Capstone courses (MATH4900/MATH4400) 2024-25

Overview.

1. The information in this page is intended for students who have passed MATH2050/2058 (or plan to pass MATH2050/2058 in the First Semester 2024-25), and who intend to graduate in MATH by summer 2025.

2. To fulfill the MATH graduation requirement, you must pass a capstone course, which is either MATH4900 (Seminar) or MATH4400 (Project). These two courses are mutually exclusive.

3. If you are a MATH student, what you need to do in order to register for a capstone course varies according to your situation or choice:

   1. To take MATH4900 in the First Semester 2024-25, having passed MATH2050/2058 already?
      • This is what most of you are expected to do. For the detail of follow-up action, click here.
   2. To take MATH4900 in 2024-25, but not in the First Semester?
      • Special action must be taken no later than 26^th July 2024. For detail, click here.
   3. To take MATH4400 instead of MATH4900?
      • Special action must be taken no later than 28^th June 2024. For detail, click here.

4. If you are a non-MATH student and intend to graduate with a second major in MATH by summer 2025, click here.

5. For add-drop matters in MATH4900, click here.

6. The topics and their descriptions can be found here, towards the end of July 2024.

To take MATH4900 in the First Semester 2024-25, having passed MATH2050/2058 already?

1. This applies to only those students who have already passed MATH2050/2058. (If you are yet to pass MATH2050/2058, click here.)

2. There are tentatively eight sections of MATH4900 in the First Semester 2024-25. Each has its own theme.

3. Registration for MATH4900 is to be done on CUSIS, during the course registration day (in early August 2024) for final-year students, on a first-come-first-serve basis.

4. By the end of the course registration day for final-year students, you are expected to have exactly one CUSIS entry across all MATH4900 sections, be it in a class list or a waiting list.

   1. During the course registration day for final-year students, if you find yourself in the waiting list of a section, you had better register for another section immediately.

   2. By the end of the course registration day for final-year students:---

      1. If you have entered the class list of one MATH4900 section, all records of yours in the waiting lists of the other sections will be regarded as null and void by the department.

      2. If you have entered the waiting list(s) of some MATH4900 section(s) but not the class list of any one MATH4900 section, the department may assign you to any MATH4900 section, regardless of your records in the waiting list(s).

         If you do not take up the place to which you are assigned, you might fail to register for the course altogether, and end up delaying graduation.

      3. If you have entered neither the class list nor the waiting list of any one MATH4900 section, the department will suppose you do not plan to take MATH4900 in 2024-25, unless you have already been approved to take MATH4400, or have been excused by the department from taking MATH4900 in the First Semester.

         While you may apply for adding into the course by writing to the department, there is no guarantee that the department can find a place for you. (For the procedure, click here.) The deadline for such applications is 1300hrs of the last day of the official add-drop period.

5. It will be up to the department to decide what to do with the vacancies of MATH4900, after the end of the course registration day for final-year students.

To take MATH4900 in 2024-25, but not in the First Semester?

1. This applies to only those students who are not taking MATH4400 and who have been excused by the department from taking MATH4900 in the First Semester 2024-25.

2. Only in exceptional circumstances (such as going for an exchange or internship, or taking MATH2050/2058 during the semester) will a student be excused by the department.

3. To request to be excused, you must write to the department no later than 26^th July 2024.

   1. In your application letter you must explain why you are prevented from taking MATH4900 in the First Semester.

      Supporting evidence, where relevant, must be provided.

      You must also attach to the letter your unofficial academic transcript and your study plan for all subsequent terms of study.

   2. If you are excused from taking MATH4900 in the First Semester 2024-25, the department will arrange for you to take the course in the Second Semester or the Summer Semester 2024-25.

   3. Late applications will NOT be guaranteed consideration.

To take MATH4400 instead of MATH4900?

1. To apply for a place in MATH4400, follow the procedure below:

   1. Check whether you are qualified for taking this course. Refer to the CUSIS for detail.
   2. Find a teacher who consents to be the supervisor for your project, whether in the First Semester or the Second Semester 2024-25.
   3. After obtaining your project supervisor's consent, submit an online application here
   The closing date of application is 28^th June 2024.
   NO late application will be entertained.

2. Be aware that it could take, say, 10 days, for the teacher to decide. So do make your approach early.

3. Applicants will be informed of the result by 5^th July 2024.

   1. Successful applicants will be pre-assigned to MATH4400 in the respective semesters, prior to course registration day.
   2. If your application is unsuccessful, you are expected to register for MATH4900 in 2024-25. For detail, click here.

