family Math4991 Capstone Project in Pure Mathematics

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Class

  lecture tutorial
Time Tuesday, Thursday Monday
10:30 - 11:50 19:00 - 19:50
Venue 4504 5510
Coordinator YAN Min HE Hongren
Office 3487 3214
Phone 23587442 60934750

Week 1-9: Lecture

Four pure math professors giving lectures. Each professor gives three lectures and assigns one homework. The homework will be graded and counted toward the final score. The professor may also ask 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 also suggests possible projects.

Weeks 1&2 (Sept 4, 8, 11, 13): Flows on Signed Graph, by Beifang Chen: Lecture 1.

Weeks 3&5 (Sept 18, 20, Oct 2, 4): Kepler Problem and Lorentz Transformations, by Guowu Meng.

Weeks 4 (Sept 27): Latex, by the teaching assistant. The typesetting tool for mathematics is LaTeX. You are required to submit your second and later homework in LaTeX.

Weeks 6&7 (Oct 9, 11, 16, 18): by Allen Moy.

Weeks 8&9 (Oct 23, 25, 30, Nov 1): Poincaré-Bendixson Theorem, by Tszho Fong.

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.

Week 10-12: Project

By November 6, the students form project teams. A team normally has 3 members, and may have 2 in exceptional cases. Each team decides the topic from lectures, and must choose one of four professors as supervisor. In case too many teams choose the same professor, the professor can refuse the later teams.

The team arranges convenient time to meet the supervisors. They should regularly meet the supervisor, at least once a week.

Week 13: Presentation

Each team gives one presentation of around 20 minutes. I will randomly choose presenter and may switch presenter in the middle of presentation. All four professors and I will grade the presentation (as team).

You also need to submit your report (written in LaTeX). Each student should have different report. If the reports from the same team are too much similar, then the grades may be lower. The supervisor will grade your report.

Grade

10% attendance, 30% homework, 30% presentation, 30% report.

Attendance is mandatory because the course is structured like a workshop, and there is no textbook.

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.