opportunity to take courses not offered at their home institution free of charge. In Winter 2021, the courses listed below will be offered in an exclusively online format. For this term, we are pleased to offer two courses in collaboration with the NSERC funded network Mathematics for Public Health (MfPH).

Students may be able to claim credit for AARMS Advanced Courses from their home institution using mechanisms similar to the AARMS Summer School. Students hoping to receive academic credit for courses in this program are strongly encouraged to consult with their home institution about this process before the start of lectures.

The application process for regular AARMS Advanced Courses and MfPH Courses is different:

**Regular AARMS Advanced Courses:**we will stop accepting applications for all courses at 11:59 pm on Friday, December 17. However, any individual course may close earlier and without notice depending on demand and course capacity. Students are encouraged to apply as soon as possible to avoid disappointment.**MfPH Courses:**registration is managed through the Fields Academy. Students should follow the instructions on this webpage.

Both students and instructors should consult the frequently asked questions. Please send any addition questions about this program to Sanjeev Seahra.

### Important dates

- November 22, 2021: Application form opens for regular AARMS Advanced courses (applications will be accepted on a rolling basis)
- December 17, 2021: Application form closes for regular AARMS Advanced courses (individual courses may close earlier without notice)
- Early January, 2022: Classes begin

Timelines for MfPH course registration are available on the Fields Academy website.

### Deep learning and deep reinforcement learning

*Alexander Bihlo (Memorial University)*

**Regular AARMS Advanced Course**

This course will provide a short overview of classical methods of machine learning before providing an introduction to the areas of deep learning, reinforcement learning, and deep reinforcement learning. An introduction to TensorFlow and Keras will be provided.

Prerequisites include: undergraduate linear algebra, multivariate calculus, elementary probability, and elementary experience with Python.

### Discrete random structures

*Jeannette Janssen (Dalhousie University)*

**Regular AARMS Advanced Course**

This course will cover basics of probability and stochastic processes, and then focus on areas where probability and combinatorics interact. Topics include: probabilistic method, stochastic graph models for complex networks, probabilistic algorithms. Probabilistic techniques include: expectation and concentration of random variables, stochastic processes, conditional expectation, Markov chains, martingales, branching processes.

Students should have taken a course in Discrete Math, Graph Theory, or a related subject, and be comfortable writing proofs. Basic knowledge of probability will be helpful, but is not required.

### Hopf algebras

*Yorck Sommerhäuser (Memorial University)*

**Regular AARMS Advanced Course**

Hopf algebras are algebras for which it is possible to form the tensor product of two representations. A typical example is the group algebra of a group. Hopf algebras play a role in remarkably many areas of mathematics, such as algebraic topology, Lie theory, or category theory, and also in physics, for example in the theory of exactly solvable models in statistical mechanics, conformal field theory, and the theory of renormalization.

The course will provide an introduction to the basics of Hopf algebra theory. Emphasis will be on results that generalize classical theorems from group theory, like Lagrange’s theorem, Cauchy’s theorem, and Maschke’s theorem. A prerequisite is a knowledge of multilinear algebra as contained in the first chapter of Werner Greub’s book on the topic. No prior knowledge of advanced algebra or group theory is required.

### Infectious disease modelling: theory and methods

*Seyed Moghadas (York University)
*

**Mathematics for Public Health (MfPH) Course**

This course will cover important topics in modelling infectious disease dynamics in human populations. Topics will include compartmental modelling (from simple classical SIR to more advanced multi-scale models); integration of public health interventions in models (both non-pharmacologic and pharmacologic measures); theory and methods to understand the dynamics of models and effect of interventions; parameter distributions and statistical analyses of model input/output; with case studies for interacting populations (e.g., metapopulation models); individual-level characteristics (e.g., agent-based modelling; household models); vector-borne diseases (e.g., Zika and Dengue); cellular-level dynamics (e.g., in-host modelling). Data-driven models will be presented, and importance of underlying assumptions and epidemiological concepts in the development, parameterization, implementation, and scenario analyses will be discussed. Policy implications of different assumptions for preventing and/or mitigating disease outbreaks are also illustrated.

Prerequisites include: Ordinary Differential Equations (undergraduate level); Linear Algebra (undergraduate level); Numerical methods/analysis and an elementary course in Statistics would be very useful.

### Machine learning statistical methods for disease transmission modelling

*Nathaniel Osgood (University of Saskatchewan)
*

**Mathematics for Public Health (MfPH) Course**

In recent decades, public health and health care decision making with respect to communicable disease has increasingly been impacted by two versatile and deep computational modeling traditions: Systems Science (particularly via transmission modeling) and Data Science (particularly via machine learning & computational statistics, and increasingly with aspects of “Big Data”). While both Systems Science and Data Science constitute cutting-edge computational traditions offering great promise for fine-temporal grained longitudinal understanding across multiple pathways of complex systems, these two traditions are often pursued in parallel rather than in a joint manner. This course systematically characterizes the theory and practice of cross-leveraging transmission modeling and machine learning and computational statistics, and demonstrates how such approaches support leveraging and informing transmission modeling with both traditional data sources and “big data” characterized by high volume, velocity, variety and veracity.

### Numerical methods for solving differential equations

*Sanjeev Seahra (University of New Brunswick)*

**Regular AARMS Advanced Course**

The principal goal of this course is to give students “hands-on” experience in solving ordinary and partial differential equations (ODEs and PDEs) using (primarily) finite difference methods. The emphasis will be on practical scientific computing; i.e., the construction of numerical algorithms to deal with actual problems in the physical, biological or engineering sciences. More details are available from an older version of the course website.

Students should have some familiarity with ordinary differential equations and programming. Lectures will make use of Maple and Python, and students will be encouraged to submit assignments and the final project in either language.

### Pursuit-evasion problems

*Danny Dyer (Memorial University)*

**Regular AARMS Advanced Course**

Description: This course will introduce the concepts of the cop and robber model in graph theory; characterize those graphs that are k-cop-win; examine Meyniel’s conjecture, and families of graphs for which Meyniel’s conjecture are met; consider the cop-number of various graph products; consider the cop number of graphs embeddable in different surfaces; and consider variants of the classic model in which cops and/or robbers have asymmetric movements and information.

Prerequisites: Some knowledge of graph theory is recommended, but not required. Students should be familiar with writing proofs.