Reading notes-"Dark Time" (2/2)

Classic excerpt

1, in fact, from the perspective of the actual development of mathematical history to teach mathematics, but also the best method of mathematical teaching methods.

2, Polya's "How to solve it" refers to the thinking method:
(1) Always remember unknown quantity
That the problem must always be on the attention level;
(2) using special cases to inspire thinking
It is easy to use the method of trial and error to help explore the internal structure of the problem.
(3) in turn derivation
Inverse problem solving implies a profound thought in the question: attribution. When solving a problem, pushing the other way is actually using another heuristic--trial and error ——。
Trial and error is the most commonly used, but also the most effective heuristics, but the trial and error is not the most efficient.

Conclusion often contains rich conditions, such as what kind of solution is to satisfy the test instructions of the constraints of the solution, in general, with the help of the knowledge contained in the conclusion, we can more "intelligently" search solution space.
Sentiment: The book mentions the Unknown solution, is uses the conclusion derivation result. This led me to reflect on the mathematical learning process from a small, unexpectedly found that a variety of solutions, the original can be summed up as a few, no matter what, should be more thinking, to summarize the law, can be harvested.

(4) Trial and error
(5) Conditions for the adjustment of the topic
(6) Solving a similar problem
In order to facilitate the knowledge structure in the brain can really "migrate", in memory mastery and analysis of the problem should be as far as possible to look at the abstract, so as to establish the essential relationship of knowledge, can maximize the associative space.
(7) List all theorems or properties that may be related to the problem
(8) Examine the opposite side and examine all other situations
(9) generalize the problem and solve the problem after generalization
Solving a class of problems is easier than solving a particular problem in this kind of problem, Polya called the inventor paradox.
Two intriguing heuristics:
(10) Consciousness hatching method
We thoroughly understand the problem first, put it in our head, and wait for our subconscious to solve it.

Sentiment: This way of thinking must be mentioned, I read the first half of the book last week, but also put forward this method, and thinking about the physical, give me an example: Recently I have been completed an operating system experiment, to write C code to implement multi-tasking processor scheduling problem, I made a day of code, how to debug, Will always appear garbled, study after a night I am sure that my ideas are OK, but also for example, a lot of examples, ran a bit of code on the paper, but it is not the final result. I put the question away for a few days. But these days, I in the gym treadmill on the thought, class distracted thinking, a person to eat when the thought, also did not think of anything, but the more I want to. A few days later, I went on debugging, changed to change suddenly on the pass, and did not change what the key code, that is, the variable increment of the code order.

(11) Hot Potato Method
is to throw the problem to someone else to solve it. In this network age, almost any intellectual problem, can quickly search or ask the answer.

3, the thinking pattern refers to subconsciously follow the existing knowledge framework thinking process.

4, how to gain the knowledge advantage, prevent being bound by the knowledge, is a technology.
Whether it is in the process of solving problems or learning, ask yourself a question, "I have mastered this knowledge the deepest and most essential thing" is very beneficial.

5, there are many problems, the key to solve their knowledge can be obtained by examining the conditions contained in the topic itself, such topics are testing the ability of the thinking itself a good topic. And if this nature is not at all through the study of the topic itself, then the topic is to test the knowledge reserves and contact ability.

6. Ex post bias: Once the results are known, all evidence pointing to the results appears to be so clear and full, while the evidence of all the counter-results appears to be so not obvious and inadequate.

7. The benefits of visible thinking (writing a clear thought process on paper):
(1) The thought process is recorded, giving us a complete review of the opportunity;
(2) Expanded our working memory, increased the thinking of the cache;
(3) as a visual clue, it may arouse more memories of the existing knowledge;
(4) Avoid thinking stereotypes wrong;
(5) Find another possibility;
(6) It is beneficial to the reflection after solving the problem.

8. If you want to nail a nail, everything looks like a hammer.

9, if you focus on the problem you want to solve, then what you see will appear in the past you do not see the side.

10, fish is the last to see water: Explain the problem of thinking set.
Ordinary people obey the rules, the bulls disregard the rules, and the great men create the rules.

11, the design pattern is a patch, its appearance often means that the language is not strong enough, its use means a lot of, and to achieve the programming purposes unrelated to the boilerplate code.

12, do not feel that the design pattern is not enough good enough, in the simplest way possible to complete the task is king.

13. Learning programming is the basic concept and accomplishment.

14. Think Out of box.

15. What we want is not the theory of relativity, but the brain that is the birth of relativity; we want not the golden egg, but the chicken with the golden egg.

16, before you understand the proof behind, any theorem is equivalent to you-equivalent to the back multiplication table.

17. Lisp, Scheme, Haskell ... These languages, which are characterized by abstract and concise beauty, are still active in the computer science, although the abstract way, which is essentially derived from the theory of lambda operators, does not conform to the habit of human thinking, and is doomed to become a mainstream programming language. However, this still does not prevent them from becoming the best textbook of programming theory and computer science.

A good algorithm book

Polya "How To Solve It"
Udimanber's introduction to algorithms: a creative approach

Reading notes-"Dark Time" (2/2)