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. The students are expected to spend a reasonable amount of time working on the assignments. In a sense, these are the real driver of the class.
There will be weekly assignments. Each week we will assign just one or two questions, to make sure that the students are following the material. Discussions with other students and using online resources are not only allowed, but encouraged. Some homework problems might require additional readings; all the extra readings required for the homework will be made available.
Some problems are marked with a star; these are more challenging (and fun) problems, and are therefore optional and do not count towards the final grades. I might (rarely) give out problems that I can't solve (marked with a bigger star) and problems that are known to be open (marked with a REALLY BIG star). Ignore the stars, solve those problems, and publish a paper with me.
(You think I'm joking? In the last offering of the class (Fall 2020), some undergrad solved open problem 2(e-f) in Homework 1 and the result has been written up and submitted to top-tier conference for publication. You can do that too.)
In addition to the assignments, the students may opt in for an optional research project. Students may choose a topic related to computational topology (broadly interpreted) of their interest, approved by the instructor; a list of possible topics will be provided. Choosing to work on research project replaces the later part of the homework sets on the more advanced topics.
For those of you who choose to work on homework sets alone: We will cover a variety of advanced topics in computational topology. It is understandable that not all of the materials will be useful for your own research. Therefore I encourge you to focus on (say) two topics that is more interesting and useful to you, and spend extra time thinking about those problems. Your grade will be based on those alone. (See the grading section.)
For those of you who choose to do a project: During the term we will ask you 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 asked to work through the problems as much as possible by yourself and submit the answers individually. It serves as an assessment to whether you have the required knowledge and skills to learn efficiently in this class.
Starting from Homework 1, you are allowed to work in groups each up to two people. Each group will submit a solution together by one of the group members; the submitted work 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 and Sources and Citations at Dartmouth 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 decide to take pictures 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, only problems from the first part of the class will have a strict deadline (one week after annoucement unless otherwise specified), and not all problems will be counted towards your final grades. The advanced problem sets and star problems do not have a deadline; feel free to submit their solutions at any time. You are encouraged to work on them and discuss with me (even after the course is over). If you believe you need any special accommodations beyond this, please come and talk to me.
The final grade will be based on the homework grades and the optional research project. The tentative weights are homework (60%) and project (40%) for people who work on projects, and homework (100%) for people who work on homework sets alone. Because we have a small-size class, I would prefer to talk to each of you and set up concrete goals after reviewing your submission to homework 0.
We will drop the lowest one-fourth problems (rounding up) from the basic homework sets, and lowest one-half problems from the advanced ones (if you choose to be graded based on homework alone). For example, if a total of 12 basic problems and 4 advanced problems are given throughout the term, only 9 basics ones and 2 advanced ones will be counted towards the final grades. You are still strongly encouraged to work on all the basic 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.
Unless specified otherwise, all the problems with be graded based on a scale from 0 to 5:
You may submit regrade requests if you think we misunderstood your solutions. We will regrade them based on the following rules.
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