# MATH Requirements in the MATH Major Programme for Broadbase Science entrants 2022

### Table of content.

- Official sources of information.
- Purpose of this page.
- First-year MATH required courses, and Honours Course options.
- MATH required courses beyond the First Year of Study.

### Official sources of information.

Every two or three years the requirements of MATH programme are revised. When you have a question concerned with study, you had better seek an official answer.

(Do not rely on hear-say: what the senior students tell you may or may not be applicable in your situation. This is especially important to you as you are in the first cohort to which the new University Core Curriculum applies.)

Below are the reliable sources of information.

**CUSIS.**The MATH study scheme and the information in the catalogue of MATH courses in CUSIS are official documents. They are what you can definitely rely upon.

**Department Homepage.**General information of the MATH major programme can be found at the homepage of the Department of Mathematics.

**Academic advisor, and course teachers.**Once you have declared for MATH or for potential major in MATH, you will be assigned an academic advisor in the Department of Mathematics.

When you have questions about the MATH programme, you may approach your academic advisor or your course teachers for help. They can at least re-direct you to the right persons who can answer your questions.

**Email enquiries.**If you have some very specific questions about the MATH programme and you can't find any answer in the CUSIS or the department homepage, you may write to the department.

Use your CWEM address. Include your name and your student ID. A clear subject title will help us identify your problem and is certainly welcome.

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### Purpose of this page.

The information in this page is meant to provide a summary of the ** basic requirements in MATH courses** (alongside key options within the requirements), leading towards graduation in the MATH programme, common to all MATH students. Such requirements as stated here are what you must take into account when you plan your study.

It is NOT the purpose of this page to give you any tailor-made advice on what is most * desirable* or most * preferrable* in the planning for your specific situation.

In fact, we understand that the specific plans of our students may vary according to the academic background, the needs and the goals of the individual students.

Therefore, to draw up a study plan which is most suitable to you, you are advised to use the information provided by this page as a basis for your plan, and to check the study scheme and the course lists in CUSIS to see whether your plan is workable.

When you are unsure whether certain detail in your plan will work out at all, you are always welcome to consult your academic advisor (but `not at the last minute'), to talk with your course teachers, or to write to the department.

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### First-year MATH required courses, and Honours Course options.

Below is the optimal pattern of **MATH required courses** for the **first year of study** leading towards a **MATH major** degree. It is expected^{(a1)} to be followed by most Broadbase Science students who intend to graduate in MATH.

Term of study | Course Code | Course Title | Number of units |
---|---|---|---|

Term 1 (First Semester) | MATH1010^{(a3)} |
University Mathematics | 3 units |

Term 1 (First Semester) | MATH1030 | Linear Algebra I | 3 units |

Term 2 (Second Semester)^{(a4)} |
MATH1050^{(a3)} |
Foundation of Modern Mathematics | 3 units |

Term 2 (Second Semester)^{(a4)} |
MATH2010^{(a2)} |
Advanced Calculus I | 3 units |

Remarks.

- (a1)
**Expected pace of progress: MATH1010, MATH1030, MATH1050.**MATH first-year students are expected to have taken at least all of MATH1010, MATH1030 in the first semester, and at least MATH1050 in the second semester, for a reasonable progress in the MATH programme in higher years.

- (a2)
**MATH2010.**If you plan to graduate in streams which are more demanding in mathematics (such as the

*Enrichment Stream*), you should consider taking MATH2010 in the Second Semester. - (a3)
**Special roles of MATH1010, MATH1050.**MATH1010 is a pre-requisite for MATH1050 and for MATH2010.

Without having passed MATH1010, you can take neither MATH1050 nor MATH2010.

MATH1050 is a pre-requisite for several `proof-type' required courses in MATH programme, namely MATH2040, MATH2050, MATH2070. If you do not take MATH1050 in the Second Semester, you may end up delaying your completion of the MATH major requirement.

