FAQ's 1: First Year in MATH (applicable to students admitted to the CUHK in 2019-20 or before)

A0.1:

The best thing to do is to 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.

A1.1:

1. You are eligible for an admission scholarship as long as certain academic conditions are satisfied. There is no restriction on quota.
2. You are eligible for ‘migration’ to the MIEG programme, subject to certain conditions. (Refer to Q1.4.)
3. You will automatically graduate in the Enrichment Stream as long as you fulfil all the requirements of the stream.
4. Guidance and advice from the department begin immediately after registration. You will be assigned an academic advisor in the Department of Mathematics, to whom you may turn to for guidance.
   This includes your being assigned to special sections of MATH courses, such as MATH1010, 1030 in the  first semester, which are oriented towards the MATH programme.
   Other students are taken care of by the Science Faculty until they have declared their major subjects.
5. Being ‘anchored’ in mathematics earlier, you have a greater chance of reaching a higher level in mathematical aptitude before graduation. This indirectly increases your chances of getting scholarships, exchange opportunities, and internships. This helps if you plan to read for a higher degree in mathematics or in any mathematics-related discipline.

A1.2:

Instead of expecting you to do so and so, we suggest you finish doing, by the end of the first year of study, at least the following:

1. MATH1010 (University Mathematics), MATH1030 (Linear Algebra I), MATH1050 (Foundations of Modern Mathematics),
2. STAT1011, which is a compulsory ‘faculty package’ course for all MATH students,
3. one further ‘faculty package’ course, from amongst physics, chemistry and life sciences as specified by the Faculty of Science.

Don’t ‘lag behind’ in the other ‘common’ courses, as required by the university and your college (such as English, Chinese, IT, general education, physical education).
There are two further issues: MATH2010 and courses from other disciplines. (Refer to Q1.5 and Q1.6, Q5.3, Q5.4 respectively.)

A1.3:

A timely completion of MATH1010, 1030, 1050 is essential for a smooth development in the Enrichment Stream.

Having done all ‘faculty package’ courses in the first year allows you more flexibility in higher years. The same can be said about the other ‘common’ courses.

A1.4:

Note that there are seven places for MIEG. To be eligible for these places, you have to do ENGG1100, 1110, 2600 on top of the courses mentioned above. (Refer to Q1.2.)

If there is over-subscription for the MIEG places, admission will be decided upon your academic performance. Please let the department know your intention once you have made up your mind, so that we can provide more guidance on the planning of your study.

A1.5:

In this case, we suggest you do MATH1010, 1030 in the first semester and MATH1050 in the second semester.

If your performance in MATH1010, 1030 is satisfactory, (for example, with at least B in each course), you may also consider doing MATH2010 in the second semester.

A1.6:

We strongly suggest you take MATH1050 in the second semester, after having done both of MATH1010, 1030 in the first semester.

MATH1050 is designed for bridging you from MATH1010, 1030 to the more abstract and theoretical courses at level 2000, such as 2040, 2050, 2060, 2070. (Refer to ‘Core Courses: Calculus, Algebra and Computing’, ‘Core Courses: Mathematical Analysis’ in ‘FAQ’s 2’.) What you learn in MATH1010, 1030 will be used in doing proofs and giving rigorous reasoning, which is the focus of MATH1050.

If you have a lot of spare time in the first semester, we encourage you to enrol for the First Year Honours Scheme and spend your time preparing for it. (Refer to ‘First Year Honours Scheme’.)

A1.7:

When such a problem happens in a specific MATH course that you are taking, one very likely reason is that you have not understood some material covered earlier in the course or covered in school maths. 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 understood, rather than to be found out by the teacher after the examination.

However, if 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 advice.

A1.8:

The answer is ‘yes and no’.

Different students have different ‘mathematical background’ (for instance, Module 1 versus Module 2 in DSE Mathematics) and ‘learning curves’; such difference may be reflected in the first and second years. It is premature to make any definite assessment on your potential, based on this alone. Our experience seems to suggest that students with good potential will eventually come good as late as the finishing of the level 2000 courses, and will have no problem graduating in the Enrichment Stream.

Nevertheless, if you are struggling a lot even in the first few MATH courses and falling a lot behind many fellow Enrichment entrants, we suggest you talk with your academic advisor. (Also refer to Q1.7.)

