### First reflection on Urss project

My Urss project has gone more than half way through. I think it is the time for me to have a little pause and review what I have done. Moreover, I shall record what I gained and where I need to improve.

**Background reading **

I spent about one week on reading background material, which included three papers and three chapters in a textbook. The difficulty of the reading was about all right, but it did require lots of efforts to concentrate to understand. For a few hard proofs, I can only scratch the main idea. Compared with attending lectures, this self-studying process is more independent with a bit more stress.

**Communication with my supervisor**

I feel that I can understand most of my supervisor's explanations and provide responses related to the topic to show my understanding. I am not afraid to ask questions even if it is sometimes basic. My supervisor explains to me with details, so everything looks very clear.

**Learning from my supervisor**

After obtaining some results, he will check it with a general estimate. If they are different, then he will look up the previous deduction for mistakes. It helps when the final result is a combination of several basic results. It narrows down the range of the mistakes if the final result is incorrect.

Due to lack of understanding of random walks, I often decompose the chain wrongly by removing some edges. This condition sometimes is so strong that the walks are pushed into one direction. Hence the later calculation go wrong. A more careful investigation of the Markov chain can help to solve ths problem.

**Progress of the project**

After learning the background knowledge about the relationship between random walks and electri networks, the analysis of random conductance model on probabilities went smooth. But the analysis on expectations did offer us some challenges. The formula became complicated and messy. We analysed the chain and calculated the formula for several times. Finally we get most of it done except one term in the formula. The simulations for the probabilities run well.

However, I had a disgreement with my supervisor. Based on my calculation, the term we want to find coincides with another term I find. So I guess they are the same, but we need more explanations. but my supervisor thinks they cannot be equal theoretically. Hence he provides me another method to find the term. I will try to investigate this term further to see the result and organise all the drafts.

**Improvement in typesetting(learning latex and bibtex)**

Previously I know TeX, which a basic typesetting program for mathematics. Due to a problem of inserting graphs, I learn latex, which is a more powerful one. It enables me to do something I cannot do before, e.g. the cross referencing within a paper.

I learned how to make a proper reference to a mathematical article. This involves saving the references in a seperate file through bibtex.

**Reflections on other things**

Most of the time, I can meet the goal set by our meeting. But when there is a long break between our meetings, I tends to be inefficient, especially when I am stuck in some mistake. Perhaps I should set a daily goal to improve self-motivation and leave extra time for the goals.

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