# Academic Advice

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

Mathematician John Horton Conway caught on von Neumann's idea of a self-replicating machine, and came up with the Game of Life, a zero-player game which generates wonderfully diverse patterns determined only by its initial state.

Similarly, everyone begins university life with different initial states. In this set of FAQ's, our faculty members give suggestions on concerns MATH students may have, based on their up-to-date understanding of CUHK and university studies. To follow our guidance takes away some of the fear, uncertainty and decision fatigue you may face in CUHK MATH's Game of Life.

CUHK MATH is a family. We encourage excellence, yet we respect each individual's choice to stray from the "safe side" – after counting the cost, of course.

More importantly, we have been restructuring the MATH and MIEG programmes since the new curriculum launched in 2012. The "oral traditions" of senior students, old or new curriculum, may or may not apply to you. Remember that we’re in the Game of Life, and senior students' initial states differed much more than yours. Therefore, before adopting "oral tradition"-based solutions, think twice.

Always pursue official answers to questions about the curriculum or university regulations. **Avoid hearsay.**

0. Enquiry

A0.1:

The best thing to do is send your enquiry to dept@math.cuhk.edu.hk. Your question will reach the person(s) in the department who can give you the official answer. Use your CWEM address; otherwise there is no guarantee that your question reaches us and our answer reaches you.

A0.2:

Include your identity information: your name and your student ID. If you use the CWEM, you give the proof of your identity (so that we know it is not an impersonator). A clear subject title will help us identify your problem and is certainly welcome.

1. First Year

2. Other Questions that may concern First-year Students

A2.1:

We suggest you make use of these spared units to explore other disciplines. This can be a starting point for your future career. (Refer to Q4.3, Q4.4.)

A2.2:

We understand that some of you may have prior exposure in mathematics beyond the school level (through, for instance, EPYMT or programmes in the HKUST, IMO, HKAGE ...). What we provide in our curriculum is an opportunity for you to not only fill in the gaps in your mathematical knowledge, but also to acquire a broader, deeper and more systematic perspective in mathematics.

We encourage you to follow the suggested pattern of Enrichment Mathematics as other students, but spend your time and effort on harder problems and deeper understanding. This gives you a solid preparation for advanced courses. Remember that starting early is no advantage if you are not prepared academically.

A2.3:

Like a headache or a fever, this kind of problems could have one or more reasons.

- When such a problem happens in a specific MATH course that you are taking, one very likely reason is that you have not learnt some material covered earlier in the course or covered in an earlier course. In such a situation, the most obvious thing to do is talk with the teacher of the course and/or the teaching assistant(s). It is better for you to discover in this way what you have not learnt, rather than to be found out by the teacher after the examination.
- When such a problem happens in a whole range of MATH courses, it could be something more serious. You can also talk with any (or every) one of the teachers of the courses and/or your academic advisor. Very likely one (or many) of them can give you the right 'diagnosis', and offer you some useful advise.

Suffering alone cannot solve your problems. So don't suffer alone.

A2.4:

Yes, for example, there is also the Computational and Applied Mathematics (CAM) Stream. For more details, refer to the curriculum document which applies to you.

Each stream has its own specific graduation requirements. For example, you have to do a specific computer science course if you want to graduate in the CAM stream. (Refer to Q5.2.)

A2.5:

As long as you fulfil the specific graduation requirements of a stream, you may graduate in that stream. So you may graduate in both Enrichment and CAM Streams if you fulfil the specific graduation requirements of both streams simultaneously. In fact, every year some students achieve this feat. But you have to plan ahead. (Refer to 'Overall Planning'.)

3. Workload and University Life

A3.1:

Yes, you will find many differences. Here we emphasize two of them:

- We are teaching at a much faster pace than your school teachers. Compared to your school teachers, we spare little time for class exercises.
- There are frequent quizzes/tests.

We expect you to do a lot of work both before and after class (not to mention during class) to keep up the pace. If you fall behind a lot very early, it is unlikely that you can make it up later.

A3.2:

One way to estimate your workload is as follows:

- Each unit of your major courses corresponds to a one-hour lesson and at least two hours' study off class per week. So each three-unit major course corresponds to a workload of ten hours per week (three hours for lectures, one hour for tutorial, and six hours for study off class).
- Take your first semester as an example. If you are doing MATH1010, MATH1030 simultaneously, you will have a workload of twenty hours per week. This is half of the amount of time you stayed at school as a school student every week. It is very likely that you will have a workload of forty hours per week if you take into account of your other courses.

A3.3:

- Remember that you are a full-time student. So 40 hours of work per week is by no means harsh: you may regard studying as your full-time job. It is only after the fulfilment of the duty in this full-time job, that you may consider your other activities.
- University is a place dedicated to intellectual pursuit. Whereas you can make all kinds of pursuits in other places for the rest of your life, you will hardly find another place where you can make intellectual pursuit.
- With careful planning and time-management, you can definitely enjoy a colourful university life. It is easier said than done: past experience suggests that students tend to under-estimate the workload and the stress in the first year, when they are still adjusting to university life. But ultimately it is your responsibility to find a balance between academic and non-academic commitments.

A3.4:

- Not only do we teach at a faster pace than your school teacher, but we also go deeper when covering material which seems to overlap with school mathematics. So when you realize that you are in 'unfamiliar territory' after half a course, you may have too many things to catch up.
- Experience suggests that a student who claims he/she will start after one month will most likely not start until there are only three days (if not hours) left before the final examination. By then it will be too late.