Finally, if after the first year you realize that the Enrichment Stream is not most suitable for you, you are free to try some other stream in the MATH programme. You are not obliged to graduate in the Enrichment Stream. Don’t feel uneasy about making changes. (See ‘Streams in the MATH Programme’ in ‘FAQ’s 2’.)

A2.1:

Instead of expecting you to do so and so, we suggest you finish doing, by the end of the first year of study, at least the following:

1. MATH1010 (University Mathematics) or MATH1030 (Linear Algebra I),
2. STAT1011, which is a compulsory ‘faculty package’ course for all MATH students,
3. one further ‘faculty package’ course, from amongst physics, chemistry and life sciences as specified by the Faculty of Science.

However, it is much better if you have done both of MATH1010, 1030, rather than just one of them, by the end of the first year of study.

You are also encouraged to do MATH1050 (Foundations of Modern Mathematics) in the second semester.

Don’t ‘lag behind’ in the other ‘common’ courses, as required by the university and your college (such as English, Chinese, IT, general education, physical education).

A2.2:

A timely completion of MATH1010, 1030 is essential for a smooth progress in higher years.

Having done all ‘faculty package’ courses in the first year allows you more flexibility in higher years. The same can be said about the other ‘common’ courses.

A2.3:

No, but we strongly suggest you do all three courses in the first year, for the following reasons:

1. If you intend to graduate in the Enrichment Stream, this ensures you can progress at a reasonable pace academically in the second year and beyond. (Refer to Q2.6.)
2. If you plan to use some major units on non-MATH courses in higher years, or you plan for a minor subject or even a second major, you may need more room in your timetable from the second year onwards so that you have a better chance in accommodating both MATH and non-MATH courses. (Refer to ‘Overall Planning’.)

In either situation, this indirectly increases your chances of getting scholarships, exchange opportunities, and internships in higher years.

A2.4:

If you have taken MATH1010, 1030 in the first semester and your performance is satisfactory (for example, with at least B in each course), you may consider taking MATH2010 on top of MATH1050 in the second semester.

A2.5

We strongly suggest you take MATH1050 after you have done at least one of MATH1010, 1030 (or ideally both). If you have done only one of MATH1010, 1030 and intend to take MATH1050, please take MATH1050 simultaneously with the other of MATH1010, 1030.

MATH1050 is designed for bridging you from MATH1010, 1030 to the more abstract and theoretical courses at level 2000, such as 2040, 2050, 2060, 2070. (Refer to ‘Core Courses: Calculus, Algebra and Computing’, ‘Core Courses: Mathematical Analysis’ in ‘FAQ’s 2’.) What you learn in MATH1010, 1030 will be used in doing proofs and giving rigorous reasoning, which is the focus of MATH1050.

If you are taking MATH1010, MATH1030 in the first semester and have a lot of spare time, we encourage you to enrol for the First Year Honours Scheme and spend your time preparing for it. (Refer to ‘First Year Honours Scheme’.)

A2.6:

Once you have declared mathematics as your major subject, you are a MATH students.

All students with MATH as first major subject are treated as equals by the department, irrespective of how they have been admitted:

1. In every course, you are taught in the same way as MATH major students. We will not distinguish you from the others inside or outside the classrooms.
2. You have the same opportunities offered by the department, such as overseas exchange, internships, and higher-year scholarships. What matters is your performance after becoming a MATH student.

We offer generous admission scholarships to new students of good quality. Upon meeting certain criteria on mathematics achievement, every MATHEMATICS ENRICHMENT entrant will be awarded an admission scholarship. Moreover, we also guarantee 8 admission scholarships, based on the same criteria on academic merit, for SCIENCE BROADBASE entrants who declare major in MATH during ‘Phase I of major declaration’. Students with MATH as second major subject will be eligible to enjoy some of the privileges, at a lower priority.

A2.7:

Every MATH student is eligible to graduate in the Enrichment Stream, as long as the student fulfil all the requirements for the Enrichment Stream.

Plan your study as MATHEMATICS ENRICHMENT entrants do: make sure you have done all the basic required courses on time, so that you have enough ‘room’ to accommodate advanced courses in the third and fourth years of studies. (Refer to Q2.3, Q2.4.)

