Capstone Course Arrangements
To: ALL students admitted in 201617 or before, who intend to graduate by summer 2020.
SUBJECT: Capstone course arrangements 201920.
 Overview:
 In order to graduate in MATH by summer 2020, you must have passed, as your capstone course, either MATH4900 (Seminar) or MATH4400 (Project), but not both, by 201920. 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 2020, and have already passed MATH2050,
 Section 4 if you intend to take MATH4900 and to graduate by the end of 2019, and have already passed MATH2050,
 Section 5 if you intend to take MATH4900 and to graduate in summer 2020, but are yet to pass MATH2050,
 Section 6 if you intend to take MATH4900 and to graduate by the end of 2019, but are yet to pass MATH2050.
 If you are a nonMATH student who intend to graduate with a second major in MATH by summer 2020, 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 201920.
 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 28^{th} June, 2019.
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 5^{th} July, 2019.
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 201920. Refer to Sections 3, 4 below.
 For MATH students who intend to take MATH4900 and to graduate in summer 2020, and have already passed MATH2050:
 You are expected to take MATH4900 in the First Semester 201920.
 If, for whatever reason, you do not intend to take MATH4900 in the First Semester 201920, you should let the department know your reasons and your study plan, no later than 28th June, 2019, 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 201920. 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 (in early August, 2019), 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.
 For MATH students who intend to take MATH4900 and to graduate by the end of 2019, 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 2020, 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 201920. However, you may apply for a place in MATH4900 in the Second Semester 201920 at
https://www.math.cuhk.edu.hk/capstoneseminar2
The closing date of the application is 28th June, 2019.
NO late application will be entertained.
 For MATH students who intend to take MATH4900 and to graduate by the end of 2019, 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 201920 at
https://www.math.cuhk.edu.hk/capstoneseminar3
The closing date of the application is 28th June, 2019.
NO late application will be entertained.  It will be the department’s prerogative on deciding into which section you will be added.
 In principle you are not eligible to take MATH4900 until you have passed MATH2050.
 For nonMATH students who intend to graduate with a second major in MATH by summer 2020:
 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 201920. You may apply for a place in MATH4900 in the First Semester 201920 at
https://www.math.cuhk.edu.hk/capstoneseminar4
The closing date of the application is 28th June, 2019.
NO late application will be entertained.  It will be the department’s prerogative on deciding 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.
 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:
 MATH4900A.
Title: 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, 
MATH4900B.
Title: Optimization methods in finance
Description: Optimization methods play a central role in financial modeling. In this section, we will explore how stateofart optimization theory, algorithms can be used to efficiently solve problems in computational finance. Students in this section are expected to have completed MATH2221; however, prior exposure to any highlevel programming language (such as MATLAB, R, C++) will also suffice, in place of completion of MATH2221. 
MATH4900C.
Title: Geometry of algebraic equations.
Description: Algebraic geometry is the study of the geometry of solution sets of polynomial equations. This subject links algebra to geometry. In this section, we will study algebraic geometry using tools from calculus and algebra. Topics include, but are not limited to: algebraic curves, affine varieties, projective varieties, sheaves and cohomology. 
MATH4900D.
Title: An introduction to hyperbolic geometry.
Description: In this section, we study hyperbolic geometry. We will start with five models of hyperbolic spaces and their interconnections. Then we will investigate the GaussBonnet Theorem for hyperbolic polygons, and tilings of the hyperbolic plane, and Fuchsian groups. 
MATH4900E.
Title: Knots.
Description: In this section, knots will be studied using methods from algebra, topology and combinatorics. Emphasis will be on polynomial invariants of knots. 
MATH4900F.
Title: Mathematics for Artificial Intelligence.
Description: The objective of this seminar is to provide students with a solid understanding of Artificial Intelligence (AI) with sufficient opportunity to accrue knowledge, experience, and competence in the methods that define the field. Artificial Intelligence concepts, methods, and systems are becoming more integrated into everyday activities. There are three main aspects of this seminar:
We will focus on issues related to AI algorithms developed in the past in terms of mathematical theories, formulations and modeling.

We will examine different AI algorithms where topics are natureinspired algorithms, deep learning algorithms and neutral network algorithms.

We will study many reallife applications of AI using algorithms described above.
Students taking this section are expected to have completed MATH2221.


MATH4900H.
Title: From calculus to algebraic topology.
Description: In this Section, we will use the knowledge from Advance Calculus to compute the "number of holes" of spaces, distinguishing an annulus from a disk and leading to the Jordan Curve Theorem. By revisiting the concept of path integrals and Stokes’ Theorem, we will see how the notions of winding number, differential forms naturally arise and how these are related to the ``number of holes" of spaces.
 MATH4900A.