'Frequently Asked Questions' intended for Broadbase Science entrants from DSE who are interested in the MATH Programme

Introduction.

This set of FAQs is intended for Broadbase Science entrants from DSE who are interested in graduating in the MATH Programme, especially freshmen who, back in school days, did not have much exposure to mathematics beyond the mathematics lessons at school.

The questions below are ones that many first-year students are too afraid to ask, or do not know whom they can approach to ask.

As a whole, the `soft information' presented in this set of FAQ's is meant to be supplementary to `hard information' contained in the page on the MATH Requirements in the MATH Major Programme for Broadbase Science entrants admitted in same year as you.

There is no need for you to read everything in this page in one go, but do come here to see if anything is useful when you have some questions related to MATH courses during the first year of study.

We make no claim that this list of Q&A's covers everything that first-year MATH students may want to ask. If you have something in mind which you believe is relevant to your study in the MATH programme but not covered here, you are welcome to ask by writing to the department, or by approaching your academic advisor.

Some questions, however, are `universal' (in the sense that mathematics major students everywhere may have encountered). You may find the answers to these questions in a book like:---

(That said, you may need to adapt what you find in such a book to your situation here.)

Table of content.

The level-1000 MATH required courses.
Question 1. What is MATH1010 about?
What can I do as specific preparation for MATH1010?		 Answer.
Question 2. What is MATH1030 about?
What can I do as specific preparation for MATH1030?		 Answer.
Question 3. What is MATH1050 about?
What can I do as specific preparation for MATH1050?		 Answer.
Study tips.
Question 1. What in the first-year MATH classes will be different from my school lessons in maths?
What are the challenges and pitfalls for first-year students from DSE?		 Answer.
Question 2. I know that class attendance is not required for passing the course.
Why should I attend lectures of a MATH course, when I cannot understand what the teacher is saying?		 Answer.
Question 3. In school days I did not have to spend much time doing mathematics after class (and I was doing fine in the examinations).
Is there something wrong that now I find myself having to spend a lot of time and effort on mathematics after class?
What kind of work is expected of me after class?		 Answer.
Question 4. How to make my learning more efficient and effective overall? Answer.
Question 5. Despite my best effort in trying to learn, I make little (if any) progress.
(Worse still, there is little to show in my scores in tests/examinations despite my efforts.)
Is it because I am not talented enough to learn mathematics?
What can I do about it?		 Answer.
Question 6. What can I do to help myself get used to theoretical treatment of mathematics more quickly? Answer.
Question 7. What can I do to help myself improve my technical skills in mathematics? Answer.
Miscellaneous matters.
Question 1. I did neither Mathematics Module 1 nor Module 2 in DSE.
Is there any realistic chance for me to graduate in the MATH programme?
What can I do to improve my chance?		 Answer.
Question 2. I can afford to take at most the two courses MATH1010 and MATH1030 in first year of study.
In view of the MATH recommended study pattern in CUSIS (which includes at least all of MATH1010, MATH1030, MATH1030 in the first year of study), will it jeopardize my study?
Is there anything that I need to take care of in course selection in the second year of study and beyond?		 Answer.
Question 3. What else besides studying is expected of me in the first year of study? Answer.
Question 4. I am thinking about doing research after graduation, but I am not sure whether I am good enough.
How shall I plan my path?		 Answer.
Question 5. I do not plan to do research after graduation, whether in mathematics or in other disciplines.
Is it very difficult for me to find work outside the education sector?		 Answer.

Back to Beginning of Table of Content

The level-1000 MATH required courses.

  1. Question.

    What is MATH1010 about? What can I do as specific preparation for MATH1010?

    Answer.

    MATH1010 extends from the topics `derivatives and their applications', `integrals and their applications' in (which are covered in Modules 1 and 2), to provide a broader and deeper coverage of calculus of one real variable.

    • If you did Module 2, it will do you no harm to recall what you have already learnt in calculus in Module 2.
    • If you did Module 1, you may start by catching up as quickly as possible what is done in Module 2 and is relevant to the topics `derivatives and their applications', `integrals and their applications', but is omitted from Module 1.

