Computer Algebra and Simulations

Course Coordinator: Dr Tony MT Chan, Grad Dip, MPhil (CUHK); PhD (CityU)

Important note
This course will be taught through a part-time face-to-face mode. The course will be presented in English. Lectures and tutorials will be scheduled on either weekday evenings, or on Saturdays or Sundays.

MATH S811F is one of the core courses in the Master of Science in Quantitative Analysis and Computational Mathematics. It is also one of the courses in the Postgraduate Diploma in Quantitative Analysis and Computational Mathematics, and the Postgraduate Certificate in Computational Mathematics.

The course aims to help students develop an understanding of the concepts of computer algebra and its applications in the fields of science, business, financial engineering, etc. Students will learn both the theoretical basis for these methods and how to apply them.

Advisory prerequisite(s)
You are advised to have some background knowledge in mathematics and quantitative science, computing or a related discipline.

Aims
This course aims to:

• Develop students’ mathematical understanding of the numerical methods used in linear algebra;
• Enable students to apply the efficiency and stability of algorithms in numerical linear algebra to various applications;
• Teach various Monte Carlo techniques, such as generation of random variables, stochastic processes, Monte Carlo integration and correlated sampling;
• Prepare students to write program code and choose a generator, or pseudo-random or quasi-random sequences;
• Demonstrate the applicability of Monte Carlo simulation methods to scientific, project management, financial engineering and transportation applications.

Contents
The course will cover the following topics:

• Introduction to symbolic computing software
• Computer algebra with applications
• Case studies and applications using computing algebra
• Random processes and Monte Carlo simulations
• The computer simulation approach
• Modelling systems with Monte Carlo simulations

Learning support
There will be regular face-to-face lectures and tutorials throughout the course.

Course assessment
Course assessment will be divided into continuous assessment (50%) and a project (50%). The continuous assessment portion will include 2 compulsory Assignments (30%), and a report on the practical exercise (20%). The project will be evaluated based on the following components: (i) an oral presentation (20%), and (ii) a written final report (30%). Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your lecturer as well as other students. To access the OLE, you will need to have access to the Internet. The use of the OLE is required for the study of this course.

Equipment
Students will need access to a computer system suitable for connecting to the Internet. The recommended minimum computing requirements are:

• Pentium IV CPU
• SVGA display card and monitor
• 1 GB RAM
• 500MB free hard disk space
• Broadband Internet access

Set book(s)
There are no set books for this course. The following books will be the main references of study:

Kroese, DP, Taimre, T and Botev, ZI (2011) Handbook of Monte Carlo Methods , Wiley.

Rubinstein, RY and Kroese, DP (2008) Simulation and the Monte Carlo Method , 2nd edn, Wiley.

Trefethen, LN and Bau, D (1997) Numerical Linear Algebra , Philadelphia: Society for Industrial and Applied Mathematics.