A3.5:

Normally we do not allow a student to drop a course after the deadline of the add-drop period. If you find that you have 'overstretched' yourself, all you can (and should) do is to re-adjust yourself: spend more time in your academic commitments, and probably sacrifice some of your non-academic commitments.

However, if it is due to some other reasons (such as family, health) that you cannot cope with your academic commitments, do not hesitate to talk with us. It is better for us to plan a solution together rather than for you alone to confront the difficulties.

4. Overall Planning

A4.1:

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

- You have to find out what you want to do first before deciding how you cope with the many academic and non-academic commitments.
- 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.

A4.2:

The following four general questions may guide your overall planning:

*'What do I want to do immediately after graduation? Study/research? Work? What kind of jobs?'**'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?'**'What are my commitments due to my various plans? Can I cope with the workload and the stress?'**'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?'*

A4.3:

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.

A4.4:

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 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 teaching 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.

5. Mathematics Courses beyond the First Year

A5.1:

The following courses at level 2000 are compulsory for all MATH students:

- MATH2010, 2020 (Advanced Calculus I, II),
- MATH2040 (Linear Algebra II),
- MATH2070 (Algebraic Structures),
- MATH2221 (Mathematics Laboratory),
- MATH2230 (Complex Variables with Applications),
- MATH2050, 2060 (Mathematical Analysis I, II).

To graduate with a degree in mathematics, you will be required to take several 'advanced courses' in mathemat- ics at level 3000 or above, together with a 'capstone course' in your final year. The pool of required 'advanced courses' may vary from one student to another, depending on the stream in which you want to graduate.

A5.2:

The answer is yes and no, depending on your progress and overall planning.

- By the end of the second year of study, we expect you to have done MATH1010, 1030, 1050, 2010, 2020, 2040, and at least one of MATH2070, 2230.
- If you want to graduate in the the Computational and Applied Mathematics Stream, we expect you to have done MATH2221 and CSCI1540 by the end of the second year of study.

We will discuss MATH2050, 2060 later. (Refer to 'Mathematical Analysis'.)

A5.3:

- MATH2010, 2020 may be done in two semesters, the former preceding the latter, after you have done MATH1010.
- MATH2230 may be done concurrently with, or subsequent to, MATH2020.
- MATH2040 may be done after you have done MATH1030 and MATH1050.
- It is slightly better to do MATH2070 concurrently with, or subsequent to, MATH2040, as long as you have done MATH1030 and MATH1050.

A5.4:

- MATH1010, 2010, 2020 are 'one story' covering calculus of one or several real variables.

MATH1030, 2040 are 'one story' covering linear algebra.

These courses provide the common background knowledge for all advanced courses. - MATH2230 covers basic topics in complex variables, and may be regarded as a continuation of calculus of real variables. MATH2070 covers basic topics in modern abstract algebra, and may be regarded as a course 'parallel' to MATH2040.

6. Mathematical Analysis

A6.1:

MATH2050, 2060 cover elementary topics in analysis. Students tend to find these two courses more challenging than the other required courses. These two courses appear to be 'furthest away' from school mathematics, in terms of both content and approach.

The following may give you an idea of the difficulty level: in recent years even students who had obtained A in Advanced Level Pure Mathematics faced difficulties with MATH2050. It often takes much more effort to get used to MATH2050 than the other required courses.

It is crucial that you reserve enough time for it when you take on these courses. This brings you to the question of your overall planning. (Refer to 'Overall Planning'.)

A6.2:

MATH2050, 2060 may be done within the second or third year of study.

- Many advanced courses may be done concurrently with MATH2050, 2060. Therefore you are not obliged to do MATH2050, 2060 in the second year.
- A few advanced courses, such as MATH3060, 3070, 4010, 4050, 4060 require a strong background in analysis. You may think of MATH2050, 2060 as pre-requisites de facto for such courses.

A6.3:

The two factors below may help you decide which term is better for you to take MATH2050:

- your overall planning,
- your mathematical preparedness. (See Q7.4.)

If a student has a reasonable grasp of the material covered in MATH2050, he/she will not have any serious problems with MATH2060. So it is important that you take on MATH2050 seriously.

A6.4:

There is no easy answer to this question. Your answers to the following questions may serve as indicators:

*'What is my overall performance in MATH1010, 1030, 1050 and possibly MATH2010?'**'Was I concerned with calculations alone, ignoring theoretical considerations almost altogether, when I was doing other required courses? Was I comfortable when the teachers talked about things that classmates regarded to be "too abstract"?'**'Did I have any revisions during the summer following the first year of study?'*

A6.5:

If you are going to do MATH2050 in the third year, you may ask yourself the following questions:

*'Will I be much better prepared to do MATH2050 in the third year?'**'Have I planned for doing MATH2050, 2060 in the third year?'*

A6.6:

The best possible preparation for MATH2050 is:

- Work hard in the other required courses in the first and second years of study.
- If time permits, sit in the lectures and tutorials of MATH2050 and do the homework.
- Make good use of the summer following the second year, putting MATH2050 as the top priority amongst other activities.

A6.7:

- Plan ahead the advanced courses for the third and fourth years, and think of any suitable summer courses. This is necessary because you may be doing more MATH courses each term on average than your class- mates.
- Try to make use of the spared units in the second year to explore other disciplines and to develop a minor degree. (Refer to Q4.3, Q4.4.)

A6.8:

Be aware that you need have passed both MATH2050, 2060 by the penultimate year of study (which is the third year for most students). The reason is that you need take the 'capstone' course in your final year of study in order to fulfil graduation requirement, and MATH2050, 2060 is a pre-requisite for the 'capstone' course. So postponing MATH2050 (and MATH2060) beyond the third year of study may result in delay in graduation.