      This includes the sub-topics below:---
      • `absolute value',
      • `mathematical induction',
      • `radian measure',
      • `compound-angle formulae',
      • `inverse trigonometric functions',
      • `differentiation of inverse function',
      • `implicit differentiation',
      • `integration-by-parts'.

      Beware that this is a genuine gap to bridge, both in terms of content, and depth in understanding.
  2. Question.

    What is MATH1030 about? What can I do as specific preparation for MATH1030?

    Answer.

    MATH1030 starts from the topics `systems of linear equations', `matrix algebra', `vector geometry' (which are covered in Module 2), and builds up the ideas and methods of linear algebra.

    • If you did Module 2, it will do you no harm to recall what you have already learnt in these topics at school.
    • If you did Module 1, you may start by catching up as quickly as possible what is done in Module 2 regarding:---
      • `systems of linear equations',
      • `matrix algebra',
      • `vector geometry'.

      Beware that this is a genuine gap to bridge, as these topics are omitted entirely in Module 1.

  3. Question.

    What is MATH1050 about? What can I do as specific preparation for MATH1050?

    Answer.

    MATH1050 is intended for preparing students who have taken MATH1010, and preferably MATH1030 also, for the more abstract and theoretical MATH required courses at level 2000, such as MATH2040, MATH2050, MATH2060, MATH2070, MATH2230.

    This preparation will take a two-pronged approach:---

    • The course covers topics which serve as background knowledge for these level-2000 courses but which MATH1010, MATH1030 cannot cover due to limitation in scope and time. They include: `language of sets, functions, and relations', `inequalities for real numbers', `complex numbers', `divisibility for integers'.
    • The course emphasizes a degree of rigour in the treatment of mathematics (through the use of the definitions, theorems, and logical reasoning) as required in these level-2000 courses.

    The best preparation for MATH1050 is:---

    • work hard in MATH1010 and MATH1030, and adapt to the way of learning abstract and theoretical mathematics in these courses.

    In MATH1010, MATH1030, while there may be more emphasis on `�concrete computations' (such as the application of theoretical results in computational examples) than on `theoretical discussions' (such as formulation of concepts in formal `definitions', formulation of general results as `theorems', and logical reasoning in the form of `proofs (of theorems)'), the latter will not disappear altogether.

    (In fact, for certain topics in MATH1010 and MATH1030, such `theoretical discussions' will dominate the content.)

    When you are taking MATH1010, MATH1030, put in some extra effort on following this kind of `theoretical discussions' given by the teachers.

    This effort will pay off when `theoretical discussions' will become more and more dominant in `theoretical' courses, starting from MATH1050.

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Study tips.

  1. What in the first-year MATH classes will be different from my school lessons in maths? What are the challenges and pitfalls for first-year students from DSE?

    First note that unlike many other subjects, there tends to be a strong hierarchical structure in the arrangement of course content within any MATH course, and across the whole MATH curriculum. For the students, this gives rise to the dictum below:---

    • To figure out what is being done in today's lesson, what was done in previous lessons (or previous courses) needs to be at least acknowledged, or better familiarized, if not thoroughly internalized yet.

    As a consequence, it will require a student to apply consistent and serious efforts in learning throughout the whole semester if the student desires to do well in a course.

    When this is translated into action, this means for the student to be mentally disciplined in:---

    • attending all the lectures and the tutorials,
    • completing (and submitting) the coursework punctually,
    • reviewing the material covered in every lesson as soon as the lesson ends, and
    • doing extra exercises (not required as coursework),

    when, unlike your school days, no one is going to tell you that you must do such a thing.

    The first biggest challenge for many a student is to pay heed to this dictum and its consequences, especially when the demands from this challenge conflict with other aspects of university life.

    The key difference between your MATH classes here and your school lessons in maths is stated below. But it needs to be understood in the light of the dictum above:---

    1. We appear to be teaching at a much faster pace than your school teachers, and to be covering `much more ground' within a lesson than your school teachers might within one whole week.