Fulfil all the requirements on the advanced courses.

For more detail refer to the section ‘Streams in the MATH Programme’ in ‘FAQ’s 2’.

A2.8:

The bottom line is do at least the other of MATH1010, 1030 in the second semester; failing to do so, you may end up delaying your progress. (See Q2.2.)

If your performance in MATH1010 or MATH1030 in the first semester is satisfactory, you may consider doing MATH1050 on top of the other of MATH1010, 1030 in the second semester. Then you will have at least done all three of MATH1010, 1030, 1050 by the end of the first year of study. (See also Q2.3, Q2.5.)

A2.9:

When such a problem happens in a specific MATH course that you are taking, one very likely reason is that you have not understood some material covered earlier in the course or covered in school maths. 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 understood, rather than to be found out by the teacher after the examination.

However, if 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 advice.

A2.10:

The answer is ‘yes and no’.

Different students have different ‘mathematical background’ (for instance, Module 1 versus Module 2 in DSE Mathematics) and ‘learning curves’; such difference may be reflected in the first and second years. It is premature to make any definite assessment on your potential, based on this alone. Our experience seems to suggest that students with good potential will eventually come good as late as the finishing of the level 2000 courses, and will have no problem graduating in MATH.

Nevertheless, if you are struggling a lot even in the first few MATH courses and falling a lot behind other first-year MATH students, we suggest you talk with your academic advisor, or to the teacher of any one MATH course you have taken. (Also refer to Q2.9.)

Finally, even though you have already declared for MATH, you are not obliged to graduate in the more mathematically demanding streams. (See ‘Streams in the MATH Programme’ in ‘FAQ’s 2’.)

A3.1:

MATH1010 is a continuation of school-level calculus, and builds up beyond what you have seen at school.

1. If you did Module 2 at school, it will do you no harm to recall what you have already learnt in calculus in Module 2.
2. If you did Module 1 at school, you may start by catching up as quickly as possible what is done in Module 2 but omitted from Module 1. Beware that there is a genuine gap between your current level of understanding and those from the Module 2 background.

A3.2:

MATH1030 picks up the miscellaneous topics ‘simultaneous equations’, ‘vector geometry’, ‘matrix algebra’ in school mathematics, and builds up the ideas and methods of basic linear algebra.

1. If you did Module 2 at school, it will do you no harm to recall what you have already learnt in these topics at school.
2. If you did Module 1 at school, you may start by catching up as quickly as possible what is done in ‘systems of linear equations’, ‘vector geometry’ and ‘matrix algebra’. Beware that there is a genuine gap between your current level of understanding and those from the Module 2 background.

A3.3:

What we state here will apply not only to MATH1010, 1030, but also to every MATH course that you will take.

1. We are teaching at a much faster pace than your school teachers.
   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.
3. We spare little time for class exercises.
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.’
   We mean it seriously!
5. There may be frequent quizzes/tests.

There is one more difference which is subtle but profound. Because you are adults (or will be adults in a few months), we will not say things like
    ‘you should attend lectures/tutorials’, ‘you should come for quizzes’, ‘you should submit homework’, ‘it is time you started preparing for the examinations’ ...
Always remember that as adults you bear the consequences of your decisions.

A3.4:

There is no single method to overcome all difficulties. Below are the starting points. (They apply to all MATH courses.)

1. Adopt an appropriate attitude and mentality. (See Q3.5.)
2. After class, review! (See Q3.8.)

A3.5:

1. Learning is acquired through both effort inside the classroom, and effort outside the classroom.
   You can’t put in any effort inside the classroom unless you are physically present for the lectures. So don’t skip MATH classes. Never let this excuse get hold of you:
       ‘because I don’t understand the lecture, it does not matter whether I attend it or not’.
   Having attended the lecture will make a difference: you will at least find out what deserves attention.
2. Don’t let this thought get hold of you:
       ‘Everyone else in the classroom looks so smart. How shameful it is to ask such a silly question, and expose the fact that I don’t understand.’
   There is nothing shameful to expose the fact that you don’t understand. Very likely your teacher expects you don’t understand this or that in the first place, because he/she as a student struggled at the same place.
   In fact, where you struggle, most other students also struggle. Most other students are no better than you. So don’t give up!
3. Mix with other MATH students. Be-friend them. Some of them can help you.
4. Know the TA’s. They are paid to help you.
5. Remember that you should regard studying as your full-time job: check whether you are putting in a sufficient amount of time both inside and outside the classroom in the first place. (See Q3.6, Q3.7, Q3.8.)

