MATH Requirements in the MATH Major Programme for Broadbase Science entrants 2025

Last updated: July 2025.

Table of content.

Official sources of information.

A major revision of the curriculum of the MATH programme has taken place in 2025, and the revised curriculum is applicable to all students admitted to the CUHK in 2025-26.

For this reason, do not rely on hear-say: what the senior students tell you may or may not be applicable in your situation.

When you have a question concerned with study, you had better seek an official answer.

Below are the reliable sources of information.

  1. 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.

  2. Department Homepage.

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

  3. 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.

  4. 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.

    When you write to the department, use your OnePass address. Also include your name and your student ID. A clear subject title will help the department identify your problem and is certainly welcome.

Back to Content

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.

Reminders.

  1. The information presented in this page is based on the assumption that you are adhering to the instructions and advice regarding a timely progress in the fulfilment of university-, faculty-level and college-level requirements.

  2. 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
    • 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'), and/or
    • talk with your course teachers, and/or
    • to write to the department.

Back to Content

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

Table (A1) gives the pattern of MATH required courses for the first year of study leading towards a MATH major degree.

Table (A1).

Term of study Course Code Course Title Number of units
Term 1 (First Semester) MATH1010 University Mathematics 3 units
Term 1 (First Semester) MATH1025 Essential Mathematical Methods 3 units
Term 2 (Second Semester) MATH1030 Linear Algebra I 3 units
Term 2 (Second Semester) MATH1090 Introduction to Set Theory 3 units

This pattern is expected to be followed by the average Broadbase Science students who intend to graduate in MATH at a reasonable pace(a1), and with a smooth progress to further MATH required courses(a2)(a3).

The STARS stream offered by the Faculty of Science is an option for Broadbase Science students who intend to graduate in MATH. Term 2 (Second Semester) is the starting point of the STARS stream in the framework of the MATH curriculum.(a4)

Remarks.

  • (a1) Reasonable pace of progress.

    The MATH study scheme is designed on the assumption that for all MATH students:---

    • all four level-1000 and six level-2000 MATH required courses (12 units and 17 units respectively) are passed within the first three years of study,
    • the other advanced MATH courses and/or non-MATH courses (for the various streams available in the MATH curriculum) are to be taken mainly in the third and fourth years of study.

    In the light of the pre-requisites of the various courses, a delay of one or more of MATH1010, MATH1025, MATH1030, MATH1090 may cause a `pile-up' of the level-2000 MATH required courses , and may indirectly restrict your options in higher years of study (not only in course selection, but also in exchange/internship opportunities, scholarships et cetera).

  • (a2) Pre-requisite matters: the roles of MATH1010, MATH1025 in the making of smooth progress to further MATH required courses.

    • MATH1010 is a pre-requisite for MATH1090 and for MATH2010.

      Without having passed MATH1010, you can take neither MATH1090 nor MATH2010.

    • MATH1025 is a co-requisite for MATH1090.

      If you do not take MATH1025 in the first term of study, you may end up postponing at least one of MATH1025, MATH1030, MATH1090 to the second year of study (because you will not have enough spare units to take all three of MATH1025, MATH1030, MATH1090 in the second term of study).

  • (a3) Pre-requisite matters: the roles of MATH1030, MATH1090 in the making of smooth progress to further MATH required courses.

    • MATH1030 is a pre-requisite for MATH2040 and for MATH2070.

      If you do not take MATH1030 in the first year of study, you may end up delaying these two courses.

    • MATH1090 is a pre-requisite for several `proof-type' required courses in MATH programme, namely MATH2040, MATH2050, MATH2070.

      If you do not take MATH1090 in the first year of study, you have to plan your MATH courses (especially the MATH required courses) in the second and third years of study so as to avoid delaying your completion of the MATH major requirement.

  • (a4) STARS stream.

    Be aware that there are some eligibility criteria for joining the STARS stream. For more information about the STARS stream, refer to this page. To apply for the STARS stream, 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, MATH1025, MATH1030, MATH1090 with the respective Honours Courses MATH1018(a5), MATH1028(a5), MATH1038(a6), MATH1098(a6), which are designed for MATH students with good abilities and with prospective further studies in mind. The pattern is displayed in Table (A2):---

Table (A2).

Term of study Course Code Course Title Number of units
Term 1 (First Semester) MATH1018 Honours University Mathematics 3 units
Term 1 (First Semester) MATH1028 Honours Essential Mathematical Methods 3 units
Term 2 (Second Semester) MATH1038 Honours Linear Algebra I 3 units
Term 2 (Second Semester) MATH1098 Honours Introduction to Set Theory 3 units

Remarks.

  • (a5) Eligibility for the First Semester Honours Courses MATH1018, MATH1028.

    For the question on eligibility for MATH1018, MATH1028, refer to the Honours Course homepage.

    Mathematics Enrichment entrants are pre-assigned to the Honours Courses MATH1018, MATH1028 in the first semester.

  • (a6) Eligibility for the Second Semester Honours Courses MATH1038, MATH1098.