      As a consequence, we will move very quickly beyond what you have learnt already, both in terms of scope and content. So never let this excuse get hold of you during the first few weeks:

      • `Because I have seen this already, I may afford to ...'

      It could be too late for you to catch up when you realize you have missed a lot.
    2. Unlike your school teachers, we tend to spare little time in the beginning of a lecture to help you recall what has been going on recently.

      We expect you to keep up the pace all the time. It can happen that a lesson starts with something entirely new which is built upon what has just been introduced in the previous lesson.
    3. We spare little time for class exercises.

      This does not mean we do not require you to do exercises. In fact, doing a lot of exercises is a learning activity that you are expected to take care of after classes.
    4. More and more often you will hear these words during the lectures:

      • `Fill in the detail (for the argument of this result, or for the calculation in this example) by yourself after class. Treat it as an (extra) exercise.'

      This is meant seriously.

    This brings us to the second biggest challenge for many a student:---

    • It takes time for the student to adapt to the changes described above by adjusting both the mindset and the mode of working.
    • It takes patience to see the benefits brought by such adjustment to be realized in the form of gradual improvement in efficiency and effectiveness in learning, and also in concrete results in tests and examinations.

  2. Question.

    I know that class attendance is not required for passing the course. Why should I attend lectures of a MATH course, when I cannot understand what the teacher is saying?

    Answer.

    We start by clarifying the purpose of lectures in the process of teaching and learning first:---

    • It is not the purpose of lectures to provide every last detail a student should learn in a subject;
    • the main purpose of lectures is to facilitate the students' study by letting the students know what the key points in the subject are.

    This is a crucial difference between lectures here and school lessons in mathematics, and is very often mis-understood by students.

    This mis-understanding tends to lead to the false impressions that:---

    • the teacher is teaching `too fast' and `too much', and
    • it is `useless' to attend lectures because except the very few `clever' ones (or the ones who have already learnt everything), most students cannot `understand' despite paying attention to what the teacher is saying.

    To appreciate why attending lectures will do you good, you should start by adjusting your expectation on lectures:---

    • No teacher will expect you to immediately understand everything during class.
    • Rather your teacher will definitely hope that you pick up the key ideas covered.
    • And your teacher will expect you to follow up with work immediately after class (or as soon as you can) to deepen and broaden understanding of the key ideas by reading through the detail, and/or performing some calculation concerned with the detail, and/or doing some exercises.

    Learning is acquired through both effort inside the classroom, and effort outside the classroom.

    You cannot put in any effort inside the classroom unless you are physically present for the lectures. So do not skip MATH classes. Never let this excuse get hold of you:---

    • `Because I do not understand what the teacher is saying duing the lecture, it does not matter whether I attend class or not.'

    Having attended the lecture will make a difference: you will at least find out what deserves attention. And do not allow this thought get hold of you:

    • `Everyone else in the classroom looks so smart. I look like a fool sitting in such a classroom. And I shall never expose my `stupidity' by asking `foolish' questions.'

    There is nothing embarrassing to be aware that you do not understand something. As stated above, your teacher probably does not expect every student to immediately understand everything during class.

    And, also, where you struggle, most other students also struggle. They are doing no better than you. So do not give up!

  3. Question.

    In school days I did not have to spend much time doing mathematics after class (and I was doing fine in the examinations). Is there something wrong that now I find myself having to spend a lot of time and effort on mathematics after class? What kind of work is expected of me after class?

    Answer.

    First recall the purpose of lectures in the process of learning and learning. (Refer to the previous Q&A.) The process presumes that:---

    • Learning is acquired through both effort inside the classroom, and effort outside the classroom.

    So there is nothing abnormal that you find yourself having to spend a lot of time and effort on mathematics after class.

    In fact, according to the university, each 3-unit course in the university should correspond to:---

    • in-class learning activities of approximately 3 hours per week, and
    • self-learning activities (outside classroom) of at least 3 hours per week.

