This Course Guide has been taken from the most recent presentation of the course. It would be useful for reference purposes but please note that there may be updates for the following presentation.
MATH S122
A Foundation in Applied Mathematics
Welcome to MATH S122 A Foundation in Applied Mathematics!
In the next forty weeks, MATH S122 will give you a foundation in applied mathematics as well as a new experience in distance learning. To gain the most out of this course, it is particularly important for you to get off to a good start and plan ahead for your study.
Including the package that you just opened for this Course Guide, MATH S122 has a total of more than 40 items of course material. Impressive? But there is a problem – where to start? The answer is simple, whether you are new to the University or not – always start an HKMU course by reading its Course Guide carefully.
About MATH S122
MATH S122 is a ten-credit two-semester course presented in HKMU's distance learning mode. It is one of the two mathematics foundation courses offered by the University, and is particularly designed for students aiming for a degree in mathematics or applied science.
MATH S122 focuses on the branch of mathematics called calculus and analytic geometry. Its intention is to broaden your view of mathematics, equip you for advances in technology and prepare you for studying higher level courses.
To take this course you need to have the standard of mathematics equivalent to a pass in the HKCE/HKDSE examination. While you are expected to have sufficient knowledge of English to study in this language, MATH S122 provides support in Chinese to assist you with the transition to university-level study in English.
About this Course Guide
This Course Guide contains important information that helps prepare you get the most out of the course. It is divided into seven sections:
Section 1 presents the aims and objectives of this course and highlights the features of its design.
Section 2 discusses what you should prepare for your study including the equipment required.
Section 3 outlines the course content and gives an overview of the constituent parts of the course.
Section 4 gives the course assessment scheme and the minimum requirements for obtaining a pass.
Section 5 describes the optional activities with your tutor and the course coordinator.
Section 6 is concerned with the assistance that you may obtain from various parties for this course.
Section 7 explains the challenges that you may encounter in studying this course.
1.1 Course aims
This course aims to:
1.2 Course objectives
On successful completion of this course, you should be able to:
1.3 Course features
The course aims and objectives form the basis of developing MATH S122. To give you an early insight into the coming journey, we now highlight some features of the course design:
This section discusses what you should prepare for this course. You'll also learn about the equipment required for your study.
2.1 For your personal preparation
2.1.1 Diagnostic Quiz
The Diagnostic Quiz is designed for self-assessment of the mathematical basics that MATH S122assumes. Your mathematical ability will affect the progress of your study and may require you to adjust your study plan. This quiz should remind you of the areas that demand immediate improvement. We therefore strongly recommend that you undertake the quiz before starting work on the study units.
2.1.1 Preparatory Package
The Preparatory Package attempts to ensure that you are ready for the demands you will face during the next 40 weeks. These demands will not only be mathematical. If you are new to distance education, you will also need to:
Even if you have experience with HKMU courses, you may find the approach adopted for MATH S122 differs from other courses because:
Time spent now preparing yourself is likely to speed up your progress through the more difficult parts of the course. It is therefore important that you set aside the first week of the course to work carefully through the Preparatory Package. You should then consider discussing with your tutor any weaknesses you may have spotted.
2.2 Equipment required for MATH S122
2.2.1 Calculator
You will be allowed to use your calculator in the final examination. The calculator should possess basic mathematical functions such as sin x, ex, log x and yx, and statistical functions such as x̅ and s. Additionally, the calculator must be battery-powered, silent in operation and without print-out or graphic/word-display facilities. The University has strict rules about which types of calculators are permitted. You should check the list of approved calculators provided by Registry.
2.2.2 Computer
You will need access to a computer connecting to the Internet throughout the course. If you have problems accessing a computer, then you can come to one of the University's PC labs.
To run the algebraic software for MATH S122, you need a PC with at least 64 MB of RAM, a CD-ROM drive, and 250 MB of free disk space. Your system must be running Windows 98 or higher. You will also need access to a printer for computer print-outs.
For Internet support provided during the course you will need the browser Internet Explorer version 5 or later.