    For the question on eligibility for MATH1038, MATH1098, refer to the Honours Course homepage.

Back to Content

MATH required courses beyond the First Year of Study.

Expected of all MATH students (irrespective of how one is admitted to the programme) is a timely completion of the MATH courses (c1) listed in Table (C0), and in Table (C1) and/or Table (C2):---

Table (C0).

Term of study Course Code Course Title Number of units
Term 3 MATH2010/MATH2018(c2) Advanced Calculus I (Non-Honours/Honours) 3 units
Term 4 MATH2020/MATH2028(c2) Advanced Calculus II (Non-Honours/Honours) 3 units
Term 3 MATH2040/MATH2048(c2) Linear Algebra II (Non-Honours/Honours) 3 units
Term 4 MATH2221 Mathematical Laboratory II 2 units
Final Year MATH4400/MATH4900(c3) Project/Seminar 3 units

Beyond what is listed in Table (C0), the exact MATH courses required for you and the optimal pattern for taking these courses very much depends on your plans regarding the choice of streams(c4) for graduation.

Seen from this point of view, there are two paths for you:---

  1. You may plan to graduate with the Enrichment Stream, whether as a single stream, or as one of the two streams forming a double-stream.(c4)

    In this situation you should append Table (C0) with Table (C1), which lists several more MATH courses required for the completion of the Enrichment Stream and the optimal schedule for a timely completion of these courses (especially the corresponding Honours courses). (c1)
  2. You may plan to graduate with a single stream or a double-stream not involving the Enrichment Stream.(c4)

    In this situation you should append Table (C0) with Table (C2), which lists several more MATH courses required or `semi-required' for the completion of any non-Enrichment stream and the optimal schedule for taking these courses. (c1)

Table (C1).

Term of study Course Code Course Title Number of units
Term 3 or 4 or 5 MATH2050/MATH2058 (c2)(c5) Mathematical Analysis I (Non-Honours/Honours) 3 units
Term 4 or 5 or 6 MATH2060/MATH2068 (c2)(c5) Mathematical Analysis II (Non-Honours/Honours) 3 units
Term 4 or 5 or 6 MATH2070/MATH2078 (c2)(c6) Algebraic Structures (Non-Honours/Honours) 3 units
Term 4 or 5 or 6 MATH2230 (c6) Complex Variables with Applications 3 units

Table (C2).

Term of study Course Code Course Title Number of units
Term 3 or 4 or 5 MATH2050/MATH2058 (c2)(c5) Mathematical Analysis I (Non-Honours/Honours) 3 units
Term 4 or 5 or 6 MATH2060/MATH2068 (c2)(c5) Mathematical Analysis II (Non-Honours/Honours) 3 units
Term 4 or after MATH2070/MATH2078 (c6) Algebraic Structures (Non-Honours/Honours) 3 units
Term 5 or after MATH2230 (c6) Complex Variables with Applications 3 units
Term 4 or after MATH3270 (c6) Ordinary Differential Equations 3 units
Term 4 or after MATH3280 (c6) Introductory Probability 3 units

The charts below display:---

  • an overall roadmap for the completion of the required courses in the MATH programme, common to all students (irrespective of the choice of streams),
  • a specific roadmap for the completion of the requirements on MATH courses for the Enrichment Stream, and
  • a specific roadmap for the completion of the requirements on MATH courses for non-Enrichment streams.
The arrows indicate the relations between the various parts of the requirements.

Remarks.

  • (c1) Timely completion of certain MATH courses.

    Mathematics is one of very few disciplines in which you will not be in a position to study an `advanced' topic without first acquiring sufficient `basic' knowledge that serves as foundation for that `advanced' topic.

    For this reason, we expect you to take the recommended study patterns for the various streams (in particular that for the Enrichment Stream) seriously.

    1. It is imperative that you take MATH2010/2018, MATH2020/2028, MATH2040/2048 on time.

      It should be understood that in every MATH course at level-3000 or above (whether it can be used for fulfilment of Enrichment Stream or not,) proficiency in the material covered by these courses is assumed.
    2. It is important that you take MATH2221 on time.

      It is assumed by the Department that all students are to take MATH2221 in Term 4.
      • If you delay the course to Term 6, you are likely going to find that there will be timeclash between MATH2221 and some other courses (amongst MATH courses at level-3000 or above).
      • If you do not take the course by the end of the Third Year of Study, you will be barred from taking the capstone course (MATH4400/4900) in the Fourth Year of Study, and may have to delay your graduation.
    3. If you intend to graduate with the Enrichment Stream, you have to give special thoughts on when you take MATH2050/2058, MATH2060/2068, MATH2070/2078, MATH2230. This is because in each MATH level-3000 or above courses relevant to the Enrichment Stream, proficiency in the material covered by one or more of these courses is assumed. In fact, it may be stated explicitly in the pre-requisites of such a MATH level-3000 or above course that to take such a course, you are required to pass one or more of MATH2050/2058, MATH2060/2068, MATH2070/2078, MATH2230 before being allowed to take the course.

