Aims and Fit of Module
This module provides an introduction into the formulation and analysis of mathematical models, covering graphical methods, differential equations as well as stochastic modeling. Graphical and stochastic modeling are powerful tools that allow one to model linear relationships among variables while accounting for the uncertainties of the data. These tools play an increasingly important role in modern applications of social and biomedical sciences. In the lectures, the participants will get hands-on training in both the fundamentals and applications of these modeling approaches to scientific problems.
A Demonstrate an understanding on the outline, formulation, and utility of mathematical models.
B Comprehend the elementary components of mathematical modeling such as scaling arguments, graph, optimization, and probability.
C Apply ordinary differential equations to model the dynamics of a system.
D Perform analysis of ODEs with local stability theorem and the global method.
E Design a stochastic model using probabilistic building blocks such as random variables, Bernoulli trials, normal distribution, and linear regression.
F Compensate the basic characteristics of networks, and be able to use graphs to represent complex relationships between variables.
Method of teaching and learning
This subject will be taught by a combination of lectures and tutorials. In lectures, students are introduced to the core concepts, major methodology and common topics of mathematical modeling. Tutorials are given as a platform to address any specific question or issue from individual students.