After you complete this Course Guide, the Diagnostic Quiz and the Preparatory Package, you should continue your study as suggested in the Presentation Schedule.
The main study materials for MATH S122 are 13 printed study units. The units are supplemented by reading selections from a set textbook and teaching presented through audio and video programmes. To deepen your understanding, each unit is also provided with a Problem Booklet.
General administrative information is supplied through a number of documents. In particular, the Presentation Schedule helps you pace yourself through the presentation; Tutorial Schedules give the date, time and venue of your tutorials and other optional activities; Stop Presses provide the latest news about this course; and Errata correct typographical mistakes in course texts.
Having so many bits and pieces to the course may be a bit frightening, but you'll see that it really isn't so hard to follow. To give you a better picture of the components, we now discuss in detail the study materials and some of the supplementary elements.
3.1 Study units
These units are the core course materials. You are expected to complete one unit over a two-week period including the associated assessment questions. The following gives a brief description of the units:
Unit 1 Relations and functions – this unit is concerned with algebraic and graphical representations of relations and functions; and considers the properties of Cartesian equations, parametric equations, and polar equations and their relationships.
Unit 2 Systems of equations – this unit presents graphical and algebraic methods for solving linear and simple non-linear systems; and discusses the errors introduced in numerical operations and the problem of ill-conditioning.
Unit 3 Matrices – this unit introduces matrices and their operations including addition, subtraction, multiplication and matrix inversion; and solves the matrix equations for linear systems by performing row operations and inversion method.
Unit 4 Modelling and models – this unit describes a mathematical modelling cycle and the roles of mathematical models; it also explains how linear, non-linear and simultaneous models can be set up and solved and how the results can be interpreted.
Unit 5 Differentiation – this unit presents the concept of limits and derivatives and various rules of differentiation, including constant multiple rule, power rule, sum rule, product rule, quotient rule and chain rule. The technique of implicit differentiation and higher order derivatives will also be discussed.
Unit 6 Transcendental functions and their derivatives – this unit discusses the properties and differentiation of transcendental functions including trigonometric, exponential, logarithmic and hyperbolic functions. The concept of inverse functions and the technique of logarithmic differentiation will be presented.
Unit 7 Applications of differentiation – this unit applies techniques of differentiation to obtain information for graph sketching. It also discusses the formulation and solution of optimization problems, rate of change problems and related rate of change problems.
Unit 8 Integration – this unit introduces the concept of indefinite and definite integrations and their evaluation. The Fundamental Theorems of Calculus will be presented.
Unit 9 Techniques of integration – this unit discusses various methods of integration including the method of substitution, the integration-by-parts formula, the method of partial fractions for rational functions and the method of trigonometric substitutions.
Unit 10 Applications of integrals – this unit considers applications of integration including finding areas, volumes and lengths of curves.
Unit 11 Vectors – this unit considers geometrical and algebraic representations of vectors and discusses their operations including addition, subtraction, scalar multiplication, scalar (dot) product, decomposition and projection.
Unit 12 Position and motion – this unit focuses on physical applications of the techniques presented in the previous units. In particular, applications on position and motion relating to linear motions and projectiles will be considered. First order ordinary differential equations will be introduced.
Unit13 Introduction to statistics – this unit presents the basic concepts of statistics and considers the graphical and algebraic methods for presenting data. Linear regression models and the method of least squares will be discussed.
3.1.1 Working through the study units
Most of the MATH S122 study units use information provided in earlier units. Therefore, you should study the units one at a time in a sequential order. It will help if you work through the Preparatory Package, where you'll learn more techniques for being a successful distance learner in the section called 'How to study an HKMU course'.
The units are divided up into sections that provide natural breaks for your study. Each unit begins with an introduction giving guidelines on what you will study and the objectives of the unit. It will conclude with a summary of the important results. Do not skip the sections that refer to the set textbook or direct you to the audio or video programmes. If you do, you'll miss some useful teaching points and explanations.
