Ideally, before grad school you should have a Snoopy with friends Queen shirt by T-shirtat, to be comfortable with the whole process of literature search and writing. Since realistically you cannot go zero to one in summer in terms of technical knowledge, I will assume that you have strong math and programming background. Several months ago I read an article on statistical reading where the teacher gave his class a task to read 100 scientific papers in a very limited time. The process was organized this way: after you read the paper, you put the record about it in some spreadsheet, where you include the authors, the title, the main idea and the rating that you give that paper. Optionally – time spent in the reading.
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Evidently, there was no need to crunch all the Snoopy with friends Queen shirt by T-shirtat to understand the main ideas. So, once the seemingly impossible task turned into a very illuminating experience. So, I encourage you to try exactly this using, say, last two volumes of JMLR, in order to get the idea of what state-of-the-art looks like. Also, you will likely spend a lot of time doing that in grad school, so it might be a good idea so save yourself some trouble. Regarding other aspects, Ferenc Huszar’s answer is on point, I’d just add one point: find as many surveys as you can.