Linear Algebra

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

Course Developer: The Open University, UK, Course Team

This course is intended to provide conceptual understandings and computational techniques of linear algebra. Linear algebra has wide applications to diverse areas in natural science, engineering, business and social science. The course is made up of seven study units: Five units cover linear algebra and the remaining two units deal with real numbers analysis and convergence of the sequence. MATH S215 is one of the compulsory middle-level courses in the BSc and BSc (Hons) in Mathematical Studies, and BSc and BSc (Hons) in Statistics and Decision Science.

This course is also suitable for any learner who wishes to consolidate their mathematical and algebraic techniques in order to enhance quantitative skills for further studies.

MATH S215 forms an excluded combination with MATH S203 / MATH S213.

Advisory prerequisite(s)
You are advised to have already studied one of the foundation mathematics courses MATH S101, MATH S111, MATH S112, MATH S121 or MATH S122.

Aims
This course aims to:

• Provide students with an introduction to the theory and techniques of linear algebra;
• Introduce students to abstract mathematics through systems of linear equations and functions of one variable;
• Develop students’ ability in handling vector-spaces and linear transformations;
• Introduce some basic properties of eigenvalues and eigenvectors;
• Develop students’ competence in numbers and sequences.

Contents
The course covers the following topics:

• Vectors and conics: Coordinate geometry: points, planes and lines; vectors; dot product; conic sections
• System of linear equations and matrices: Simultaneous linear equations; row-reduction; matrix algebra; matrix inverses; determinants
• Vector spaces: Linear combinations and spanning sets; bases and dimension; subspaces; orthogonal bases
• Linear transformations: Matrices of linear transformations; composition and invertibility; image and kernel
• Eigenvectors: Eigenvalues and eigenvectors; diagonalising matrices; symmetric matrices; conics and quadrics
• Numbers: Real numbers; inequalities; proving inequalities; least upper bounds
• Sequences: Null sequences; convergent sequences; divergent sequences; monotone convergence theorem

Learning support
There will be six two-hour tutorials and three surgeries.

Assessment
There will be two assignments and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirements
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 tutor and the Course Coordinator 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 and you can use it to submit assignments.

Set book(s)
There are no set books for this course.

Students with disabilities or special educational needs
The audio and visual components of this course may cause difficulties for students with an audio or visual impairment. You are encouraged to seek the advice from the Course Coordinator before enrolling on the course.