- (a4)
**Stars stream.**Students interested in the STARS stream may consider taking STAR courses in the second semester; for more information, contact the faculty.

If you have already made up your mind to declare for MATH and satisfy certain eligibility conditions, you may opt to replace MATH1010, MATH1030, MATH1050, MATH2010 with the respective ** Honours Courses** MATH1018^{(a5)}, MATH1038^{(a5)}, MATH1058^{(a6)}, MATH2018^{(a6)}, which are designed for MATH students with good abilities and with prospective further studies in mind:

Term of study | Course Code | Course Title | Number of units |
---|---|---|---|

Term 1 (First Semester) | MATH1018 | Honours University Mathematics | 3 units |

Term 1 (First Semester) | MATH1038 | Honours Linear Algebra I | 3 units |

Term 2 (Second Semester) | MATH1058 | Honours Foundation of Modern Mathematics | 3 units |

Term 2 (Second Semester) | MATH2018 | Honours Advanced Calculus I | 3 units |

Remarks.

- (a5)
**Eligibility for the First Semester Honours Courses MATH1018, MATH1038.**If you have obtained 5** or 5* in Mathematics Module 2 or 90% or above in Gaokao mathematics subject, you may apply for a place in MATH1018, MATH1038.

*Mathematics Enrichment*entrants are pre-assigned to the Honours Courses MATH1018, MATH1038 in the first semester. - (a6)
**Eligibility for the Second Semester Honours Courses MATH1058, MATH2018.**If you take MATH1018, MATH1038 in the first semester, you may continue with MATH1058 and MATH2018 in the second semester as long as you have obtained B- or above in MATH1018 and MATH1038.

If you take MATH1010, MATH1030 in the first semester, you may apply for a place in MATH1058, MATH2018 as long as you have obtained A- or above in MATH1010 and MATH1030.

More information on the Honours Courses can be found here.

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### MATH required courses beyond the First Year of Study.

Below is the list of ** MATH required courses ** at level-2000 or above, ** common to all MATH major students**, ** irrespective of the streams**^{(b1)} in which they graduate.

Optimal term(s) of study^{(b2)} |
Course Code | Course Title | Number of units |
---|---|---|---|

Term 2 or 3 | MATH2010^{(b3)}^{(b7)} |
Advanced Calculus I | 3 units |

Term 3 or 4 | MATH2020^{(b3)}^{(b7)} |
Advanced Calculus II | 3 units |

Term 4 or 5 or 6 | MATH2230^{(b3)} |
Complex Variables with Applications | 3 units |

Term 3 or 4 | MATH2040^{(b7)} |
Linear Algebra II | 3 units |

Term 3 or 4 or 5 or 6 | MATH2070^{(b7)} |
Algebraic Structures | 3 units |

Term 4 or 6 | MATH2221^{(b4)} |
Mathematical Laboratory II | 2 units |

Term 3 or 4 or 5 | MATH2050^{(b3)}^{(b7)} |
Mathematical Analysis I | 3 units |

Term 4 or 6 | MATH2060^{(b3)}^{(b4)}^{(b7)} |
Mathematical Analysis II | 3 units |

Third or fourth year | MATH3060^{(b5)} |
Msthematical Analysis III | 3 units |

Final Year | MATH4400/MATH4900^{(b3)}^{(b6)} |
Project/Seminar | 3 units |

Remarks.

- (b1)
**Streams and elective courses for streams.**Every MATH students will graduate in one of the streams below:

- Enrichment Stream.
^{(b8)} - Enrichment and Computational and Applied Mathematics Stream.
^{(b8)} - Computational and Applied Mathematics Stream.
- Computational Big Data Analytics Stream.
- Mathematics Stream.
- Mathematics-Education Stream.
- Mathematics-Multidisciplinary Stream.

For each stream, there will be some specific stream requirements. They usually translate into the taking of a further 27 units of courses, as specified for that stream. For some streams, however, there may be some special requirements on major GPA.