    As for the kind of work expected of you, this may vary from time to time. But most likely it is from amongst:---

    • doing regular exercises which count in course assessment,
    • doing further exercises which seem not to count in course assessment,
    • organizing what you see and hear during a lecture, possibly with help of the material supplied by the teacher,
    • filling the detail in the arguments for various results or in the calculations in various examples that the teacher omits during a lecture,
    • reading extra material (say, from the library,) which enriches your understanding on a certain topic,
    • studying previous examination papers for a course.

  4. Question.

    How to make my learning more efficient and effective overall?

    Answer.

    First and foremost, do not skip classes. If you skip a one-hour lecture, it may take you several hours of extra work outside the classroom to acquire what you could have obtained in that one-hour lecture.

    As for work outside the classroom, you may try the following:---

    1. At the start of the semester, plan your own timetable which incorporates a weekly regular pattern of work outside classroom.

      Exactly how such a pattern will look like depends on your various commitments. But it should consist of sessions of appropriate length, possibly of one hour or two hours. (It is no good being too short or too long.)
    2. Before you start working in a session, remove everything that may distract you. (For example, leave your phone at another place, and use a device which does not give you easy access to your favourite online games.)

      Get used to sitting still and focusing on the mathematics in front of you.

    Work done inside the classroom and work done outside the classroom complement each other, and consolidate your gains acquired through either activity. Making one of them more efficient and effective will make the other more efficient and effective.

  5. Question.

    Despite my best effort in trying to learn, I make little (if any) progress. (Worse still, there is little to show in my scores in tests/examinations despite my efforts.) Is it because I am not talented enough to learn mathematics? What can I do about it?

    Answer.

    First check whether your best effort in trying to learn attains the minimum that the university expects in terms of `in-class learning activities' and `self-learning activities outside classroom', and whether you are taking the correct approach that will help you focus in your work. (Refer to the previous Q&A's.) If it is not, it is natural that your progress is not satisfactory.

    If you are attaining this minimum and still struggle, perhaps what is said here applies to you:---

    • The estimate in workload by the university is made under the assumption that the student who takes such a course is sufficiently prepared in the background of the course. However, for most first-year students coming from DSE (like you), this is not necessarily the case (although we are not saying you are the one to blame):---

      If you did Module 1, you should be aware that:---
      • Module 1 is not intended for students who plan to use mathematics in science and engineering, not to mention study theoretical mathematics).

      If you did Module 2, you should be aware that:---
      • while your training in mathematics may have equipped you adequately to use mathematics in science and engineering, more likely than not it does not suffice for your beginning a serious study of theoretical mathematics, (unless your school teachers put undue emphasis on the theoretical aspects of mathematics, which was inessential for you and your classmates to do well in public examination).

    This deficiency in your preparation may leave you frustrated in one or both scenarios, described below:---

    1. You feel lost when confronted with a piece of theoretical mathematics (so much `unlike' school mathematics) that it gives you just a few definitions to be followed by a number of theorems and proofs of these theorems.

      (For example, you get stuck in trying to comprehend the definition of linear dependence and appreciate the point of exponding on the consequences of something being linearly dependent.)
    2. You feel overwhelmed by the many technicalities contained in a piece of mathematical manipulation.

      (For example, you get stuck from step to step in an example which your teacher regards as a routine calculation made of `just a few lines'.)

    These are genuine difficulties, and if you do nothing, these problems will cripple you in every MATH course. But with patience and perseverance you can overcome them methodically.

    (For suggestions on what to do, see the next Q&A's.)

    According to our experience, it is pre-maure to make any definite assessment on your potential, based on your experience in the first few MATH courses. Students with good potential and with correct application of efforts will eventually come good by the time of their completion of the level-2000 MATH required courses.

  6. Question.

    What can I do to help myself get used to theoretical treatment of mathematics more quickly?

    Answer.

    Theoretical treatment of mathematics will dominate various topics in MATH1010 and MATH1030, and will be central in MATH1050. For this reason, coming for the classes and paying attention will help tremendously. (Running away from it so as to avoid frustration will do you no good.)

