Capstone Course Arrangements
To: ALL students admitted in 201516 or before, who intend to graduate by summer 2019.
SUBJECT: Capstone course arrangements 201819.
 Overview:
 In order to graduate in MATH by summer 2019, you must have passed, as your capstone course, either MATH4900 (Seminar) or MATH4400 (Project), but not both, by 201819. These two courses are mutually exclusive.
 MATH4900 will be offered in both semesters. Most students will take MATH4900 to fulfill their graduation requirements, and do so in the first semester.
However, if you intend to take MATH4400 or if you cannot take MATH4900 in the first semester, you need to take special action.  If you are a MATH student, refer to the relevant section below:
 Section 2 if you intend to take MATH4400,
 Section 3 if you intend to take MATH4900 and to graduate in summer 2019, and have already passed MATH2050,
 Section 4 if you intend to take MATH4900 and to graduate by the end of 2018, and have already passed MATH2050,
 Section 5 if you intend to take MATH4900 and to graduate in summer 2019, but are yet to pass MATH2050,
 Section 6 if you intend to take MATH4900 and to graduate by the end of 2018, but are yet to pass MATH2050.
 If you are a nonMATH student who intend to graduate with a second major in MATH by summer 2019, refer to Section 7.
 For adddrop matters in MATH4900, refer to Section 8.
 For the topics of the various sections of MATH4900, refer to Section 9.
 For MATH students who intend to take MATH4400:
 You are required to check whether you are qualified for taking this course. Refer to the CUSIS for detail.
 It is your own responsibility to look for a potential project supervisor and obtain his/her consent to supervise the project, whether in the first semester or the second semester 201819.
 After obtaining your supervisor’s consent, you should make an online application at
https://www.math.cuhk.edu.hk/project/
The closing date of application is 29^{th} June, 2018.
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.
 You will be informed of the result by 2^{nd} July, 2018.
Successful applicants will be preassigned to MATH4400 in the respective semesters, prior to course registration day.
If you application is unsuccessful, you are expected to register for MATH4900 in 201819. Refer to Sections 3, 4 below.
 For MATH students who intend to take MATH4900 and to graduate in summer 2019, and have already passed MATH2050:
 You are expected to take MATH4900 in the First Semester 201819, unless you are yet to pass MATH2060.
 If, for whatever reason, you do not intend to take MATH4900 in the First Semester 201819, you should let the department know your reasons and your study plan, no later than 4th July, 2018, by filling in the online form (and submitting appropriate supporting documents) at
https://www.math.cuhk.edu.hk/capstoneseminar1
Failing to do so may result in delay in graduation.
 There are seven sections of MATH4900 in the First Semester 201819. Each has its own theme. The themes are available in Section 9.
 Registration for MATH4900 is to be done on CUSIS, during your course registration day (presumably 8^{th} August, 2018), on a firstcomefirstserve basis.
The quota of every section is a hard quota. 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, 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 the department’s prerogative on what to do with the vacancies of MATH4900.
 If you are yet to pass MATH2060, you apply for a place in MATH4900 in 201819 at
http://www.math.cuhk.edu.hk/capstoneseminar2A
The closing date of the application is 4th July, 2018.
NO late application will be entertained.
 For MATH students who intend to take MATH4900 and to graduate by the end of 2018, and have already passed MATH2050:
 Refer to Section 3 above, ignoring Paragraph 3b.
 For MATH students who intend to take MATH4900 and intend to graduate in summer 2019, but are yet to pass MATH2050:
 In principle, you are not eligible to take MATH4900 until you have passed MATH2050.
 You are NOT allowed to take MATH4900 in the First Semester 201819. However, you may apply for a place in MATH4900 in the Second Semester 201819 at
https://www.math.cuhk.edu.hk/capstoneseminar2
The closing date of the application is 4th July, 2018.
NO late application will be entertained.
 There are two sections of MATH4900 in the Second Semester 201819. Each has its own theme. The themes are available in Section 9.
 For MATH students who intend to take MATH4900 and to graduate by the end of 2018, but are yet to pass MATH2050:
 In principle you are not eligible to take MATH4900 until you have passed MATH2050.
 However, you may apply for a place in MATH4900 in the First Semester 201819 at
https://www.math.cuhk.edu.hk/capstoneseminar3
The closing date of the application is 4th July, 2018.
NO late application will be entertained.
 There are seven sections of MATH4900 in the First Semester 201718. Each has its own theme. The themes are available in Section 9.
 For nonMATH students who intend to graduate with a second major in MATH by summer 2019:
 If you intend to take MATH4400, refer to Section 2.
 If you intend to take MATH4900, you are expected to do so in the First Semester 201819. You may apply for a place in MATH4900 in the First Semester 201819 at
https://www.math.cuhk.edu.hk/capstoneseminar4
The closing date of the application is 4th July, 2018.
NO late application will be entertained.
 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.
 You are reminded that you are supposed to have read the information about the various topics of MATH4900 prior to course selection. For this reason, 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:
 First Semester 201819
 MATH4900A: Interesting facts in geometry and topology
 MATH4900B: Mathematics Education

This course is designed for students who are interested in mathematics education. Students will have chances to take part in design of teaching materials, development of elearning products and secondary school teaching.
Students in this section are expected to be able to speak Cantonese.

 MATH4900C: Problems in Euclidean Geometry and Beyond

In this section, we will study some of the intuitive problems in Euclidean spaces which are easy to state but sometimes require ingenious new ideas to approach a solution. The idea is look into the motivation, history and development of certain specific problems, some of which may still be unsolved, and get an understanding of the current state of affairs and possible generalizations. Topics include for example convex geometry, isoperimetric problems, billiard dynamics, circle packings etc.

 MATH4900D: Topics in Image Segmentation

In this section, topics are surrounding the study of a flexible approach for image segmentation and its various applications in different fields. Students will first study some background knowledge together and then divide into small groups of two to work on different problems, including vessel segmentation, hyperspectral image classification, pointcloud classification and CryoEM imaging.

 MATH4900E: Mathematics related to some current issues
 MATH4900F: Machine Learning  A Bayesian and Optimization Perspective
 The objective of this seminar is to provide students with a solid understanding of machine learning from the Bayesian and optimization perspectives used in data mining problems. By revealing the underlying structure and regularities of the data at hand, which is viewed as learning from data, we developed a model that could be used to provide predictions. Bayesian estimation and optimization theories are very broad concepts and we will focus on issues related to machine learning algorithms. We will examine different learning algorithms using Bayesian estimation and optimization theories.
 The objective of this seminar is to provide students with a solid understanding of machine learning from the Bayesian and optimization perspectives used in data mining problems. By revealing the underlying structure and regularities of the data at hand, which is viewed as learning from data, we developed a model that could be used to provide predictions. Bayesian estimation and optimization theories are very broad concepts and we will focus on issues related to machine learning algorithms. We will examine different learning algorithms using Bayesian estimation and optimization theories.
 MATH4900G: Number Theory

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, quadratic forms.

 First Semester 201819