      For more detail, refer to the relevant remarks below (c5)(c6). As for pre-requisite and co-requisite matters, refer to this page.

  • (c2) 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 broader and deeper understanding in mathematics, and if you want to reap the full benefits of the Enrichment Stream.

    There is a pre-requisite for each such Honours course, very often in the form `B- or above' in a group of Honours Courses that you are expected to have taken.

    As the individual MATH Honours course is offered only in a specific semester, you should take into account of the overall pattern of the offering of Honours courses in your planning. For more detail, you should refer to the MATH Honours Courses homepage.

    In any case, even if you are not taking any individual Honours course, you can still take its non-Honours counterpart to fulfil graduation requirement.

  • (c3) Capstone courses.

    You are required, and allowed, to take only one of MATH4400, MATH4900. Most students take the MATH4900, and do so in Term 7.

    Be aware of the pre-requisites for taking MATH4400/MATH4900, and plan your courses accordingly. In principle:---

    • without having first passed MATH2050/2058/2060/2068 and MATH2221, you will not be allowed to take MATH4400;
    • without having first passed MATH2050/2058 and MATH2221, you will not be allowed to take MATH4900.

  • (c4) Streams.

    Every MATH student is required to specialize in (at least) one stream, as listed in the MATH study scheme. They are:---

    • Enrichment Stream,
    • Computational Big Data Analytics Stream,
    • Computational and Applied Mathematics Stream,
    • Mathematics Stream,
    • Mathematics-Education Stream,
    • Mathematics-Multidisciplinary Stream.
    The Science, Technology and Research Stream, which is offered to all students of the Faculty of Science, is also available to MATH students admitted through the Broadbase Science Programme.

    You are also eligible for graduating with any one double-stream specified in the study scheme in CUSIS, as long as you fulfil simultaneously the stream requirements of the two streams that make up the double-stream concernd.

    (Note. Every Enrichment Mathematics entrant is entitled to graduate in the Enrichment Stream as long as the student fulfills the stream requirements.(c7) Unlike Enrichment Mathematics entrants, you will have to satisfy some GPA requirements in order to be eligible for graduating in the Enrichment Stream, whether as a single stream, or as one of the two streams forming a double-stream.)

    In any case, you have to make sure you have made up your mind at least one semester prior to graduation, because you need to declare your stream to the Department at least several months before you graduate. (For your information, the stream declaration usually takes place in October and February.)

    For more detail on the matter of streams, including the specific requirements for each stream, consult the study scheme in CUSIS. A quick reference (though not necessarily most updated) on streams is available here.

  • (c5) Mathematical Analysis I, II (Honours and non-Honours courses).

    If you intend to graduate in the Enrichment Stream, it is best to take MATH2050/2058, MATH2060/2068 in Terms 3 or 4 respectively, or as early as possible. This is because without taking these two courses, it will be hard for you to acquire a sufficiently strong background in analysis assumed in further analysis-type courses.

    However, if you indeed need room to `kick-start' a second stream alongside the Enrichment Stream during the Second Year of Study, you may consider postponing MATH2050/2058, MATH2060/2068 to as late as Terms 5, 6 respectively. That said, you should bear in mind that such a postponement may result in your being ill-prepared to take certain advanced pure-maths type courses during Year 3 and Year 4.

    In deciding when to take MATH2050/2058, MATH2060/2068, you should also note that:---

    • MATH2050/2058 is part of the pre-requisites for MATH2060/2068, and so without first taking MATH2050/2058, it is extremely unlikely for you to be allowed to take MATH2060/2068;
    • MATH2058 is likely to be offered in the First Semester only;
    • MATH2068 is likely to be offered in the Second Semester only;
    • While MATH2050 is likely to be offered in both the First and Second Semesters, MATH2060 is likely to be offered in the Second Semester only.

  • (c6) Algebraic Structures, Complex Variables with Applications, Ordinary Differential Equations, Introductory Probability as `semi-required' courses (MATH2070/2078, MATH2230, MATH3270, MATH3280).

    1. If you want to graduate with the Enrichment Stream whether as a single stream, or as one of the two streams forming a double-stream, you are required to take both MATH2070/2078 and MATH2230 as partial fulfilment of the major course requirements for graduation with the Enrichment Stream.

      Be aware that:---
      • MATH2230 covers the background in theory of functions of one complex variable which is indispensible preparation for various `pure maths type' courses in analysis and geometry, and
      • MATH2070/2078 covers the background in abstract algebra which is indispensible preparation for various `algebra type' courses.
      So, if you want to take more `pure maths' type courses in Year 3 and Year 4, a timely completion of these two courses (say, in Term 4, or Term 5 at the latest,) is important. In regard to the matter of planning your courses, you should note that:---
      • MATH2230 and MATH2070 are offered every semester. MATH2078 is likely to be offered in the second semester only.
    2. If you want to graduate with any non-Enrichment stream(s), you are required to take any three out of MATH2070/2078, MATH2230, MATH3270, MATH3280 as partial fulfilment of the stream requirement(s) for such a stream. (MATH3280 may be replaced by STAT2001.)

Back to Content