Capstone Course Arrangements
Capstone courses (MATH4900/MATH4400) 202324
Overview.

The information in this page is intended for students who have passed MATH2050 (or plan to pass MATH2050 in the First Semester 202324), and who intend to graduate in MATH by summer 2024.

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.

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:
 To take MATH4900 in the First Semester 202324, having passed MATH2050 already?
 This is what most of you are expected to do. For the detail of followup action, click here.
 To take MATH4900 in 202324, but not in the First Semester?
 Special action must be taken no later than 27^{th} July 2023. For detail, click here.
 To take MATH4400 instead of MATH4900?
 Special action must be taken no later than 2^{nd} July 2023. For detail, click here.
 To take MATH4900 in the First Semester 202324, having passed MATH2050 already?

If you are a nonMATH student and intend to graduate with a second major in MATH by summer 2024, click here.

For adddrop matters in MATH4900, click here.
 The topics and their descriptions can be found here, towards the end of July 2023.
To take MATH4900 in the First Semester 202324, having passed MATH2050 already?

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

There are seven sections of MATH4900 in the First Semester 202324. Each has its own theme.

Registration for MATH4900 is to be done on CUSIS, during the course registration day (in early August 2023) for finalyear students, on a firstcomefirstserve basis.

By the end of the course registration day for finalyear students, you are expected to have exactly one CUSIS entry across all MATH4900 sections, be it in a class list or a waiting list.
 During the course registration day for finalyear students, if you find yourself in the waiting list of a section, you had better register for another section immediately.

By the end of the course registration day for finalyear students:

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.

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.

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 202324, 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 adddrop period.

 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 finalyear students.
To take MATH4900 in 202324, but not in the First Semester?

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 202324.

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

To request to be excused, you must write to the department no later than 27^{th} July 2023.
 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 subsequet terms of study.

If you are excused from taking MATH4900 in the First Semester 202324, the department will arrange for you to take the course in the Second Semester or the Summer Semester 202324.
 Late applications will NOT be guaranteed consideration.
 In your application letter you must explain why you are prevented from taking MATH4900 in the First Semester.
To take MATH4400 instead of MATH4900?

To apply for a place in MATH4400, follow the procedure below:
 Check whether you are qualified for taking this course. Refer to the CUSIS for detail.
 Find a teacher who consents to be the supervisor for your project, whether in the First Semester or the Second Semester 202324.
 After obtaining your project supervisor's consent, submit an online application here
NO late application will be entertained. 
Be aware that it could take, say, 10 days, for the teacher to decide. So do make your approach early.

Applicants will be informed of the result by 11^{th} July 2023.
 Successful applicants will be preassigned to MATH4400 in the respective semesters, prior to course registration day.
 If your application is unsuccessful, you are expected to register for MATH4900 in 202324. For detail, click here.
Capstone courses for second major in MATH.

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

If you intend to take MATH4900, you are expected to do so in the First Semester 202324.
Write to the department, no later than 27^{th} July 2023, to apply for a place in MATH4900 in the First Semester 202324.
Late applications will NOT be guaranteed consideration.
It will be up to the department to decide into which section you will be added.
Adddrop matters in MATH4900.

The department will impose departmental adddrop consent to MATH4900 in CUSIS after the end of the CUSIS course registration day for finalyear students. You are not free to do electronic adddrop on CUSIS.

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

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


The deadline for adddrop applications is 1300hrs of the last day of the official adddrop period. NO late application will be entertained.
Topics of the various sections of MATH4900.
 MATH4900A: Knots.
Time. Tuesday 15301815hrs.
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 will be useful but not required.  MATH4900B: Applications of applied and computational mathematics.
Time. Wednesday 14301715hrs.
Description.
Mathematics are all around us. Different scientific computation methods and approaches are adopted to govern daily life phenomenon, solve partial differential equations, and analyze big data originated from various applications. This seminar course aims at equipping students with opportunities to explore the trends and techniques of applied and computational mathematics, and connecting these physical principles and modeling framework with appropriate case studies.Expected/preferred background skills/knowledge.
MATH2010, MATH2020, MATH3230 and MATH3270 are expected. Exposure to MATLAB (e.g., MATH2221 and/or CSCI1540, or equivalent) are preferred but not a must.  MATH4900C: Financial data analysis and algo trading.
Time. Monday 15301815hrs.
COSINE: CASH Internship Program 2024Description.
The learning outcome of this section is to conduct financial data analysis for algo trading. Through studying academic research paper and practical experience sharing as well as handson implementation of trading strategies, students are expected to equip with practical skills in this field.Expected/preferred background skills/knowledge.
Basic probability theory and statistics, programming languages such as Python or R.  MATH4900D: Topics in modern geometry.
Time. Monday 14301715hrs.
Description.
Various topics for small group projects, mainly related to modern geometries, including nonEuclidean Geometry.Expected/preferred background skills/knowledge.
MATH2230 is expected.  MATH4900E: Number theory.
Time. Tuesday 10301315hrs.
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, cryptography, factorizations, elliptic curves, computational number theory, padic numbers.Expected/preferred background skills/knowledge.
MATH2070 is expected.  MATH4900F: Isoperimetric problems.
Time. Thursday 14301715hrs.
Description.
Isoperimetric problem is an extremal problem which arises naturally in many areas of mathematics especially in differential geometry and calculus of variations. We plan to first have a bird'seye view of the historical origin as well as the development of the problem starting from plane geometry. Subsequently, we will look at its various ramifications in different areas of mathematics. The goal is to understand some wellknown differential geometric objects such as the minimal surfaces, constant mean curvature surfaces etc.Expected/preferred background skills/knowledge.
MATH2010, MATH2020 and MATH2060 are expected.  MATH4900G: Graph theory.
Time. Monday 12301515hrs.
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.