# Capstone Course Arrangements

#### Capstone Course Arrangements 2017/18

To: ALL students admitted in *2014-15 or before*, who intend to graduate *by summer 2018*.

- Overview:
- In order to graduate in MATH by
*summer 2018*, you must have passed, as your capstone course, either MATH4900 (Seminar) or MATH4400 (Project), but not both,*by 2017-18*. These two courses are*mutually exclusive*. - MATH4900 will be offered in both semesters. Most student 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 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 2018, and have already passed both of MATH2050, MATH2060,
- Section 4 if you intend to take MATH4900 and to graduate by the end of 2017, and have already passed both of MATH2050, MATH2060,
- Section 5 if you intend to take MATH4900 and to graduate in summer 2018, but are yet to pass both of MATH2050, MATH2060,
- Section 6 if you intend to take MATH4900 and to graduate by the end of 2017, but are yet to pass MATH2050.

- If you are a non-MATH student who intend to graduate with a second major in MATH
*by summer 2018*, refer to Section 7. - For add-drop matters in MATH4900, refer to Section 8.
- For the topics of the various sections of MATH4900, refer to Section 9.

- In order to graduate in MATH by

- 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 details.
- 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 2017-18*. - After obtaining your supervisor’s consent, you should make an online application at

http://www.math.cuhk.edu.hk/project/

The closing date of application is**30th June, 2017**.**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
**3rd July, 2017**.

Successful applicants will be pre-assigned to MATH4400 in the respective semesters,*prior to course registration day*.

If you application is unsuccessful, you are expected to register for MATH4900 in 2017-18. Refer to Sections 3, 4 below.

- For MATH students who intend to take MATH4900 and to graduate
*in summer 2018*, and have already passed both of MATH2050, MATH2060:- You are expected to take MATH4900
*in the First Semester 2017-18*. - If,
*for whatever reason*, you do not intend to take MATH4900 in the First Semester 2017-18, you should let the department know your reasons and your study plan, no later than**5th July, 2017**, by filling in the online form (and submitting appropriate supporting documents) at

http://www.math.cuhk.edu.hk/capstone-seminar-1*Failing to do so may result in delay in graduation.*

- There are seven sections of MATH4900 in the First Semester 2017-18. Each has its own theme. The themes is available in Section 9.
- Registration for MATH4900 is to be done on CUSIS, during 9 th August, 2017, (which is your CUSIS course selection day,) on a first-come- first-serve 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. -
After 9 th August 2017, it will be the department’s prerogative what to do with the remaining vacancies of MATH4900.

If you had not already entered the class list of any one section on 9 th August 2017, you might fail to register for the course at all, and end up delaying graduation.

- You are expected to take MATH4900

- For MATH students who intend to take MATH4900 and to graduate
*by the end of 2017*, and have already passed MATH2050, MATH2060:- Refer to Section 3 above, ignoring Paragraph 3b.

- For MATH students who intend to take MATH4900 and intend to graduate
*in summer 2018*, but are yet to pass both of MATH2050, MATH2060:- In principle, you are not eligible to take MATH4900 until you have passed both of MATH2050, MATH2060.
- You are NOT allowed to take MATH4900
*in the First Semester 2017-18*. However, you may apply for a place in MATH4900 in the*Second Semester 2017-18*at

http://www.math.cuhk.edu.hk/capstone-seminar-2

The closing date of the application is**5th July, 2017**.**NO late application will be entertained.**

- There are two sections of MATH4900 in the Second Semester 2017-18. Each has its own theme. The themes will be posted in Section 9 below and communicated to you via CWEM by
**mid-June**.

- For MATH students who intend to take MATH4900 and to graduate
*by the end of 2017*, 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 2017-18 at

http://www.math.cuhk.edu.hk/capstone-seminar-3

The closing date of the application is**5th July, 2017**.**NO late application will be entertained.**

- There are seven sections of MATH4900 in the First Semester 2017-18. Each has its own theme. The themes will be posted in Section 9 below and communicated to you via CWEM by
**mid-June**.

- For non-MATH students who intend to graduate with a second major in MATH by summer 2018:
- 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 2017-18.

You may apply for a place in MATH4900 in the First Semester 2017-18 at

http://www.math.cuhk.edu.hk/capstone-seminar-4

The closing date of the application is**5th July, 2017**.**NO late application will be entertained.**

- Add-drop matters in MATH4900:
- Once the CUSIS course selection day is over, the department will impose
*departmental add-drop consent*to MATH4900 in CUSIS.*You are not free to do electronic add-drop 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 add-drop 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 add-drop applications is 1300hrs of the last day of the official add-drop period.
**NO late application will be entertained.**

- Once the CUSIS course selection day is over, the department will impose

****Topics of the various sections of MATH4900:**First Semester 2017-18**- MATH4900A: Topics in topology or geometry
- Detail to be announced.

- MATH4900B: Model reduction
- Many applications involve highly oscillatory solutions, and approximating these functions require many degrees of freedoms. In this course, we will study some model reduction techniques to achieve the goal using a small number of degrees of freedom without sacrificing the accuracy.

- MATH4900C: Knots
- In this section, knots will be studied using methods from algebra, topology and combinatorics. Emphasis will be on polynomial invariants of knots.

- MATH4900D: Topics in number theory
- Detail to be announced.

- MATH4900E: Inverse problems and numerical PDEs
- In this capstone course, the following two topics will be discussed. Two students are working as a group on one topic.
- Inverse problems include importance and applications of inverse problems, formulations of mathematical models of inverse problems, mathematical properties and analyses of inverse problems; mathematical and numerical methods for solving inverse problems.
- Numerical methods for partial differential equations (PDEs) include background and applications of PDEs, numerical methods for solving PDEs, stability and convergence of numerical methods.

- In this capstone course, the following two topics will be discussed. Two students are working as a group on one topic.
- MATH4900F: Elliptic and parabolic equations
- In this section, topics are to about elliptic and parabolic equations including fundamental solutions, maximum principles, mean value theorem and their applications in some regularity theories.

- MATH4900G: Mathematical theory of rarefied gas
- In this section, topics cover the basic knowledge of kinetic theory in both physical and mathematical aspects. Discussions will be focused on not only the informal derivation from Newton to Boltzmann and then to Euler and Navier-Stokes, but also the mathematical analysis of related PDEs.

- MATH4900A: Topics in topology or geometry
**Second Semester 2017-18**- MATH4900H: Topics in Mathematical Imaging in Real World Applications
- In this section, topics are surrounding the study and applications of mathematical imaging using PDE and optimization models. Applications may include medical imaging, computer graphics, and computer visions.

- MATH4900I: Elliptic equations.
- In this section, topics are to about elliptic equations including fundamental solutions, maximum principles, mean value theorem and their applications in some regularity theories.

- MATH4900H: Topics in Mathematical Imaging in Real World Applications