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 homework 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 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. Same with another student in Fall 2022 during the metric embedding course, resolving an open question which leads to two important results that opens up a research direction. 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 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 Gradescope. 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.)
The final grade will be based on presentations, class participation, homework assignments, and the optional research project (if choose to). The tentative weights are 50% on presentation, and 50% on homework. If the student chooses to do a project it will serve as substitute for the later part of the homeworks. Because we are likely to 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. The grading will also take into account the difference between student groups (undergrads vs graduates).
Unless specified otherwise, all the problems with be graded based on a scale from 0 to 5:
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