A3.6:

One way to estimate your workload is as follows:

1. Each unit of your MATH courses corresponds to a one-hour lesson and at least two hours’ study off class per week. So each three-unit MATH 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).
2. Take your first semester of the first year 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.

A3.7:

1. First of all, remember that you are a full-time student. So 40 hours of work per week is by no means harsh: you should 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.
2. Also remember that 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.
3. 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.
   

A3.8:

We emphasize (again) that the progress in the lectures tend to be very quick compared to what you have experienced at school, and that learning is acquired through both effort inside the classroom, and effort outside the classroom. (See Q3.3, Q3.5.)

For this reason, review (and preview) done outside the classroom is an integral part of your effort. (See Q3.9.)

A3.9:

1. At the start of a 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 cause distractions. (For example, switch off your phone.) Get used to sitting still and focusing on the mathematics in front of you.
3. The kind of work to be done in the sessions may vary from time to time over the whole semester. But most likely it is from amongst:
   1. doing regular exercises which count in course assessment,
   2. doing further exercises which seem not to count in course assessment,
   3. organizing what you see and hear during a lecture, possibly with help of the material supplied by the teacher,
   4. filling the detail in the arguments for various results or in the calculations in various examples that the teacher omits during a lecture,
   5. reading extra material (say, from the library,) which enriches your understanding on a certain topic,
   6. studying previous examination papers for a course,

   and so forth and so on.

4. Go through all the material for a lecture in sessions as soon after the lecture as possible, when your memory for that lecture is still fresh. Don’t let things pile up.
5. Don’t give up and don’t put off, even if initially you make little progress each time.

A3.10:

You will not learn how to play a violin by only watching musicians play the violin. You must get your hands on the violin first.

You will not learn how to play football by only watching football games. You must get yourself kicking the ball first.

The same can be said for learning mathematics.

Through doing exercises and ‘filling in detail omitted by the teacher’, you will:

1. get familiarized with the the concepts and techniques that your teacher regards to be important, and
2. discover what you are yet to understand.

We understand that it is a tough learning process, especially for beginners. But you will be well rewarded when you get used to it: working in this way you will definitely be able to keep up the pace.

A3.11:

A teacher chooses to omit some detail in the argument for a result or in the calculation for an example usually because the method or the technique involved has been used for similar results or examples covered earlier in the lecture or in the course.

If you really can’t spot the relevant method or technique, there is nothing wrong to ask the teacher where it is.

A3.12:

This line of thinking can lead to the slippery path of failing the course(s):

1. (Refer to Q3.3.) We emphasize (yet again) that we are teaching at a much faster pace than your school teachers, and as a consequence, we will move very quickly beyond what you have learnt already, both in terms of scope and content.
   So when you realize that you are in ‘unfamiliar territory’, you may have too many things to catch up.
2. 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 three hours) left before the final examination. By then it will be too late.

A3.13:

MATH1050 is designed for bridging you from MATH1010, 1030 to the more abstract and theoretical courses at level 2000, such as 2040, 2050, 2060, 2070. What you learn in MATH1010, 1030 will be used in doing proofs and giving rigorous reasoning, which is the focus of MATH1050.

You are going to do MATH1050 in the second semester of the first year of study. The best preparation for MATH1050 is: work hard in the first semester, and adapt to the way of learning mathematics here. (See Q3.5, Q3.8, Q3.9.)

In MATH1010, 1030, there may be more emphasis on ‘concrete computations’ than on ‘theoretical discussions’, but the latter will not disappear altogether. Put in some extra effort on following the ‘theoretical discussions’given by the teachers in MATH1010, 1030 whenever you hear something like:
    ‘There is no need to worry about it if you are not going to be a MATH major student ...’
This effort will pay off when ‘theoretical discussions’ will become more and more dominant in ‘proof-type’ courses, starting from MATH1050.

A3.14:

We suggest you make better use of these spared units, for example, exploring other disciplines by taking courses offered by other departments.

