From c05c1fde756d052e23c31e8b051350ce717b00fd Mon Sep 17 00:00:00 2001 From: Talal Alrawajfeh Date: Thu, 18 Jun 2020 11:21:06 +0300 Subject: [PATCH] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index efda607..5740eb3 100644 --- a/README.md +++ b/README.md @@ -27,7 +27,7 @@ Learning Mathematics is a tedious task that requires long periods of conscious e * Motivation for any new concept is a must. This includes historical development of the subject which is sometimes crucial to understanding, analogies, drawings, and many other methods. Thought is induced by problems, questions, and misconceptions; thus, knowing what questions were asked in the mind of the mathematician who developed the subject and the problems he confronted really helps guiding thought in the right direction of understanding. -* Always question the way the subject is presented. This includes questioning everything from the way terms are defined, to the way theorems are proved, even questioning whether the subject deserves the time and effort mathematicians put to it. We could use a good quote here from the mathematician Paul Halmos: "Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?". +* Always question the way the subject is presented. This includes questioning everything from the way terms are defined, to the way theorems are proved, even questioning whether the subject deserves the time and effort mathematicians put to it. Sometimes, there could be many different ways to define something; however, a particular definition is chosen among others for some conveniences and goals, so learning about these conveniences and goals would motivate the use of that definition. Some other times, more than one definition are studied independently so one can easily see the consequences of different definitions. We could use a good quote here from the mathematician Paul Halmos: "Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?". * Solve as many exercises as you can to challenge your understanding and problem-solving skills. Exercises can sometimes reveal weaknesses in your understanding. Unfortunately, there is no mathematical instruction manual for problem-solving, it is rather an essential skill that requires practice and develops over time. However, it could be greatly impacted by your level of understanding of the subject. The processes of learning and problem-solving are interrelated and no one of them is dispensable in the favor of the other. There are also general techniques that could be helpful in most cases which are found in some books on problem-solving (which are included in the roadmap).