Personally I firmly believe that the real learning doesn't happen in lectures, but only when we are wrestling with a concept through a set of problems, designed specifically at the right difficulty so that it is challenging, sometimes frustrating, but rewarding and expands our knowledge and skills after solving them (maybe with some help from your colleagues). Therefore it is okay if you find the problems hard; that is by design.
We will have problem set coming out every two weeks. Some problems are marked with a star; such problems are optional to the undergrads, but mandatory to all graduate students. A few problems are marked with a bigger star; they are more challenging (and fun) problems, and is optional to everyone. I might (rarely) give out problems that I can't solve; those problems will be marked with a REALLY big star. Ignore the stars, solve those problems, and publish a paper with me.
During the term we will ask everyone to submit a research proposal; people then join in groups to work on the projects. Be creative with your projects; they can be surveys, theory research, implementation of some topological algorithms, art pieces generated using topological tools, etc. You are encouraged to work on problems that is relevant to your own research. It is not necessary for you to work on your own proposal; if you find others' more attracting, join forces with them! At the end of the term each group will give a short presentation about your findings, and submit a summary documenting everything. More details will come out as the course progresses.
For Homework 0, you are encouraged to work through the problems as much as possible by yourself, because it serves as an assessment to whether you have the required knowledge and skills to learn efficiently in this class. I don't mind you chatting with others and Google for solutions after you made an honest effort trying.
Starting from Homework 1, you are allowed to work in groups each up to three people. Each group will submit a solution together by one of the group members; the solution should be clearly marked with the names of all group members.
You are strongly encouraged to use all the resources online/offline toward solving the problems. You are also encouraged to work with other groups (and also people outside the course) and discuss your progress, as long as in the end each group individually writes down and submit their own version of solutions in their own words, and properly cites everyone and everything you have consulted. In particular, if you find a solution manual online that contains an answer to the problem, cite the solution manual. If chatting with your friends at gaming night gives you an idea to solve the problem, cite your friends. If your cat walks across your keyboard and sends you to a Wikipedia page you never seen that contains a crucial construction to the proof, cite your cat. However, you don't have to cite the lectures and any course related materials listed on the schedule webpage.Please refer to the Academic Honor Principle if you have doubts.
Homeworks will be announced in class and posted on this page. All homeworks should be submitted through Canvas. There is no strict format requirements about your solutions; the only important thing is to present and communicate your ideas in a clear and succinct fashion. Also make sure the lighting works out if you take a picture of your handwritten solutions. (I recommend you to convert the photos to black and white first.)
No late submissions will be allowed. On the other hand, not all problems will be counted towards your final grades. We will drop the lowest one-third (rounding up) of all the homework problems. For example, if a total of 15 problems are giving throughout the term, only 10 of them will be counted towards the final grades. You are still strongly encouraged to work on all the problems; this lenient policy is in place to prevent any unforeseen situations coming up. If you can only devote limited time to the class, feel free to strategically skip some of the problems and focus on the ones that is more interesting/relevant to you. On the other hand, problems marked with stars do not have a deadline. Feel free to submit solutions to them at any time. You are encouraged to work on them and discuss with me anytime (even after the course is over). If you believe you need any special accommodations beyond this, please come and talk to me. The online learning experience can be hard for many of us, so please don't hesitate to reach out to me anytime.
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