1. When you take courses in mathematics-related disciplines, you will see how the mathematics you learn here will be used in other disciplines. This may become a starting point for your minor subject, your second major subject, or your postgraduate degree, or your future career.
2. When you take language courses (French, German, Italian, Spanish, Russian, Japanese, Korean, or even Greek, Latin), you will learn a new language which may not only enrich your life, but also (at a more pragmatic level) open up new opportunities in the university life or in your future worklife. Knowledge in a second European language will also help improve your English.
3. When you take non-mathematics-related courses or general education courses, you will broaden your horizon. This in turn may un-expectedly help you after graduation (for instance, in job interviews).

So don’t be stuck with MATH courses alone.

A3.15:

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 you stand to gain no advantage by simply doing things earlier than others, if you are academically not prepared.

And you can certainly make good use of your time by participating in the First Year Honours Scheme. (Refer to ‘First Year Honours Scheme’.)

A3.16:

1. You may drop a course prior to the deadline of the add-drop period. For regular semesters, this is likely to be the end of the office hours of the Friday of Week 3.
2. In normal circumstances, 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 on study, and probably sacrifice some of your non-academic commitments. NO LATE-DROP FOR GPA REASONS.
3. However, if it is due to some other reasons (such as family, health) that you cannot cope with study, do not hesitate to talk with us and/or your academic advisor. It is better for you and your teachers to plan a solution together rather than for you alone to confront the difficulties.

A4.1

Since 2015, the department has set up the First Year Honours Scheme for the freshmen of each year. We hope that through this scheme, we will:

1. help first-year students prepare for MATH courses at the 2000 level, and
2. enhance an atmosphere that promotes the discussion of mathematics within the department.

All first-year students who will become a MATH major student by the end of academic year are eligible for this scheme.

Various learning activities (such as lectures and workshops) associated with the scheme will be arranged throughout the academic year.

There will be a test in May most probably; this covers the content of MATH 1010, 1030, 1050, as well as questions similar to those that appeared in past HKALE Pure Mathematics examinations.

A4.2

The answer is ‘yes and no’.

Since the commencement of the new curriculum in 2012, many MATH students have encountered the same problem in its various disguise, such as:

• ‘I am told that the topic so-and-so is “school mathematics” and I am assumed to know it well. But it was definitely not covered at school.’
• ‘I am aware that the topic so-and-so was indeed covered at school. But I never expect that it would be applied in this context.’
• ‘I am given the definitions and “basic results” on the topic so-and-so and then assumed to have understood the topic thoroughly. But when I look at some “school mathematics” textbooks for the old curriculum, I realize that were this topic covered at school, it would have spanned several weeks.’

In terms of content, the ‘school mathematics’ that these students (and probably you) have missed is:

1. for students with neither Module 1 nor Module 2, the whole of additional mathematics and the whole of pure mathematics;
2. for students with Module 1, much of additional mathematics and almost the whole of pure mathematics;
3. for students with Module 2, bits and parts of additional mathematics and much of pure mathematics.

But most importantly, these students (and probably you) have lacked the skills and techniques, and the experience in applying them, that can only be acquired by doing exercises in ‘school mathematics’.

The First Year Honours Scheme is where you will receive help in learning the ‘school mathematics’ that you have missed at school.

A4.3

A study has been undertaken to assess the effectiveness of the Scheme on students admitted in 2016-17 (who have by now completed two years of study).

The preliminary results seem to suggest:

• If Student A and Student B performed similarly in MATH1010, 1030, 1050, but Student A had participated in the Scheme whereas Student B had not, Student A would outperform Student B by half a sub-grade in the level-2000 courses.

A4.4

No, this is entirely voluntary, but the scheme is designed to help first-year MATH students build a more solid foundation on which they will succeed in MATH courses at 2000 level (and beyond).

A4.5

Although it is called an ‘honours scheme’, we expect most (if not all) first-year MATH students to participate. We hope that regardless of your mathematical background, you will all learn something through participationm in this scheme.

A5.1

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.

A5.2

The following four general 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?’

A5.3

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.

A5.4

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 to demonstrate not only quantitative skills but also

1. knowledge in other subjects (such as statistics, economics, finance, computing),
2. proficiency in language(s),
3. ‘previous experience’ (such as internship), and
4. 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.