# Higher Years in MATH

#### First Year in MATH

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.**

#### This is meant to be a continuation of ‘FAQ’s 1: First year in MATH’.

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. Core MATH Courses beyond the First Year

A1.1:

The courses below 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).

Together with MATH1010, 1030, 1050, these MATH courses at level 2000 can be regarded as the ‘core’ of the curriculum of the MATH programme. Most of the ‘advanced courses’ in mathematics (MATH courses at level 3000 or above) presume background in one or several (or even all) of these courses.

To graduate in the MATH programme, you will be required to take a number of MATH courses at level 3000 or above, including the ‘Capstone’ course. The pool of these courses may vary from one student to another, depending on the stream in which you want to graduate. (See ‘Capstone Courses’, ‘Streams in the MATH Programme’.)

A1.2:

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. A few advanced courses may require a strong background in specific level 2000 courses. (For instance, if you take MATH3030, you may be assumed to have learnt everything covered in MATH2070, whether you have formally the latter or not.)
- 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’.)

A1.3:

The optimal arrangement is described below:

- MATH2010, 2020 may be done in two semesters, the former preceding the latter, after you have done MATH1010 and MATH1030.
- MATH2230 may be done after you have done 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.

A1.4:

- 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 and skills for all ‘advanced courses’ in mathematics. - 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.

A1.5:

In many cases any such change, even if allowed by CUSIS, is not
desirable in light of rationale behind this arrangement.

Also note that some
change you have in mind may be forbidden by the CUSIS straightaway. For
instance, MATH2010 is a pre-requisite for MATH2020, and MATH2020 is a
pre-requisite for MATH2230. So to take MATH2230 in a certain semester, your
CUSIS record must indicate a pass grade in MATH2020 prior to the beginning of
that semester; otherwise you will be automatically dropped from MATH2230 even
though you have successfully registered for a place in MATH2230 through CUSIS.

2.Mathematical Analysis

A2.1:

MATH2050, 2060 cover elementary topics in mathematical analysis.

- MATH2050 covers the theory of limits and continuity.
- MATH2060 is a continuation of MATH2050: it covers the respective theories of differentiation and integration, and the theory of uniform convergence.

Note that MATH2050 is a pre-requisite for MATH2060. To take MATH2060 in a certain semester, your CUSIS record must indicate a pass grade in MATH2050 prior to the beginning of that semester; otherwise you will be automatically dropped from MATH2060 even though you have successfully registered for a place in MATH2060 through CUSIS.

A2.2:

Indeed students tend to find these two courses more challenging than the other core MATH courses. These two courses appear to be ‘furthest away’ from school mathematics, in terms of both content and approach.

This may give you an idea of the difficulty level. Students who have comfortably passed (say, in B range) in other core MATH courses may struggle in MATH2050. Most of them find that a much greater effort, applied consistently throughout the semester, is needed in getting used to MATH2050, in contrast to the other core MATH courses.

It is crucial that you reserve enough time for it when you take on MATH2050, 2060. This brings you to the question of your overall planning. (Refer to ‘Overall Planning’ in ‘FAQ’s 1’.)

A2.3:

They may be done within the second or third year of study, but the exact timing depends on whether you are ready to take the courses.

- Many advanced courses may be done concurrently with MATH2050, 2060. Therefore you are not obliged to complete MATH2050, 2060 in the second year, if you are not ready for them.
- A few advanced courses, such as MATH3060, 3070, 3093, 4010, 4050, 4060 require a strong background in analysis. You may think of MATH2050, 2060 as pre-requisites de facto for such courses.

A2.4:

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

- your overall planning,
- your mathematical preparedness. (See Q2.5.)

If a student can handle MATH2050 comfortably, it is unlikely that he/she will run into trouble with MATH2060. So it is important that you take on MATH2050 seriously.

A2.5

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 are regarded by fellow classmates to be “very abstract”?’
- ‘Did I participate in the First Year Honours Scheme? Did I seriously prepare for the test of the First Year Honours Scheme? How did I perform?’
- ‘Did I do any revisions during the summer following the first year of study?’

A2.6:

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?’

A2.7:

The best possible preparation for MATH2050 is:

- Work hard in the other core MATH courses in the first and second years of study:
- Ideas directly related to the course content of MATH2050, 2060 may often come up in MATH2010, 2020, 2230.
- Although MATH2040, 2070 seem to have little do with MATH2050, 2060 in terms of content, these courses will help you get used to the more formal and theoretical aspects of the latter.