    There are various `guidebooks' (intended for beginners) on how mathematicians conduct this kind of `theoretical discussions', such as:---

    • Lara Alcock, How to study for a mathematics degree. Oxford University Press. (Access through CUHK library; access through Internet Archive.)

      (Refer to Chapters 3, 4, 5 in particular.)

  7. Question.

    What can I do to help myself improve my technical skills in mathematics?

    Answer.

    The one and only one method for improving your technical skills in mathematics is to do a lot of exercises.

    Therefore it is important for you to not skip any coursework in MATH1010, MATH1030, MATH1050.

    Also, when supplementary exercises are offered (whether they count in the assessment or not, and whether they are immediately relevant to the examination or not), treat them seriously. When you get stuck, approach the teaching assistants (or the MATHGYM) for help.

    Moreover, when your teacher asks you to `fill in the detail (for the argument of some result, or for the calculation in this example) by yourself after class', treat it as a serious task.

    Furthermore, as preparation for MATH1050 and your level-2000 MATH required courses, it will be for your own good to improve your technical skills in many topics that were covered at school but not given adequate treatment as befitted future mathematicians. To obtain some guidance, you are welcome to join the First Year Honours Scheme.

    But in the longer run, it will be your own responsibility to do more exercises to improve your technical skills. One useful source is:---

    • the past-papers of the Pure Mathematics subject in the old Hong Kong Advanced Levels Examination.

      (It is available in the Special Collections Hong Kong Government Documents on 1st Floor of the University Library.)
    Below is a (non-exhaustive) list of relevant resources that you may find useful as well:---

    • V. Litvinenko, A. Mordkovich, Solving problems in algebra and trigonometry. Mir Publishers Moscow.

      (It can be accessed here.)
    • C. J. Tranter, Techniques of mathematical analysis. English Universities Press.

      (It can be accessed here.)
    • W. Briggs, G. H. Bryan, G. Walker, The tutorial algebra, Volumes 1 and 2. University Tutorial Press.

      (Volume 1 can be accessed here. Volume 2 can be accessed here.)

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Miscellaneous matters.

  1. Question.

    I did neither Mathematics Module 1 nor Module 2 in DSE. Is there any realistic chance for me to graduate in the MATH programme? What can I do to improve my chance?

    Answer.

    The MATH programme is designed on the assumption that students admitted from DSE start with a background of at least Mathematics Module 1 or Module 2.

    According to our records, while there were Broadbase Science students with neither Module 1 nor Module 2 who successfully graduated in the MATH programme, they were rare. Moreover:---

    • they needed to put in much extra efforts in self-learning Module 2, and in drastically improving their technical skills in the first two years of their study (especially before taking MATH1010 and MATH1030);
    • (because of the need to catch up), they needed to take more time to complete the level-1000-and-2000 MATH required courses, and had to very carefully plan their study.

    Dependent on what your state of preparation is, you may have a higher or lower chance of succeeding in graduating in the MATH programme within four years.

    To have a better picture on your chances and to figure out any realistic plan, you had better contact the department for further advice.

  2. Question.

    I can afford to take at most the two courses MATH1010 and MATH1030 in first year of study. In view of the MATH recommended study pattern in CUSIS (which includes at least all of MATH1010, MATH1030, MATH1030 in the first year of study), will it jeopardize my study? Is there anything that I need to take care of in course selection in the second year of study and beyond?

    Answer.

    First of all, be aware that the timetable of MATH courses (and non-MATH courses relevant to the MATH major students) is planned with reference to the MATH recommended study pattern in CUSIS, and resources are allocated accordingly.

    For this reason, if your study pattern deviates substantially from the recommended study pattern right from the first year of study, there will be a serious risk of timeclash amongst courses which you are required to take and/or which you want to take in the second year of study and beyond. This will indirectly limit your choices of courses, and limit your opportunities, in higher years of study. Also, there will be less buffer against accidental events which delay your progress, and this will increase the risk of delaying your graduation.