Capstone courses for second major in MATH.

1. If you intend to take MATH4400, follow the same procedure as that for MATH students.

2. If you intend to take MATH4900, you are expected to do so in the First Semester 2024-25.

   Write to the department, no later than 26^th July 2024, to apply for a place in MATH4900 in the First Semester 2024-25.

   Late applications will NOT be guaranteed consideration.

   It will be up to the department to decide into which section you will be added.

Add-drop matters in MATH4900.

1. The department will impose departmental add-drop consent to MATH4900 in CUSIS after the end of the CUSIS course registration day for final-year students. You are not free to do electronic add-drop on CUSIS during the semester.

2. You may apply for adding into, and/or dropping from, MATH4900.

   1. For `drop', submit to the General Office of the Department of Mathematics an add-drop form signed by the teacher of the respective section.

   2. For `add', you need to write to the department to apply for a place in MATH4900.

      The department will approve such an application only in exceptional situations. Also, it will be entirely the department's right to decide to which MATH4900 section you will be assigned.

3. The deadline for add-drop applications is 1300hrs of the last day of the official add-drop period. NO late application will be entertained.

Topics of the various sections of MATH4900 (First Semester 2024-25).

• MATH4900A: Knots.

  Time. Tuesday 1330-1615hrs.

  Description.
  In this section, knots will be studied using methods from algebra, topology and combinatorics. Emphasis will be on polynomial invariants of knots.

  Expected/preferred background skills/knowledge.
  Basic knowledge on topology (such as having taken MATH3070) will be useful.
  

• MATH4900B: Mathematics education and lesson plan development.

  Time. Wednesday 1330-1615hrs.

  Description.
  This course requires students to select a specific mathematical topic from Grades 10-12 Mathematics curriculum or from Undergraduate Level Mathematics, develop a lesson plan and relevant lesson materials (which include either a supporting platform or some e-learning tools) of the chosen topic. Students will have opportunities to understand pedagogical principles behind the lesson plan development process, and associate them with current education development and policies.

  Expected/preferred background skills/knowledge.
  Previous experience in tutoring and/or mentoring work is expected. Solid foundation in basic mathematics (such as calculus and linear algebra) and some experience in using programming software is expected.
  

• MATH4900C: Topics in financial mathematics.

  Time. Friday 1530-1815hrs (tentative).

  Description.
  Through going through some of the standard techniques for analysis of quantitative trading strategies, this course equips students with the essential skill for quantitative strategy development. The course involves empirical work with support of learning in programming languages such as Python, R, and Rust. There will be three individual topics available for further research and students are welcome to propose topics they are interested in.

  Expected/preferred background skills/knowledge.
  Probability theory, basic statistics, finance/investment, and basic programming.
  

• MATH4900D: Topics in modern geometry.

  Time. Tuesday 1430-1715hrs.

  Description.
  Various topics for small group projects, mainly related to modern geometries, including non-Euclidean Geometry.

  Expected/preferred background skills/knowledge.
  MATH2230 is expected.
  

• MATH4900E: Number theory.

  Time. Tuesday 1030-1315hrs.

  Description.
  In this section, we will study different topics of number theory. Students can choose any topics related to number theory that includes but is not limited to: theory of primes, Diophantine equations, continued fractions, cryptography, factorizations, elliptic curves, computational number theory, p-adic numbers.

  Expected/preferred background skills/knowledge.
  MATH2070 is expected.
  

• MATH4900F: To be announced.

  Time. Thursday 1430-1715hrs.

  Description.
  To be announced.

  Expected/preferred background skills/knowledge.
  To be announced.
  

• MATH4900G: Expander families and Cayley graphs.

  Time. Monday 0930-1215hrs.

  Description.
  The theory of expander graphs has applications to communication networks, error-correcting codes, cryptography and complexity theory. In this course, we will study four invariants that measure the quality of a Cayley graph as a communication network: the isoperimetric constant, the second-largest eigenvalue, the diameter, and the Kazhdan constant.

  Expected/preferred background skills/knowledge.
  Nil.
  

• MATH4900H: Numerical optimization.

  Time. Wednesday 1330-1615hrs.

  Description.
  In this section, we will study some basic theoretical results of optimization and investigate several numerical optimization methods. Apart from exploring the idea and properties of the methods, students will be encouraged to apply the methods and perform numerical experiments.

  Expected/preferred background skills/knowledge.
  Exposure to any programming language is preferred but not required.
  

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