- Participate in the First Year Honours Scheme.
- During the second year, 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.

A2.8:

- 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 classmates.
- Try to make use of the spared units in the second year to explore other disciplines and to develop a minor degree. (Refer to Q5.3, Q5.4 in ‘FAQ’s 1’.)

A2.9:

A2.9:

Be aware that MATH2050 is a pre-requisite for:

- MATH2060, and
- the ‘Capstone’ course.

Both courses are part of the graduation requirement for the MATH programme.

For this reason, postponing MATH2050 beyond the third year of study is very risky; you may end up delaying graduation. (See ‘Capstone courses’.)

3. Streams in the MATH programme

For the official description of each stream, refer to the CUSIS.

For a more down-to-earth description, you may visit http://www.math.cuhk.edu.hk/undergraduates/streams

Our purpose here is to provide some reminders which are not on the curriculum level but nonetheless need be taken care of when you plan the courses.

A3.1:

These are the streams available to you in the MATH programme:

- Enrichment Stream,
- Computational and Applied Mathematics Stream,
- Mathematics Stream,
- Mathematics-Education Stream,
- Mathematics-Multidisciplinary Stream
- Computational Big Data Analytics Stream (available for students admitted in the academic year 2018-19 or after).

Students who fulfill the respective requirements of both the Enrichment Stream and Computational and Applied Mathematics Stream may graduate with the ‘double stream’.

Furthermore, for those students admitted in the academic year 2017-18 or after, the STARS stream is available. As the STARS stream is administered by the Faculty of Science, any enquiry on this stream should be referred to the Faculty.

A3.2:

- One key requirement for graduation in the Enrichment Stream is MATH3060 (Mathematical Analysis III). It is a continuation of MATH2050, 2060. This course is likely to be offered in the first semester only.
- Several ‘advanced courses’ which count as electives for the Enrichment Stream, such as MATH3040, MATH4080, MATH3093, MATH4060, are likely to be offered in alternate years.
- For students not admitted as Enrichment Mathematics entrants, there is a minimal GPA qualification for the Enrichment Stream.

A3.3:

CSCI1540 is a required course for the Computational and Applied Mathematics Stream. It is likely to be offered in the first semester only.

A3.4:

BMED3011 is the pre-requisite for all other BMED courses. This is likely to be offered in the second semester only.

A3.5:

CSCI1540, which is likely to be offered in the first semester only, is a pre-requisite of the required course MATH3330 for the Computational Big Data Analytics Stream. The latter will in turn be a pre-requisite of the required course MATH4280.

4. Capstone Courses

Our purpose here is to give you an overall picture on the capstone course arrangements. You may find the detail about the current academic year in the department homepage:

https://www.math.cuhk.edu.hk/undergraduates/

capstone-course-arrangements

The precise arrangements for any specific academic year will likely be announced very soon after the Second Semester examinations for the previous academic year.

A4.1

In order to graduate as a MATH major, you must pass either one of:

- MATH4900 (Seminar),
- MATH4400 (Project).

They are the ‘Capstone’ courses in the MATH programme. Note these points as well:

- These two courses are mutually exclusive: having taken either course you will be barred from taking the other.
- MATH2050 is a pre-requisite for MATH4900. You will not be allowed to take MATH4900 until you have passed MATH2050.
- As for MATH4400, refer to Q4.3.

A4.2

Most MATH students are expected to use MATH4900 as their ‘Capstone’ courses, and to take the course in the first semester of the final year of study. For this reason, you are expected to have passed MATH2050 by the end of the third year of study. (See Q2.8, Q2.9.)

If, for whatever reason, you are deviating from the above pattern, you will likely be required to go through some special application process.

A4.3

MATH4400 is intended for MATH students who have strong potential for doing research in mathematics.

To be allowed to take MATH4400, you need fulfill certain conditions in terms of your major GPA. Moreover, you must find a teacher who is willing to supervise you in this course.

It is likely that you need submit the application to the department (which includes obtaining consent from your potential supervisor) during the summer prior to the academic year in which you take MATH4400.

As it may take some time for the teacher to know sufficiently about you to decide whether to supervise you or not, you need start the planning (for example, looking for an area of study, approaching potential supervisor) even earlier. (Refer to ‘Overall planning’ in ‘FAQ’s 1’.)

Last updated: August 2018