Linear Algebra

Welcome to MATH S215 Linear Algebra! This course teaches the introductory Linear Algebra.

Linear algebra has wide applications to areas in statistics, applied science, engineering, business, economics and decision science. The course mainly focused on vectors, vector spaces and linear transformations. A vector has both a length (or magnitude) and a direction, so that vectors can be used to represent, for example, translations. We study the properties of vectors, and show how vectors form vector spaces and give a convenient description of ordinary space. We also show how matrices operate on vectors, giving linear transformations of vector spaces. One application of these ideas is to the solution of linear equations.

The course is made up of seven study units. Five of the units cover linear algebra and the remaining two units introduce the real numbers system and convergence of the sequences.

You start with vectors. You then consider systems of linear equations in several variables. You learn the algebraic skills in finding solutions of these systems and interpret these solutions geometrically. You will work with matrices and row operations. You will learn vector spaces and linear transformations before your study on quadric surfaces in 3-dimensional space.

The remaining two units will consolidate your knowledge on real numbers and discuss the ideas of convergence of the sequences.

To summarise, 7 units of the course are assessed through assignments and in examination.

Structure of the Units

The Introduction to each unit gives a brief outline of the various sections of that unit and indicates how the sections depend on one another. Most units have four or five sections, each corresponding very roughly to two evenings work (some longer, some shorter!). You should be able to complete the study of each unit within two weeks as specified in the Presentation Schedule.

Television Programmes

MATH S215 has 2 television programmes. A television programme is indicated by a TV symbol in the study units. Each television programme lasts for 25 minutes. Plan your study schedule so that you can watch the relevant programme at the appropriate time. MATH S215 has some abstract concepts that will not always be easy to grasp. The TV programmes help your study by showing you 'concrete' examples and guiding you through abstract concepts.

Audio CD

MATH S215 has 3 audio CDs. They contain audio lessons that are characterized by 'frames' in the study units. You must listen to these audio lessons. You will frequently need to stop the listening to solve a problem or answer a question. The lesson has indicated these points by a few bars of music. 'Pause' or 'stop' your machine while you are working on an audio section.

Problems and exercises

There are many problems for you to solve as you work through the texts. It is important to work the problems as you come to them, since they constitute a carefully designed part of the teaching materials. The solutions to the problems are collected together in an appendix at the end of each unit.

The final section of each unit consists of a collection of exercises. Their solutions are given in the Appendix of the Unit. These exercises aims to test your understanding of the material and practice the various techniques you have learned.

MATH S215 Handbook and Regulation

The Course Handbook provides a convenient source of basic definitions and formulas for use throughout the year of your study. You will not be allowed to bring the Course Handbook to the exam. Another copy of the handbook will be given to you together with the exam paper.

Calculator

You can use a calculator to evaluate mathematical functions such as exponential, logarithmic, and trigonometric (and their inverses) when you study the course.

Calculators are allowed in the examination. The University has a List of Approved Models of Calculators so that students know what types of calculators are allowed in the examination. This List is updated according to the types of calculators approved by the Hong Kong Examinations and Assessment Authority. You will receive the List from Registry before the examination.

You are NOT allowed to use a non-approved calculator or a calculator without 'HKEA/HKEAA Approved' label in the examination.

A list of approved calculators is attached in Appendix I for reference.

Presentation Schedule

The Presentation Schedule gives full details of the week in which you are advised to study the unit. It shows which units are covered by which assignments, the cut-off dates for the assignments, the title of the television programme and of the audio lessons associated with each unit, and the weeks which have been left free for you to catch up with your work.

The assessment of the course includes 2 assignments and a three-hour final examination. MATH S215 does not have any assignments (multiple choices). The continuous assessment and the examination count equally towards your final grade for the course. All assignments are required, that is, your marks on these assignments are all counted towards your course result. If you do not submit an assignment, you will be given a zero mark for that assignment in your assessment record.

To summarize:

• each assignment contributes 50% towards your overall continuous assessment score;
• 2 assignments will contribute 50% towards your course score;
• the examination contributes 50% towards your course score.

You need to get a minimum of 40 marks on both the continuous assessment score and the examination score in order to pass the course.

You must obtain at least 40 marks in your OCAS and at least 40 marks in the examination if you want to obtain the 10 credits from MATH S215.

Continuous assessment

The course has 2 assignments that are related to the study units as follows:

You are allowed to submit MATH S215 assignments electronically or by post. MATH S215 assignments contain a lot of mathematical symbols and formulas. If you can typeset them using Scientific Workplace or Scientific Notebook, your tutor can mark them with the software that you used. In this case, you can send your assignment to your tutor through the 'Assignment Submission & Extension' component in OLE. If you use other mathematical software, your tutor may not be able to open your file. We encourage you to typeset your assignment answers using any mathematical software but send the hard copy of your assignment to your tutor by post.

