Capstone Course Arrangements
Capstone courses (MATH4900/MATH4400) 202122
Overview.

The information in this page is intended for students who have passed MATH2050 (or plan to pass MATH2050 in the First Semester 202122), and who intend to graduate in MATH by summer 2022.

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 202122, having passed MATH2050 already?
 This is what most of you are expected to do. For the detail of followup action, go here.
 To take MATH4900 in the Second Semester 202122, having passed MATH2050 already?
 Special action must be taken no later than 3rd July 2021. For detail, go here.
 Yet to pass MATH2050 as of summer 2021?
 Special action must be taken no later than 3rd July 2021. For detail, go here.
 To take MATH4400 instead of MATH4900?
 Special action must be taken no later than 3rd July 2021. For detail, go here.
 To take MATH4900 in the First Semester 202122, having passed MATH2050 already?

If you are a nonMATH student and intend to graduate with a second major in MATH by summer 2022, go here.

For adddrop matters in MATH4900, go here.
 For the topics of the various sections of MATH4900, go here.
To take MATH4900 in the First Semester 202122, having passed MATH2050 already?

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

There are seven sections of MATH4900 in the First Semester 202122. Each has its own theme.

Registration for MATH4900 is to be done on CUSIS, during your course registration day (in early August, 2021), on a firstcomefirstserve basis.

The quota of every section is a hard quota. For this reason:
 No student in the waiting list of any section may be added to the respective section unless some student already registered to that section drops from the course.
 If you find yourself in the waiting list of a section during the course registration day, you had better register for another section immediately.
 If you had not already entered the class list of any one section after your course registration day, you might fail to register for the course at all, and end up delaying graduation.
 It will be up to the department to decide what to do with the vacancies of MATH4900, after the end of the course registration period.
To take MATH4900 in the Second Semester 202122, having passed MATH2050 already?

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

The number of places in MATH4900 in the Second Semester 202122 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. 
To apply for a place in MATH4900 in the Second Semester 202122, write to the department, no later than 3rd July, 2021, stating your reasons.
NO late application will be entertained.  Applicants will be informed of the result by 11th July, 2021.
 Successful applicants will be preassigned to MATH4900 in the Second Semester, prior to course registration day.
 If your application is unsuccessful, you are expected to register for MATH4900 in the First Semester 202122. For detail, go here.
Yet to pass MATH2050 as of summer 2021?

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 202122. 
You may apply for a place in MATH4900 in the Second Semester 202122, by writing to the department, no later than 3rd July, 2021.
Failure to comply by this deadline may result in delay in graduation.
You will be preassigned 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 202122.
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.
 Look for a potential project supervisor and obtain his/her consent to supervise the project, whether in the First Semester or the Second Semester 202122.
 After obtaining your supervisor's consent, you should make 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 11th July, 2021.
 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 202122. For detail, go 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 202021.
Write to the department, no later than 3rd July, 2021, to apply for a place in MATH4900 in the First Semester 202122.
NO late application will be entertained.
It will be up to the department to decide into which section you will be added.
Adddrop matters in MATH4900.

Once the CUSIS course selection day is over, the department will impose departmental adddrop consent to MATH4900 in CUSIS. You are not free to do electronic adddrop on CUSIS.

You may apply for adding into, and/or dropping from, MATH4900.
In such an application, you have to submit to the General Office of the Department of Mathematics the following documents: An adddrop form with the detail of your application.
(In the case of dropping from MATH4900, the form needs be signed by the teacher of the respective section.)  A letter justifying your application.
 An adddrop form with the detail of your application.

The department will approve such an application only in exceptional cases.

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: Number theory.
Description.
In this section, we will study different topics of number theory. Students can choose any topics related to number theory, which include but are 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.  MATH4900B: From calculus to topology.
Description.
Our aim is to study fundamental concepts in algebraic topology by means of calculus. More precisely, we will try to see how calculus can be used to detect the topology of open domains in R^{2}. Along the way, we will be led to fundamental topological concepts like winding numbers, degrees, homology and cohomology, as well as important results such as Brouwer Fixed Point Theorem, Jordan Curve Theorem, etc.Expected/preferred background skills/knowledge.
MATH2010 and MATH2020 are expected.
Exposure to basic topology (at the level of MATH3070) is preferred but not required.  MATH4900C: Modern computational mathematics.
Description.
Numerical analysis is a classical branch of mathematics. The subject involves the development and mathematical analysis of computational techniques for the approximation of complicated mathematical problems. Recently, datadriven scientific computing has gained much attention, and provides a complementary technique to strengthen the ability of classical approaches to solve mathematical problems. The aim of this project is to investigate some modern techniques in computational mathematics.Expected/preferred background skills/knowledge.
MATH2010, MATH2020, MATH2040 are expected. MATH2221 and/or CSCI1540 (or equivalent) are expected.
Exposure to other programming languages and to basic numerical mathematics (at the level of MATH3230, MATH3240) is preferred but not required.  MATH4900D: Studies in operations research.
Description.
In this section, small projects and problems in the area of operations research will be explored. The aim is to lead students to a thorough understanding of the art and science of practical applications in operations research. Students may realize the successful way of undertaking projects and what obstacles are present to thwart success.Expected/preferred background skills/knowledge.
MATH2221 is expected.
Knowledge in other programming languages (such as Python), and exposure to operations research (at the level of MATH3215) are preferred but not required.  MATH4900E: Geometries and transformations.
Description.
In plane geometry, we consider distancepreserving transformations such as reflections, rotations and translations. They can be used to understand the symmetry and geometry of the plane. In this section, we will study different types of geometries from the point of view of transformation groups. Examples such as hyperbolic and elliptic geometries will be discussed.Expected/preferred background skills/knowledge.
MATH2010, MATH2020, MATH2040 and MATH2070 are expected.  MATH4900F: Graph theory.
Description.
Graphs are mathematical objects consisting of vertices and edges. They can be used to model many realworld situations. 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 realworld tasks. In this seminar, we will explore how differential geometry and deep learning can be utilized, as well as nicely combined, to tackle various realworld 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.