MA3264: Mathematical Modeling
AY2014/2015, Semester 1, Lecturer: Liu Jie
Course Coverage:
1. Optimization Models
2. Ordinary Differential Equation (ODE) Models
3. Probability Models
4. Game Theory Models
5. Graph Theory Models
This module focus modeling social and scientific phenomena using mathematical methods. The main class of model studied is the ODE models.
The module begins with the introduction of optimization methods and their applications in physics, chemistry and economics. Basically formulating linear/nonlinear programming problems and solving them. The focus, however, is on how we utilize the details to formulate the problem mathematically instead of the solving the problem.
The next part is on ODE models. We begin with analyzing discrete model using difference equations. The focus of such models are on the conditions of equilibrium stability. Then, we consider the continuous case, which is very much similar to the discrete version. Examples from different fields are introduced. The highlights are population and predator-prey models from life science, rocket trajectory from physics and relationship models from social sciences. Almost half the module is on ODEs, so prior knowledge with ODE would be advantageous. Nevertheless, such advantage is limited because this module focus on the process of modeling, so in-depth analytical knowledge is not necessary.
Probability models are covered with application to decision science. Fortunately, queuing models are not covered here. Prof Liu decided to keep things simple for this module. In this chapter, the focus is on cost-benefit analysis using decision trees, so as long as the tree is drawn correctly, the solution should be simple to derive.
Game theory models are extensions of decision models to strategic interactions between 2 or more parties. Only the simplest concept, static games of complete information, is covered. So, as long as you understand pure and mixed strategy Nash equilibrium, this topic should be a breeze-through. The few methods used in this module are movement diagrams, maximin-minimax method, equating expected value and method of oddments. They are pretty much the same thing anyway.
Graph theory models are covered at the end of the module. The last homework assignment has one graph theory question but it was not tested for finals. For this module, we only covered the basic problems: Shortest-path problems, maximum-flow/matching problems and vertex cover problems.
This module does not require in-depth/abstract knowledge of mathematics because it focus more on interpreting social and scientific phenomena and the process of converting them into mathematical problems. Thus, it is a good module for electives because of its straightforward concepts and exposure to many real world problems where mathematics are heavily involved. Highly recommended for applied mathematics majors because it provides the missing link between mathematics and real world phenomena, that is, the thought process of modeling.
Workload: Heavy
Difficulty: Easy
Grade: A
Course Coverage:
1. Optimization Models
2. Ordinary Differential Equation (ODE) Models
3. Probability Models
4. Game Theory Models
5. Graph Theory Models
This module focus modeling social and scientific phenomena using mathematical methods. The main class of model studied is the ODE models.
The module begins with the introduction of optimization methods and their applications in physics, chemistry and economics. Basically formulating linear/nonlinear programming problems and solving them. The focus, however, is on how we utilize the details to formulate the problem mathematically instead of the solving the problem.
The next part is on ODE models. We begin with analyzing discrete model using difference equations. The focus of such models are on the conditions of equilibrium stability. Then, we consider the continuous case, which is very much similar to the discrete version. Examples from different fields are introduced. The highlights are population and predator-prey models from life science, rocket trajectory from physics and relationship models from social sciences. Almost half the module is on ODEs, so prior knowledge with ODE would be advantageous. Nevertheless, such advantage is limited because this module focus on the process of modeling, so in-depth analytical knowledge is not necessary.
Probability models are covered with application to decision science. Fortunately, queuing models are not covered here. Prof Liu decided to keep things simple for this module. In this chapter, the focus is on cost-benefit analysis using decision trees, so as long as the tree is drawn correctly, the solution should be simple to derive.
Game theory models are extensions of decision models to strategic interactions between 2 or more parties. Only the simplest concept, static games of complete information, is covered. So, as long as you understand pure and mixed strategy Nash equilibrium, this topic should be a breeze-through. The few methods used in this module are movement diagrams, maximin-minimax method, equating expected value and method of oddments. They are pretty much the same thing anyway.
Graph theory models are covered at the end of the module. The last homework assignment has one graph theory question but it was not tested for finals. For this module, we only covered the basic problems: Shortest-path problems, maximum-flow/matching problems and vertex cover problems.
This module does not require in-depth/abstract knowledge of mathematics because it focus more on interpreting social and scientific phenomena and the process of converting them into mathematical problems. Thus, it is a good module for electives because of its straightforward concepts and exposure to many real world problems where mathematics are heavily involved. Highly recommended for applied mathematics majors because it provides the missing link between mathematics and real world phenomena, that is, the thought process of modeling.
Workload: Heavy
Difficulty: Easy
Grade: A