In the units you will come across examples, exercises and activities. Section 2.2 of the Preparatory Package will explain their purpose and how you should use them. You should work through the exercises and activities included in the units. It is important to try solving them before looking at the suggested solution; don't just turn to the solution as the easy way out. On the other hand, don't ignore the solution – always read through it and compare it with yours.
On completing your study of a unit, you should start working on the corresponding assignment questions. Although it is tempting to use the unit or ask your tutor for help, you will gain more by making your first attempt at solving the questions without any assistance. You can, of course, refer back to the units before you finalize your solutions.
3.2 Set textbook
These units are the core course materials. You are expected to complete one unit over a two-week period including the associated assessment questions. The following gives a brief description of the units:
You are required to purchase the following set textbook for MATH S122 :
Weir, Hass and Giordano (2010)
Thomas' Calculus,
12th edn, Pearson Education.
Note that the textbook will be referred to as 'T&F'. Details of where you can purchase T&F (and the software for this course) will be sent to you separately. Instructions on using it will be given in the study units.
3.3 Scientific Notebook
You are also required to purchase the algebraic software Scientific Notebook. The software combines the ease of preparing documents mixing mathematics and text with the power of symbolic computation and the convenience of direct Internet access.
These features allow you to make discoveries with mathematics as well as to tackle more realistic problems without the burden of mechanical calculations. They also enable you to discuss mathematics with your tutor or fellow students over the Internet.
Technical details of the software are given in the booklet Getting started with Scientific Notebook that comes with the software. You can also refer to Section 2.5 of the Preparatory Package that introduces the basic functions of the software and gives guidance on exploring its features.
| You can download a trial version of the software at http://www.mackichan.com |
3.4 Audio and video programmes
Several of the units incorporate teaching based on audio and video programmes. These programmes should provide you with some variety in your study. The content of each programme will be briefly introduced in the corresponding unit. The unit will also tell you exactly when you should start a programme.
You will need to have your unit, a pencil and some paper to hand before you start a programme. You should stop the programme whenever you are instructed to do so, and then work on the suggested exercises or return to the unit. Of course, you may want to stop it at other times to replay parts of it in order to gain a better understanding.
As part of our language support, audio programmes are supplied in both English and Chinese. The video programmes are in English with Chinese subtitles provided.
3.5 Other materials
The course materials include a number of supporting documents that provide academic support as well as administrative information. Effective use of these documents will make an important contribution to your success in MATH S122.
3.5.1 Checklist
Each package of course materials for MATH S122 will include a Checklist that lists the items included in the package. As soon as you receive a package you should go through the list and make sure that all the items are there. Instructions on how to obtain the missing items will be given in the Checklist.
3.5.2 Course Handbook
The Course Handbook is a summary of the standard results introduced in MATH S122. 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.
3.5.3 Chinese Language Summary
The summary aims to assist you in your transition to developing English language study skills. The level of this support will be decreased as the course progresses.
3.5.4 Problem Booklet
Each unit comes with a Problem Booklet that provides additional practice to help reinforce your understanding of the material. The Problem Booklet is divided up into sections corresponding to those in the study unit so you can work through the corresponding exercises after completing each section.
3.5.5 Presentation Schedule
The Presentation Schedule sets out an overall schedule for the course presentation as well as when each assignment should be completed.
In the schedule we suggest when a unit should be studied. You don't have to follow our suggestion, but it is important to keep up your progress. You should aim to finish the units for an assignment at least one week before its cut-off date. In addition, you should start the assignment questions for a unit as soon as you finish the unit.
3.5.6 Tutorial Schedule
The Tutorial Schedule tells the exact date, time and venue of your tutorials and other optional activities for this course. One schedule will be provided for each semester before the semester begins. For MATH S122, the first semester begins in April and the second semester begins in October.
3.5.7 Stop Presses
You will receive a number of Stop Presses throughout the course. They are a sort of newsletter containing useful information about the course.
3.5.8 Errata
Errata will let you know of any typographical mistakes in the printed course materials (i.e. the study units and assignments). When you receive an errata, you should correct the listed items immediately.
