A Foundation in Applied Mathematics

Welcome to MATH 1220SED A Foundation in Applied Mathematics!

In the next 38 weeks, MATH 1220SED 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.

Included in your course pack are rich resources for your study of MATH 1220SED — but 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 1220SED

MATH 1220SED is a six-credit-unit 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 1220SED 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, as well as sufficient English knowledge to study in this language.

About this Course Guide

This Course Guide contains important information that helps prepare you to 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 information on 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:

• provide you with experience of distance learning;
• develop your study skills to help you become an independent learner;
• lead you to appreciate the discipline of mathematics;
• provide you with a transition between school and university mathematics and the associated learning environments;
• develop your analytical skills in handling mathematical activities;
• develop your mathematical techniques for further study in mathematics or applied science; and
• improve your confidence in studying in English.

1.2 Course objectives

On successful completion of this course, you should be able to:

• describe and analyse mathematical relations graphically and algebraically;
• set up mathematical models; solve the systems of equations and interpret the results;
• recognise and manipulate matrices and vectors;
• differentiate and integrate expressions involving algebraic and transcendental functions;
• utilise calculus to solve optimisation problems;
• solve physical problems using calculus;
• summarise statistical data and interpret the results; and
• use an algebraic software to help handle mathematical problems.

1.3 Course features

The course’s aims and objectives form the basis of developing MATH 1220SED. To give you an early insight into the coming journey, we now highlight some features of the course design:

• HKCE/HKDSE mathematics will be taken as the starting point of the mathematical development in MATH 1220SED.
• English will be the medium of instruction.
• An average student is expected to spend about seven to ten hours per week on the course.
• A Diagnostic Quiz and a Preparatory Package will be provided to prepare students for the course.
• The core study materials include one set textbook and 11 study units.
• Course assessment will be based on your performance in assignments and the final examination.
• You will be assigned to a tutorial group supported by one tutor.
• An orientation, a computer training session, tutorials and surgeries will be provided as optional face-to-face activities.
• Consultation hours will be arranged with tutors to assist with your study.
• An algebraic software package like GeoGebra or other free mathematical software will be integrated into the course content and is required for assessment.
• The Internet will be included as a study tool for assessment, communication, and support purposes.

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 1220SED assumes. 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.

2.1.2 Preparatory Package

The Preparatory Package attempts to ensure that you are ready for the demands you will face during the next 38 weeks. These demands will not only be mathematical. You probably will also need to:

• adjust your study to the new challenges that will face you; and
• develop new study skills for learning independently.

Even if you have experience with HKMU courses, you may find that the approach adopted for MATH 1220SED differs from other courses because:

• an algebraic software is integrated into the course content; and
• the Internet is included as a study tool.

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 1220SED

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 y_x, 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 connected to the Internet throughout the course. If you have problems accessing a computer, you can come to one of the University's PC labs.

To run algebraic software for MATH 1220SED, you need a PC which satisfies the corresponding requirements. You may also need access to a printer for computer printouts.

For Internet support provided during the course, you may need a web browser such as Chrome, Firefox or Edge. Further details of hardware and software requirements can be found via the following link: https://itresources.hkmu.edu.hk/hkmu/content.php?pid=03_ole

After you have gone through 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 1220SED are 11 study units. The units are supplemented by reading selections from a set textbook. To deepen your understanding, a Problem Booklet is also provided with each unit.

General administrative information is supplied through several 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.

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 will 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 their properties.

Unit 2 Systems of equations — this unit presents graphical and algebraic methods for solving linear and simple non-linear systems.

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 the inversion method.

Unit 4 Modelling and models — this unit 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 and logarithmic 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 optimisation 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, and the method of partial fractions for rational functions.

Unit 10 Applications of integrals — this unit considers applications of integration including finding areas and volumes.

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.

3.1.1 Working through the study units

Most of the MATH 1220SED 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. 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 finalise your solutions.

3.2 Set textbook

You are required to acquire the following set textbook for MATH 1220SED:

Weir, Hass and Giordano (2020) Thomas' Calculus, 14th edn, Pearson Education.

Note that the textbook will be referred to as 'T&F'. Details of where you can purchase T&F will be sent to you separately. Instructions on using it will be given in the study units.

3.3 GeoGebra or other software

You are also required to use algebraic software such as GeoGebra. This is recommended because it is free and versatile. You can simply use it through a web browser without any installation. Of course, there are alternatives. Do not hesitate to consult your tutor if you need help with the software.

The software allows 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 user manual: https://wiki.geogebra.org/. You can also refer to Section 2.4 of the Preparatory Package that introduces the basic functions of the software and gives guidance on exploring its features. Please also bear in mind that technology changes every day. The software may change or even be replaced by other ones.

3.4 Other materials

The course materials include several 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 1220SED.

3.4.1 Checklist

Each package of course materials for MATH 1220SED 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.

3.4.2 Course Handbook

The Course Handbook is a summary of the standard results introduced in MATH 1220SED. This will be uploaded to the OLE in due course. 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.

3.4.3 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.

3.4.4 Presentation Schedule

The Presentation Schedule, which is available on the OLE, 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 due date. In addition, you should start the assignment questions for a unit as soon as you finish the unit.

3.4.5 Tutorial Schedule

The Tutorial Schedule, also on the OLE, gives 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 1220SED, the first semester begins in September and the second semester begins in January.

3.4.6 Stop Press

You will receive several Stop Presses throughout the course. They are a sort of newsletter containing useful information about the course.

3.4.7 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 erratum, 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 30% and 70% respectively. To be assured of achieving a pass, you must score at least 40% in each of them.