    Exactly how you may select MATH courses at any stage in your higher years of study depends on the degree of your preparation at that stage. But we (again) emphasize that there is a strong hierarchical structure in the arrangement of course content across the whole MATH curriculum. Hence it would be unwise for you to just take MATH courses in a random order (for the purpose of trying to catch up in terms of the number of units taken for fulfilling MATH requirements), even if your action is not banned by CUSIS.

    • The order of level-1000 and level-2000 MATH courses is regulated by the pre-requisites and co-requisites in CUSIS, and is displayed on the first page of these charts.
    • As for level-3000-and-above MATH courses, besides what has been stated explicitly in CUSIS (in terms of pre-requisites, co-requisites, and `course advice to students'), below are a few guiding principles that may help you, though they are both simplified and non-exhaustive (for ease of understanding):---

      • For all level-3000 and level-4000 MATH courses, a background of MATH1010, MATH1030, MATH2010 is a `must', and a background of MATH2020, MATH2040 is preferrable and advantageous even if it is not a `must'.
      • For all `analysis type' courses (MATH3060, MATH3070, MATH3093, MATH4010, MATH4050, MATH4060), a background of MATH2050, MATH2060 is a `must'.
      • For all `algebra type' courses (MATH3030, MATH3040, MATH3080, MATH4080), a background of MATH2040, MATH2070 is a `must'.

    If you are unsure whether a certain MATH course is suitable for you (given what you have only done at the time), you should consult your academic advisor.

  3. Question.

    What else besides studying is expected of me in the first year of study?

    Answer.

    The most important thing is to start figuring out your overall planning. The reasons are:---

    1. You have to find out what you want to do first before deciding how you cope with the many academic and non-academic commitments.
    2. You will find that time flies by in university life. Start planning for your future now, or you will miss one chance after another chance unaware.

    The following questions may guide your overall planning:---

    1. `What do I want to do immediately after graduation? Is it study? Or research? Or Work? What kind of jobs?'
    2. `What do I want to do before graduation? Any academic/non-academic objectives? Any stream(s)? Any minor subject(s)? Double major? Exchange? Internship? Clubs and societies? College life? Part-time jobs? Have I made any plans?'
    3. `What are my commitments due to my various plans? Can I cope with the workload and the stress?'
    4. `What is my answer to the previous question for each term?'

    To be more specific with the last question:---

    • `Am I doing a lot of courses in this term? Will I be spending a lot of time on non-academic commitments in this term? Can I cope with this workload?'

    One further question needs be asked as well:---

    • `What shall I do if, one or two or three years later, I find that my entire plan does not work? Do I have any back-up plan? Do I have another option?'

  4. Question.

    I am thinking about doing research after graduation, but I am not sure whether I am good enough. How shall I plan my path?

    Answer.

    First of all, `doing research' is not restricted to `doing mathematical research in a department of mathematics'. There are many other disciplines (such as physics, economics, finance, computing) in which literacy in higher mathematics is crucial.

    So besides working hard in mathematics, broaden yourself by exploring other disciplines. If possible, develop a minor subject or even a second major.

    Be open-minded to possible `migrations to other disciplines', no matter how much you want to `stay in mathematics'. It may happen that a minor subject bridges you to your research area after graduation.

  5. Question.

    I do not plan to do research after graduation, whether in mathematics or in other disciplines. Is it very difficult for me to find work outside the education sector?

    Answer.

    This is more fiction than reality. There are jobs in industry and commerce which require very high ability in quantitative skills.

    However, candidates for such jobs will need to demonstrate not only quantitative skills but also:---

    • knowledge in other subjects (such as statistics, economics, finance, computing),
    • proficiency in language(s),
    • `previous experience' (such as internship), and
    • other social skills, possibly.

    (In fact, to find work in the education sector, you also need each of the above to some extent.)

    Again this has a lot to do with overall planning: you have a good chance in acquiring all these if you are willing to spend three years preparing.

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