The final grade awarded to you at the end of the course depends on two components – continuous assessment and a final examination. The weightings of the two components are respectively equal to 30% and 70%. To be assured of achieving a pass, you must score at least 40% in each of them.
4.1 Continuous assessment
There are two kinds of assignment for continuous assessment:
4.1.1 CMAs
Your solution to each CMA must be received by the University by the relevant cut-off date; e.g. if the cut-off date is April 15, then your solutions must be submitted before midnight of April 15.
There are two CMAs, each covering five or six study units, including the Preparatory Package. All CMA marks are used in determining your final grade. Each CMA is relatively short and assesses your understanding of the basic concepts/skills in the unit. Each question will include a list of possible answers and you must choose the option that you consider represents the correct answer.
Your choice of option for each question must be submitted to the University through the MATHS122OLEWebsite (see Section 6.4).Select Assignments → CMA Submission. Read the instructions for CMA submission and practice the sample CMA. The University does not permit any late submission of CMAs.
The correct options are released on the day following the cut-off date. |
4.1.2 TMAs
There are four TMAs, each covering two or three study units. All TMA marks are used in determining your final grade. It is important that you understand that TMAs are not simply a form of 'test'. All assignments fulfil a number of objectives:
So, the TMAs should be seen as an opportunity for both teaching and learning as well as for assessment. To maximise the benefits you need to start work on the TMA as early as possible so that you can ask for help if needed, and to work through the tutor's comments to correct any errors asking for further help if needed.
A common request from students is for model answers to be provided for all assessment questions. Experience shows that simply reading a model answer does not always help a student understand the cause of any errors. Attempting a similar question often results in the same error being repeated. It is only when a student discovers how to correct the error and then complete the solution that the student fully understands a technique.
All TMAs must be submitted directly to your own tutor. There are two ways that you can do this:
The main advantages of submitting your solutions through the OLE are that you will be sure that they will not get lost or delayed in the post and you can submit literally at any time up to midnight on the last day.
Whichever method you use for submission your tutor will provide feedback on the script. The marks awarded will be entered into your account in the MATH S122 OLE together with any general comments. You will be able to view these as soon as your tutor has completed this entry. Again refer to the User Guide for instructions.
You should always try to get your TMAs to your tutor by the cut-off date. This is to ensure that you keep to the schedule and that you are ready to start the next assignment on time. When unusual circumstances arise that prevent you from submitting on time, then the University allows you to apply through the MATH S122 OLE for permission to submit your solutions late, except for the last TMA. To whom you apply for permission depends on the amount of time that you require:
The OLE system presents you with these three options and will automatically forward your application to the appropriate individual for consideration. You will need to check with your account in the OLE for the decision. Note that requesting an extension is meant to be an exception – any delay for one TMA will make it harder for you to meet the cut-off date for the following assignments. In some circumstances it may be better to omit one or two of the questions in a TMA so as to submit on time rather than making it harder for later assignments.
4.1.3 Determining your final continuous assessment mark
Each of the four TMAs will contribute 20% towards your overall continuous assessment score (OCAS); each of the two CMAs will count for 10%. The combined marks from both types of assignments then contributes 30% of your final score for the course.
4.2 The examination
There is a three-hour examination at the end of the course – this is based upon the whole course. A specimen examination paper with solutions will be provided through the OLE. You should work through this paper carefully some time before the examination. You will be allowed to take your calculator into the examination. No other course materials will be allowed.
The examination mark constitutes the remaining 70% of your overall score for the course. You should refer to your Student Handbook for the method by which the University determines the final grade based on your continuous assessment score and examination mark.
Optional activities are designed to provide supplementary support. You can decide whether you need to attend any of these activities and there will be no penalty for being absent from them.
5.1 Course orientation
An orientation session will be held at the beginning of the course presentation. This session aims to give you an overview of the course structure, course materials and policies for MATH S122. It also provides an opportunity to seek clarifications about this course and your study at the HKMU.
