1. Learning mathematics is a way to cultivate logical thinking ability. One-dimensional quadratic equation or vector is just a tool to exercise logical thinking. "Logical thinking ability" is a kind of ability that everyone should have regardless of arts and sciences.

When I was a child, I always thought that mathematics was just a subject, but when I grew up, I found that many things were influencing us subtly. Many times, I will sigh that some people are meticulous because they have their own rigorous way of thinking and logic, from A to B.C.D, and then grow branches like leaves.

But I think the cultivation of logic, like the cultivation of habits, needs to be accumulated over time. It's crazy to change your logic just by this book, but with the awareness of change, change will happen.

2. Language ability is the foundation of mathematics ability. When people think about things, the tool they use is language.

I really agree with this sentence. As for how and why I agree, I can't say it. Look, Chinese is very important.

3. The first chapter "Wake up your math power"

The question at the beginning of the first chapter, judging who is lying, makes me feel very much like the killing game of "Please close your eyes when it is dark" that everyone usually plays, or the script killing that is very popular in recent years. I have never understood it, because I don't think back, and I judge by my sixth sense and intuition. There is no logic. At most, I will say "I think so", so I won't participate in such activities, and I will set myself a limit invisibly. When I saw this problem, it reminded me immediately.

I don't understand the example in the following paragraph. What kind of individual groups can exist as a group for the same goal? In short, he introduced three methods in this exercise: the premise of logical analysis is the ability to read and interpret; The second is to learn to use charts to help you understand, even if the problem is specific; The most important thing is the ability to integrate a large amount of information, which is an abstract ability to grasp the essence.

4. Chapter 2 "What is mathematical power?"

This chapter says a lot of "correct nonsense". For example, to cultivate good mathematical logic, we must think carefully; You can't learn math by rote and so on.

5. Chapter 3 "Seven Aspects of Mathematical Rational Thinking"

1) collation: the purpose of collation is to discover new information hidden in existing information; Choose the most suitable standard to judge whether new information can be obtained; How to increase the amount of information? Increase useful information through multiplication, that is, through comprehensive consideration of abscissa and ordinate;

2) Order: This concept is helpful for some choices in life, involving some necessary and sufficient conditions, but I think many of these mathematical ways of thinking are just compromise choices made under the limited conditions of life.

3) transformation: there are two ways, in other words: use different ways and expressions to achieve your goals; To use causality, we must first learn to judge whether there is causality in a relationship, and then there is only one or more reasons. After reading it for a long time, in most cases, the decisive factor is not whether there is mathematical thinking, but the size of the cognitive range.

4) Abstraction, that is, summarizing the essence of * * * and discovering the essence of things. Therefore, both names, formulas and graph theory are abstract tools and methods.

5) concretization, that is, using deduction and induction to explain.

6) Reverse thinking should have multiple perspectives and look at problems from different angles. The most difficult thing to prove in mathematics is to make it clear that one thing cannot happen. With this mentality, you can go ahead in everything you do. It also introduces the opposite of absurdity and antinomy, which makes me feel that this book is more like a logic lesson than an introduction to mathematics.

7) Mathematical aesthetic feeling. The author tries his best to introduce mathematics in various ways, whether it is logical proof or music conductor, but I think his introduction is very pale, because music and mathematics are inherently logical, or many people who are good at mathematics like music. Is this the way to wake up the math brain? It's really confusing