4.1 Continuous assessment

There are three assignments, which contain questions requiring you to prepare and submit written answers to your tutor for marking.

4.1.1 Assignments

There are three assignments, each covering two to three study units. The marks for all assignments will be used to determine your final grade. It is important that you understand that assignments are not simply a form of 'test'. All assignments fulfil several objectives:

• The due dates encourage you to stay on schedule.
• In preparing your answers, you will discover how much or how little you understand of the unit. Hopefully, this will encourage you to revise a particular section and to contact your tutor for help.
• In marking your solutions, your tutor will try to give comments identifying where you have made an error and guide you on how this error can be corrected.
• The mark obtained would represent your level of understanding for assessment purposes.

So, the assignments should be seen as an opportunity for both teaching and learning as well as for assessment. To maximise the benefits, you should start working on the assignments 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.

A common request from students is for model answers to be provided for all assignment 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 completes the assignment that the student fully understands a technique.

All assignments must be submitted directly to your own tutor. There are two ways that you can do this:

• Write your solutions on paper and scan them as a PDF file. Then upload your scanned answers via the OLE e-submission function.
• Use Microsoft Word to prepare your answers and then upload the file on the OLE.

The main advantages of submitting your solutions through the OLE are that you can be sure that they will not get lost or delayed in the post and you can submit your work 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 1220SED 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 assignments to your tutor by the due 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 preventing you from submitting your assignment on time, you may to apply through the MATH 1220SED OLE for permission to submit your solutions late, except for the last assignment. To whom you apply for permission depends on the amount of time that you require:

• 1–7 days — your tutor;
• 8–21 days — the Course Coordinator;
• more than 21 days — the Dean.

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 on the OLE for the decision. Note that requesting an extension is meant to be an exception — any delay for one assignment will make it harder for you to meet the due date for the assignments that follow. In some circumstances it may be better to omit one or two of the questions in an assignment so as to submit it on time rather than making it harder for later assignments.

4.1.2 Determining your final continuous assessment mark

Each of the three assignments will contribute 33.3% towards your overall continuous assessment score (OCAS), which accounts for 30% of your final score for the course.

4.2 The examination

There is a two-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 1220SED. 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 GeoGebra or other software, 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 1210SED OLE. Attendance at tutorials is optional but 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 assignments. 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 assignments, 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 1220SED Coordinator are given on the OLE.

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:

• Discussion: A discussion board is shared by all students and tutors on the course. Problems can be posted for anyone to offer help. In the past this has possibly been the most popular way of getting help.
• Email: Each student and tutor has an email account for direct communication between individuals and groups. Most of the news and comments from the Course Coordinator will be sent to you through this email system.
• News: Any stop press will be posted on the MATH 1220SED OLE. An alert will be displayed to indicate any new items posted.
• Units: Softcopies of the units will be available on the OLE.
• Assessment: All assignments are provided on the OLE.

Requests for a delay in submitting assignments must also be done through the OLE.

The MATH 1220SED 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. The OLE User Guide will explain 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 principal 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 in the course, it is always worthwhile to seek help before giving up.

The one biggest cause of student dropout is time management. MATH 1220SED 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:

1. Tom hands over a cheque to HKMU for the course MATH 1220SED. He receives a package of material. His first impression is that there’s a lot of English text involved and a lot of new things to understand about how the course and the University operate. Three weeks into the semester, Tom puts the material in a cupboard.
   First mistake Tom: start now! Read through the Course Guide and familiarise yourself with the different elements. Prepare a study schedule indicating when in the week you will study — perhaps two hours per night during the week, or both evenings at the weekend. Start this study schedule now by working through the Preparatory Package.
2. Mary has looked through the material and feels reasonably confident that she can handle it. After all, she’s done mathematics at school. She notices that the first assignment must be handed in during week 3 of the course. So, she decided that she’ll start working on the material a couple of days before the submission date.
   Sorry Mary, but you’re heading for trouble! When you do start working on the first assignment you may find that you don’t remember as much of your school mathematics as you thought. There’s material to help you refresh your memory, but now you won’t have enough time to work through it. You will score low on the first assignment and get depressed. Talk this over with your tutor who’ll explain that this is only a small problem that need not affect the rest of the course.
3. Arthur has made a reasonable start to the course. He has found the first couple of units fairly easy and got good scores on the first assignment. Confident about his ability to complete the other assignments, Arthur begins to reduce the amount of study time he does each week.
   Bad news. Arthur’s boss wants him to work overtime all week and the second assignment is due at the end of the week! He still has one unit to finish studying as well. Arthur applies for a two-week extension, but now he finds that this makes it harder for him to prepare the following assignment.
   Arthur, it’s always better to get ahead of the course schedule if you have the chance. Then if the demands of your job or family change, you will be in a position to reduce the time spent studying in one particular week without getting behind on the course.
4. Jessica feels that after eight weeks there’s no point in continuing with the course. She was late in starting her work on the material and missed the first two assignment due dates. Her mark for the third assignment was low because she simply couldn’t find enough time. Her tutor has rung a couple of times to see if there’s any problem, but Jessica is too embarrassed to admit that she’s having problems.
   Jessica, you really need to let your tutor help you. He/She can explain that performing badly on the first assignment does not necessarily mean that you will fail! The tutor can discuss with you how much time you can now commit to your study each week. On this basis, he/she can reassure you that with a little hard work you can still catch up with the schedule and still have an excellent chance to successfully complete the course. But, your tutor can only help if you ask for it.

As a general rule, work ahead of 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 workspace 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!