【英語要約】数学的に考える力をつける本

Review

I think many people are not good at mathematics. One such person is the summarizer. Since I was a student, I've been very bad at mathematics, and I've had a bitter memory of holding it up to the point where it didn't become a red dot.

Although this book is a book on mathematics, there is no such thing as "calculation" or "mathematical theory". Even if you are allergic to mathematics, you can read it without worry, and in fact, this is the essence of mathematics!

In this book, the author explains that mathematics is not a study to improve math, but a study to learn how to use Kotoba. You may be wondering if it is a national language to learn how to use words, but in mathematics, words are used logically to solve problems. That is why mathematics is a study to learn how to use words.

"Mathematics words" such as "temporarily" and "because" are essential for easy explanation. By putting mathematical words between short sentences, you can explain things logically. In addition, the ability to grasp the structure of each thing will dramatically increase, and 1% of the techniques for demonstrating without contradiction will be acquired, and it will be possible to explain easily and concisely. It seems that this technology has the power to change lives.

After reading this book, I felt that the mathematical way of thinking was actually not that difficult. If you are allergic to mathematics, please take this book in your hand. I'm sure my view of mathematics will change.

Main points of this book

Point 1

If you use "math words" such as "for example" and "that is", "structure grasp → argument → explanation" will be successful. You will be able to speak in short sentences using math words.

Point 2

If you give a “definition” such as “I will talk about three points from now” at the beginning of the story, the listener can feel secure and ready to listen.

Point 3

The act of "demonstrating without contradiction" in mathematics is also an act of convincing oneself. A person is a creature that cannot act without consent.

The essence of mathematics

Is math useful?

The author was absorbed in soccer and math when he was a boy. As the teacher said, soccer did not endeavor to practice with the belief that patience and cooperation will be useful in the future. I just liked soccer. Mathematics is the same, I didn't think it would be useful when I was an adult, but I was absorbed in it because I liked it and had fun.

One of the reasons why I didn't study mathematics was that no one told me what it was useful for. But if he had taught me what mathematics could help, would he really study? The answer is probably no. The only reason for this is retrofitting.

But these guys are not bad. Poor education may have led to a dislike of mathematics.

Mathematics is useful if you want it, and it doesn't. If you know the essence of mathematics through this book, you should be able to use it in your real life.

The protagonist of mathematics is Kotoba

What is mathematics? Many will answer "calculate". In fact, many mathematics classes focus on calculations.

But calculation is just a task. Anyone can give the correct answer by following the rules, and you don't even have to think with a calculator or Excel. In other words, if the scholarship is mainly about mathematics, "math = work". Is that really so?

What does mathematics do?-The author's answer to this question is "mathematics is the learning of how to use words." What is important in mathematics is not to calculate accurately, but to grasp the structure of a problem using logical words. For example, if you think about a pentagon, you can explain how to calculate the area by connecting facts with logical words such as "because" and "because". In other words, the logical word "logical word" is the protagonist of mathematics.

Life-changing math word

The author uses the expression "mathematical word" as a word that expresses logical words in a straightforward manner and fills the sense of distance between the two concepts of "mathematics" and "words". Mathematics Kotoba, for example, expresses a transformation "in other words," "turns it back," expresses a conflict "but" "on the other hand", expresses a condition "and" "or" "at least", a hypothesis There are "provisionally" to express, "because" to express a reason, "more than" and "that is" to express a conclusion.

If you use math words, "Structure grasp → Argument → Explain" will be dramatically improved. In other words, the ability to grasp the structure of each thing will dramatically increase, and 1% of the techniques for demonstrating without contradiction will be acquired, and it will be possible to explain easily and concisely.

In fact, most of what we do consists of any of these three, or a combination. This includes changing jobs and confessing to someone you are interested in. It can be said that if you can master these three steps, you can become compelled at the point of your life.

[Must-read point!] Tell in "Math Words"

Model is car navigation

Those who talk a lot to waste are "criminals of conversation" that take away people's time. To avoid becoming a criminal in conversation, you should use the model of car navigation as a model. Car navigation will tell you the shortest route without saying anything extra.

In fact, if you analyze how car navigations are transmitted, you will find that they are extremely mathematical. First of all, he will tell you the next action in advance, saying, "Turn right now." By doing so, the recipient can continue to drive with that knowledge. