SECTION L1, Classroom 1511, Tue/Thu 13:30-14:50

TA: CHAN Chin Hei and YAU Cheuk Wai ( Mon 17:00 ‐ 17:50, LSK1027)

This section is one of the 4 Capstone sections offered in the Fall of 2016. Capstone classes by nature involve projects, and this class will be no exception. What is unique about this class is that you will be exposed to a diverse group of professors and distinguished scholars who will present topics in various old and new branches of mathematics.

A typical 4-year curriculum in mathematics is actually quite limited in its scope, and often it does not have enough time to show the broadness of mathematics and its extremely diverse applications. In this class selected topics in mathematical sciences will be presented and discussed. The goal is to illustrate the beauty and diverse applications of mathematics. The class will be talk in the style of presentations, albeit there will be more discussions. The lectures will be delivered by several professors over the semester. Each professor will teach for a week, focusing on one topic of his/her choice. The selected topics are meant to be very diverse, ranging from classical areas in pure mathematics to modern applications of mathematics. The latter topics will be important because this section islisted for the pure math track, and knowing how mathematics can be applied to the real world is necesssary to gain deeper appreciation for mathematics.

As with any other mathematics courses, there will be some exercises after each class to reinforce the concepts from the lectures. These exercises will be collected weekly. Furthermore, there might be some open ended questions that will test your imagination and your ability to think independently. You will be encouraged to go online to look for related articles. One of the main goals in this course is to give you a feel for how mathematical research is done, which is where the project comes in. You will be asked to form small groups to do a project on a topic of your choice. Some of you will go on to become PG students in mathematics or other disciplines. It is my hope that by the end of the semester each one of you will be excited about mathematics and eager to look for a topic to do your own research.

Some important questions you may have, such as the grading scheme, office hours, TA information, can be found in this MATH4999 (pure math) Course Policy Document. Please also download the guidelines for submitting your work.



Schedule for Lectures
Dates Lecturer Topic Notes
01/09 and 06/09
Wing Lung LEE
Sphere Packing
Jingsong HUANG
Regular Polyhedra and Finite Symmetry Groups
13/09 and 15/09
Fibonacci Numbers and the
Golden Ratio
20/09 and 22/09
Frederick FONG
Poincare-Bendixon's Theorem
27/09 and 29/09
Weiping LI
Perspective Drawing and Projective Geometry
04/10 and 06/10
Guowu MENG
Kepler Problem
11/10 and 13/10
18/10 and 20/10
25/10 and 27/10
Maosheng XIONG
Congruence Number Problem
01/11 and 03/11
Picard's Theorem
08/11 and 10/11
Kin LI
Hardamad Matrices and Reed-Mueller Code
Guest: Wu-Yi Hsiang
Kepler and Newton Revisited
Please note Rm 2503
Kin LI
Hardamad Matrices and Reed-Mueller Code
22/11 and 24/11
Beifang CHEN
Topics in Graph Theory
Yongchang ZHU
Eliptic Curves

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