family Math4991 Capstone Project in Pure Mathematics

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Course

This is one of 4 mathematics capstone courses.

A typical 4-year curriculum in mathematics is quite limited in its scope. In this class, a diverse group of professors and distinguished scholars who will present topics in various old and new branches of mathematics. These lectures will 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. The course is intended for the pure math track, and knowing how mathematics can be applied to the real world is necessary to gain deeper appreciation for mathematics.

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 to test your imagination and your ability to think independently. You are encouraged to go online to look for related articles. This gives you a feel for how mathematical research is done, and is where the project comes in. You will be asked to form small groups to do a project on a topic of your choice. I hope that, by the end of the course, you will be excited about mathematics and eager to look for a topic to do your own research.

Class

  lecture tutorial
Time Monday Friday Monday
13:30 - 14:50 9:00 - 10:20 19:00 - 19:50
Venue 4503 2406
Coordinator YAN Min CHEUNG Tsz Yung
Office 3487 3215
Phone 23587442 23587468

Lecture

Date Lecturer Topic
Sept 4 and 8 Min Yan Tiling
Sept 11 and 15 Weiping Li Perspective Drawing and Projective Geometry
Sept 18 and 22 Tszho Fong Poincaré-Bendixson Theorem
Sept 25 and 29 Jingsong Huang Regular Polyhedra and Finite Symmetry Groups
Oct 6 and 9 Guowu Meng Kepler Problem and Lorentz Transformations
Oct 13 and 16 Kinyin Li Hardamad Matrices and Reed-Mueller Code
Oct 20 and 23 Yongchang Zhu Eliptic Curves and Theta Functions
Oct 27 and 30 Huailiang Chang An introduction to Arithmetic and Riemann Surface​
Nov 3 and 6 Beifang Chen Flows on Signed Graph
Nov 10 and 13 Maosheng Xiong Congruence Number Problem
Nov 17 and 20 Yikman Chiang Picard's Theorem and Ramanujan
Nov 24 and 27 Eric Marberg Random Sorting Networks

Attendance, 20 points

Attendance is mandatory because the course is structured like a workshop, and there is no textbook. Your attendance will count toward the final grade.

Homework, 30 points

Exercises will be given after a lecture. The homework is usually due on Friday (for September lectures) or Wednesday (for October and November lectures) in the following week after the lecture. There may also be discussion problems or open ended questions that are not required to be turned in, but can be the basis for your term project. Homework will count for 30% of your total final grade.

The typesetting tool for mathematics is LaTeX. You need to learn LaTeX in the first four weeks, and are required to submit your homework in LaTeX after Oct 1.

You are allowed to discuss homework with your fellow students. However, copying is suspected because of the similarity of an unusual argument, especially if the argument is wrong, those suspected of copying will be called into Prof. Yan’s office and questioned. If copying is confirmed, an automatic reduction of 10 points in the final homework grade will be made to all involved parties for each incidence.

Project, 50 points

The project is team based. The team decides the topic and how to collaborate. A team normally has 3 members, and may have 2 in exceptional cases. The project consists of a presentation and a written final report.

Each team gives one presentation of around 20 minutes. The professor will randomly choose presenter and may switch presenter in the middle of presentation. A panel of professors determines the grade of the presentation, which is 25 out of total of 50.

The report must be written separately by each individual. Copying and any form of plagiarism from the web or team members is strictly forbidden, and will result in 0 point for all parties involved, regardless who copied from who. The report should be at least 5 pages long, but should not be overly long. The grade of the report is another 25 out of total of 50.

Not doing a project, or submitting an unacceptable project, will result in an F grade regardless how well you do in attendance and homework.

Grade

20% attendance, 30% homework, 50% project. Additional bonus points may be given to exceptional homework, presentation, or report.

LaTeX

Learn: Wiki on LaTeX. Wikibook on LaTeX (open source guide to how to use LaTeX).

For Apple computer: TeXShop.

For Windows: MikTeX, proTeXt, TeX Live.

Miscellaneous

Each professor will make himself available to you for that week and beyond. In addition, your TAs should also be available to help you. You are encouraged to talk to the professor and TA regarding your homework and project.

Showing respect to the professors and your fellow students is a basic courtesy all of you should understand and practice in all your classes. There is no exception in this class. During the class, please turn your cell phone to the silent mode. Also, you are not allowed to turn on your laptop or tablet unless it is for note-taking. Anyone who violates this code of conduct will receive a warning. A second violation will result in dismissal from the class, as well as a 10 points deduction on the attendance grade.

The course arrangement is subject to change as circumstances arise.