When facing to some new material in mathematics, I feel easily to be overwhelmed by lots of details with losing the woods for the trees. So is there some good strategy to study the materials particularly for the first few times(e.g. reading textbook) ?

e.g. is it generally recommended to mentally review when finish reading each chapter, or even section in a textbook, by summarizing the ideas with blank papers and pens, for example ? What I am doing so far is to just continue after reading each section, but it seems easily get lost somewhere later, either convinced by logical steps but do not know what it is really doing, or even just forget the previous step/idea to understand the current staff.

It is quite strange that even though it is understood at least in some level for a certain knowledge when reading a textbook, but after some time, there are some 'knowledge points' are forgotten even the ideas


Actually this question is very general, so let express my thoughts on this. Before reading any new topic say for example Sylow's Theorem, I try to have a general idea beforehand that what that topic is all about. Most of the textbooks give some nice introduction in the beginning of each section that what actually is the goal of that particular section, else I read about that on Wikipedia or Wolfram etc. In this way, the objective of reading that topic is always in my mind and hence I am able to appreciate the logical sequence of the steps taken towards a proof and most of the time it allows me to see that why $this\ idea \ is\ working \ here $.

Secondly, as you mentioned to write down the key ideas of each chapter. Instead I write down whatever idea I get basically after every page of the textbook. It sometime happens that at the end of the chapter some of them are worthless, but even that helps in seeing that why are they $worthless$.

Third and perhaps the most important is that I try to solve as many problem as I can on a particular topic. This automatically helps in clarifying that which concept of the previous section can be applied to what sort of problem. In this way I get an experience of some $concrete$ situations in which I can apply my understanding. Moreover, it also helps in pointing out the points where I have misunderstood something. For example, merely knowing Sylow's Theorem won't help you until and unless you use to to classify groups of small order, or you use them to prove that certain groups are not simple.


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