Do not send your assignment answers electronically in portable document format (PDF). The University has not provided tutors with printers and papers for printing assignment answers. If your assignment answers are in PDF, you must print them yourself and send the hard copy to your tutor for comments and marking.

Although the University encourages students to discuss problems and assignment questions with one another through meetings, tutorials and online discussions, you must submit your own attempt at an assignment. Assignments are part of the learning and teaching process. If two assignments are detected with the same errors and the same wordings, the scores on these assignments will be changed to a zero score if both students cannot give a reasonable explanation.

You can view your assignment scores from the 'Assignment Submission & Extension' component in the OLE. You must use this component to extend assignment cut-off dates. Your application must be before the cut-off date of the assignment. You must state your reason clearly. Reasons like 'busy', 'out of town' will not be considered. You must remember that there is no extension on Assignment 02 as it is the final assignment of the course.

The number of marks assigned to each part of a question is printed in the right-hand margin of the Assignment Booklets. This should give you a rough indication of the relative difficulty or importance of each part of a question.

Tutors will comment fully on each question and use every opportunity to teach on the basis of your solutions. Always spend some time looking at your tutor's comments when you get the assignment back, and try to rewrite any wrong answers along the lines the tutor suggests. You will find such time well invested when you come to use the assignments for revision purposes before the examination.

The final examination

Schedule your revision of the course at the end of the course. It is so easy to run short of time as the examination day approaches. The MATH S215 Handbook and the Exercises Section in each unit help your revision.

The Specimen Examination Paper and its solutions give you the format of the examination paper. You can use them to prepare for the examination.

You must read emails from the account provided by the University and access the Online Learning Environment so frequent that you will not miss any information from us. We do not want you to be isolated while you study the course. If you have difficulties in accessing the Internet, you can use the online computers in the PC Labs at the OUHK campus and at the Island Learning Centre.

MATH S215 Online Learning Environment (OLE)

Owing to the rapid development of information technology, online learning has become very popular especially for distance learners. In order to provide MATH S215 students with the same online support as other courses, this course has been arranged to join the Online Learning Environment (OLE) system.

Some of you already know how to use the OLE system, but some will ask 'what is OLE?'. OLE is a Web-based learning system (Internet system) developed by the OUHK and is an interactive online learning environment used for communication among students, tutors and the Course Coordinator. This system can enhance student's learning experience through its interactive tool. To help you to use the OLE system, the OUHK will send you a User Guide: "Online Learning Environment", together with Mailing 1.

Where to Get Help for Your Study

(i) From your tutor

Your tutor is the direct person to help your study. They will mark your assignment and answer all your queries. When your assignment is returned, you should go through the assignment comments marked on the assignment script and take note of the comments written by your tutor. They will help you avoid similar errors in later assignments again and in the examination. Make every effort to attend tutorials and surgeries; there you will have the opportunity to talk to your tutor directly and to discuss with other students.

(ii) From your fellow students

One of the best ways of learning is by discussing about your study with other fellow students. Unfortunately, you will see them only at the infrequent tutorials during the year. You should collect the address and telephone number of other students in your class; through this way, you could keep in touch with them all the time. You may form a self-help group among students to meet regularly; this is a good way of getting people together to discuss common study difficulties, especially in the assignment questions.

(iii) From the Course Coordinator

If there are any queries which your tutor cannot settle for you, he/she will probably advise you to contact the Course Coordinator. The Course Coordinator is a full-time staff member of the School of Science and Technology at OUHK and is responsible for the course presentation. Ways of contacting the Course Coordinator can be found in the Letter to Students enclosed in the package of course materials that you have received.

If there is any academic query, which your tutor cannot settle for you, then your tutor will probably advise you to contact the Course Coordinator. The Course Coordinator of this course is Simon CHEUNG, at Room A0314 of Ho Man Tin OUHK campus, the office telephone is 2768 6811, email: scheung@ouhk.edu.hk.

(iv) From OLE

The OLE - OLE provides you with an interactive learning environment for communication among students, tutors and the Course Coordinator. When you find problems that you like to discuss with other students, you are welcome to post your problem on the OLE Discussion Board. Details of how to use the OLE component should be referred to the OLE User Guide.

Before you start working on the units, you should get familiar with the Online Learning Environment at the first week. The last page of the User Guide states where you can get technical help. Do contact them if you need extra help. If you are familiar with using the online learning environment then we advise you to start reading the Unit 1 as soon as you get the material without necessarily waiting for the dates on the Presentation Schedule.

An earlier start gives you more flexibility in learning the course.

(In addition to the following models, calculators bearing the "HKEA/HKEAA Approved" labels are also allowed.)

A.MAX

ATABA/AURORA

BISTEC

BLT

CANON

CASIO

CITIZEN

HEWLETT‑PACKARD

KARCE

SHARP

TEXAS INSTRUMENTS

TRULY

 [End of calculator list]