5.2 Computer training session
A computer training session will be held at the HKMU computer laboratory, also at the beginning of the course. This session aims to introduce the use of Scientific Notebook and the OLE system. It will also help you learn how to communicate with your tutor and fellow students over the Internet.
5.3 Tutorials
These are face-to-face sessions run by the tutor. The tutor will discuss any difficult parts and problems of the units which you will be working through according to the Presentation Schedule. Details of the tutorials will be provided on the MATH S121 OLE Web site. Attendance at tutorials is optional although you are encouraged to attend.
5.4 Surgeries
Surgeries are different from tutorials, in that they are designed to offer a more personal level of consultation. A tutor will chair each surgery session. You will prepare and bring along your own individual study problems. Hopefully, you can then discuss these with the tutor and gain an insight into the problems or figure out an appropriate direction from which to tackle them.
Distance education promotes independent study, but it does not prevent you from obtaining support. In fact, student support has been an important component in distance learning. In addition to the prearranged supplementary materials and support, we encourage you to seek help from other people when having problems in your study.
6.1 From your tutor
You will be allocated a tutor to whom you must send your TMAs. Your tutor will not only mark the assignments for assessment purposes, but will also use them as a teaching tool by showing you how to correct errors, giving further explanation to any points of difficulty and suggesting alternative or better methods. Therefore it is important for you to take note of the comments given by your tutor.
Apart from handling your TMAs, your tutor is also available at tutorials, on the telephone and over the Internet for personal consultation. You should feel free to contact your tutor for academic assistance. Your tutor's contact details, including the available hours for telephone consultation, will be sent to you at the beginning of the course.
6.2 From your fellow students
As mentioned before, fellow students can be an important support to your study. Therefore you are encouraged to attend the tutorials and meet at least some of them. If possible, you should exchange contact numbers with each other so that the support can be extended to outside the classroom.
You may also form a study group with fellow students so that the group can meet and discuss course-related problems. You are allowed to discuss assignment questions within the group.
Nevertheless, you must submit your own work for assessment purposes.
6.3 From your course coordinator
Each course at HKMU is supported by a course coordinator who is responsible for the delivery of the course. Details of the MATH S122 coordinator are given in Stop Press 1 included in the package for this Course Guide.
You usually do not need to contact the course coordinator for assistance as the tutor is the first person to contact. However, if you have any problems regarding your study and you are not sure what to do, you are encouraged to contact your course coordinator for a discussion.
6.4 Over the Internet
The University provides the Online Learning Environment (OLE) for all courses. This provides a variety of features to support the presentation of a course:
The MATH S122 OLE should become a regular part of your study habits. Check the site regularly for updates or news as well as useful and interesting postings on the discussion board. You will have received a copy of the OLE User Guide, which explains how to use the system.
Obviously some students simply find the mathematical topics covered in the course too difficult; however, for many students there are other factors that are the principle reasons for their inability to successfully complete the course. Unfortunately too many students drop out of the course believing that there is no hope; however, contacting their tutor or course coordinator could lead to a way of continuing to the end of the course with a reasonable chance of passing. Given the money and time that each student invests into the course it is always worthwhile to seek counselling before giving up.
The one biggest cause of student dropout is time management. MATH S122 is a big course. An average student will require about 300 hours to study it – the equivalent of over seven weeks of full-time work! In addition, there is no detailed, structured study timetable to make you spread this study load evenly over the course. On average you should be aiming to spend about seven to ten hours each week studying. You need to be strict with yourself in finding this time each week. If you are unable to do so in one week, then make sure that you make up for this in the following week.
Here are some typical scenarios with an indication of what the student should have done:
As a general rule, work ahead of the schedule. Force yourself to keep to your planned study pattern. Make use of any opportunity to study – on the bus when travelling to and from work, at lunchtime. Put a copy of your payment receipt for the course fee on the wall next to your work space to remind you about how much you have committed financially to your successful completion of the course. Never give up on the course without first talking about your difficulties with the tutor or course coordinator.
Finally, remember that hundreds of students just like you have successfully completed this course. They have faced similar challenges and obstacles. They have overcome these and so can you!
