---------------------------- Learning scientific concepts ---------------------------- To learn scientific concepts, one needs to know what one should aim for - what it means to have understood a concept. If you look at worked examples (or at your own solution after you found it by trial and error), you need to ask yourself: _Why_ did this work here? On which property of the problem did this argument depend? How could I recognize when to apply the same trick, argument, transformation, substitution, etc., in a different situation? and similar questions. Your understanding is the better the better you can give a running commentary on every step of a worked solution (or of a textbook presentation of the matter), in a form such as: ''At first results in . Then leads to . Now the key step is to do , reducing the problem to .'' etc., in a way that everything is clear to you (and to someone listening, if there is one). Learning a concept means learning how it connects to other concepts, techniques, tricks, examples that you know already. Science is a very dense web of relations, and concepts are nothing else than named things expressing such relations. The better connected your web of concepts is (and the fewer false connections it has) the better is your understanding, and the clearer your perception of what you study. These connection grow mainly by practicing, and by reading the same things from as many perspectives as feasible. Therefore instructors, textbooks, additional readings, discussions with classmates or in an online forum, worked exercises, doing your own exercises, and explaining things to others complement each other.