It's been a long semester, and I have to drop a course because i am not doing well in all others. Well, frankly, I think I have learnt my lesson, that is study is not about concentration and resource, the more time you spend and the more resources you used, the better understanding you will have. So the plan for this winter is first, finish complex variable, and prof it at the beginning of the semester, also, check the am I still in the group, then study some part of 427,436,and of course if possible 470. This seems to be impractical, I will make time table for each in detail. Hope, I won't be lost again for the next semester, and also I have to start to search for summer research. So, the winter is clearly not a break for me. Living in busy time is kind of pleasure, if I can retrieve passion from it, no matter success or failure.
The step towards a subject, you should first sketch a rough blueprint for that, like a content table for a book, and then list some of the important theorem or methods or concepts for each topic, and then practice them for some amounts of problems (find a good problem book) to get a concrete understanding for each of the concept. THIS IS VERY CRUCIAL!!!!!!!!