You are required to declare your stream to the Department at least several months before you graduate.

For more detail on the various streams, including the specific requirements for each stream, consult the study scheme in CUSIS.

- Enrichment Stream.
- (b2)
**Optimal term(s) of study.**The time frame suggested by this list is of

*advisory*nature only, based on the progress of the average MATH student, and the course offering pattern of the department in the recent past. The latter may change by the time you are in the higher years of study.In principle you may take any one of these MATH required courses after you have satisfied the respective pre-requisites and co-requisites for the course.

However, be careful when you plan to take any specific course in this list:

- If you take the course too early, you may be mathematically not sufficiently prepared for it. As a consequence, you may fail to gain maximum benefit from the course, and your academic result may suffer.
- If you take the course too late, you run the risk of delaying your overall progress. In the worst scenario you might end up delaying your graduation. Moreover, your options for advanced courses may become more limited, because those advanced courses could assume background knowledge in that particular course, or even require that particular course as pre-requisite.

- (b3)
**Pre-requisite matters.**MATH2010 is a pre-requisite for MATH2020; MATH2020 is a pre-requisite for MATH2230.

MATH2050 is a pre-requisite for MATH2060 and for MATH4900.

Be aware that you will not be allowed to take a course unless you have fulfilled the pre-requisite for that course.

Take into account of the above, or you will risk delaying graduation.

- (b4)
**Course offering pattern for MATH2060, MATH2221.**MATH2060, MATH2221 are likely to be offered in the Second Semester only.

- (b5)
**Mathematical Analysis III and its alternatives.**For the purpose of fulfilling graduation requirements, MATH3060 may be replaced by STAT2001 or STAT2006.

MATH3060 is a continuation of MATH2060/2068, and it is usually offered in the First Semester only.

- (b6)
**Capstone courses: MATH4400, MATH4900.**You are required, and allowed, to take only one of MATH4400, MATH4900.

Most students are expected to take MATH4900, and are expected to do so in Term 7.

- (b7)
**MATH Honours Courses beyond the First Year of Study.**While you are not obliged to take Honours courses in order to graduate in the MATH programme, you are encouraged to do so if you intend to acquire a wider and deeper understanding in mathematics, and if you want to reap the full benefits of the

*Enrichment Stream*or the*Enrichment and Computational and Applied Mathematics Stream*.Under the assumption that you have taken MATH1050/MATH1058 and MATH2010/MATH2018 in your first year of study, the tentative schedule for the offering of the Honours Courses during your second year of study will be:

Term of study Course Code Course Title Number of units Term 3 MATH2028 Honours Advanced Calculus II 3 units Term 3 MATH2048 Honours Linear Algebra II 3 units Term 3 MATH2058 Honours Mathematical Analysis I 3 units Term 4 MATH2068 Honours Mathematical Analysis II 3 units Term 4 MATH2078 Honours Algebraic Structures 3 units There is a pre-requisite for each such Honours course, in the form `B- or above' in a group of Honours courses that you should have taken. In any case, if you are not taking an Honours course, you can still take its non-Honours counterpart to fulfil graduation requirement.

- (b8)
**Pre-requisites for advanced pure maths courses.**A timely completion of MATH2050/2058, MATH2060/2068, MATH2070/2078, MATH2230 will allow for more flexibility in course selection for the fulfilment of the Enrichment Stream requirements. The reason is that the pre-requisites for various electives for this stream, such as MATH3040, MATH3070, MATH4010, MATH4050, MATH4060, MATH4080, involve MATH2050 or MATH2058, MATH2060 or MATH2068, MATH2070 or MATH2078, MATH2230, MATH3030, MATH3060.

The first chart here summarizes the MATH major requirements, with the arrows indicating the relations between the various parts of the requirements, and the parenthesis indicating the specific terms for certain required courses to be completed. The other charts provide the `road-maps' for sample streams.