Capstone courses (MATH4900/MATH4400) 2022-23

Overview.

1. The information in this page is intended for students who have passed MATH2050 (or plan to pass MATH2050 in the First Semester 2022-23), and who intend to graduate in MATH by summer 2023.

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 2022-23, having passed MATH2050 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 the Second Semester 2022-23, having passed MATH2050 already?
      • Special action must be taken no later than 27th July 2022. For detail, click here.
   3. Yet to pass MATH2050 as of summer 2022?
      • Special action must be taken no later than 27th July 2022. For detail, click here.
   4. To take MATH4400 instead of MATH4900?
      • Special action must be taken no later than 2nd July 2022. For detail, click here.

4. If you are a non-MATH student and intend to graduate with a second major in MATH by summer 2023, 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 2022.

To take MATH4900 in the First Semester 2022-23, having passed MATH2050 already?

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

2. There are seven sections of MATH4900 in the First Semester 2022-23. Each has its own theme.

3. Registration for MATH4900 is to be done on CUSIS, during the course registration day (in early August, 2022) 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 2022-23.

         You may still apply for adding into the course, by writing to the department. (For the procedure, click here.) However, there is no guarantee that the department can find a place for you.

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 the Second Semester 2022-23, having passed MATH2050 already?

1. This applies to only those students who have already passed MATH2050, as of 30th June 2022. (If you are yet to pass MATH2050, click here.)

2. The number of places in MATH4900 in the Second Semester 2022-23 is very limited.
   The places will be open to only those students who can explain satisfactorily why they cannot take MATH4900 in the First Semester.

3. To apply for a place in MATH4900 in the Second Semester 2022-23, write to the department no later than 27th July, 2022. In your application letter you must explain why you cannot take MATH4900 in the First Semester and you must attach your unofficial academic transcript and your study plan for all future terms of study.
   NO late application will be entertained.

4. Applicants will be informed of the result by 29th July, 2022.
   1. Successful applicants will be pre-assigned to MATH4900 in the Second Semester, prior to course registration day.
   2. If your application is unsuccessful, you are expected to register for MATH4900 in the First Semester 2022-23. For detail, click here.

Yet to pass MATH2050 as of summer 2022?

1. In principle, you are not eligible to take MATH4900 until you have passed MATH2050.
   For this reason, you are NOT allowed to take MATH4900 in the First Semester 2022-23.

2. You may apply for a place in MATH4900 in the Second Semester 2022-23, by writing to the department, no later than 27th July, 2022.
   Failure to comply by this deadline may result in delay in graduation.
   You will be pre-assigned to MATH4900 in the Second Semester, prior to course registration day, and will be allowed to take up the requested place on condition of passing MATH2050 in the First Semester 2022-23.

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. Look for a potential project supervisor and obtain his/her consent to supervise the project, whether in the First Semester or the Second Semester 2022-23.
   3. After obtaining your supervisor's consent, you should make an online application here
   The closing date of application is 2nd July, 2022.
   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 11th July, 2022.
   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 2022-23. 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 2022-23.
   Write to the department, no later than 27th July, 2022, to apply for a place in MATH4900 in the First Semester 2022-23.
   NO late application will be entertained.
   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.

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.

• MATH4900A: Topics in modern geometry.

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

  Expected/preferred background skills/knowledge.
  Having taken MATH2230.
  

• MATH4900B: Modern Scientific Computation Techniques.

  Description.
  Developing new and efficient scientific computation mechanisms have become hot topics nowadays, because these approaches can be generalized to govern daily life physical phenomenon, solve partial differential equations, and analyze big data originated from different daily life applications. This course aims at equipping students with modern techniques in applied and computational mathematics, and connecting these physical principles and mathematical models with case studies from different scientific aspects.

  Expected/preferred background skills/knowledge.
  MATH2010, MATH2020, MATH3270 are expected; MATH2221 and/or CSCI1540 are preferred. Basic understanding of numerical mathematics and relevant experience (such as MATH3230, MATH3240, MATH3290, MATH3330 or equivalent) are preferred.
  

• MATH4900C: Numerical Optimization.

  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.
  

• MATH4900D: Cryptography.

  Description.
  Cryptography is the study of communication security (private messaging, online transactions, etc.) and modern cryptography heavily relies on basic Number Theory such as modular arithmetics, prime numbers, etc. In this course, we will first study some basic knowledge in number theory. Next, we will explore its applications in cryptography, including some classical systems such as Caesar cipher, Vigenere cipher and some modern systems such as DES, RSA, Diffie-Hellman key exchange. Finally, we will explore the AKS primality test, a deterministic primality-proving algorithm which runs in polynomial time.

  Expected/preferred background skills/knowledge.
  MATH2070, and preferably MATH3030 as well.
  

• MATH4900E: Number Theory.

  Description.
  In this section, we will study different topics of number theory. Students can choose any topics related to number theory, that includes but not limited to: theory of primes, Diophantine equations, continued fractions, theory of Riemann zeta-function, modular forms, Maass forms, theory of L-functions.

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

• MATH4900F: Graph Theory

  Description.
  Graphs are mathematical objects consisting of vertices and edges. In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects. In this section, we will study the basics and several interesting applications of graph theory.

  Expected/preferred background skills/knowledge.
  Nil.
  

• MATH4900G: From Computational Differential Geometry to Deep Learning.

  Description.
  Computational differential geometry has attracted much attention in recent years and found important applications in various fields, including image processing, geometry processing and computer visions. Deep learning has also advanced dramatically and significantly improved the performance of many real-world tasks. In this seminar, we will explore how differential geometry and deep learning can be utilized, as well as nicely combined, to tackle various real-world problems. The mathematics behind the ideas will also be explored in detail.

  Expected/preferred background skills/knowledge.
  MATH2010, MATH2020 and MATH2040 are expected. Exposure to basic differential geometry (at the level of MATH4030) is preferred but not required.
  

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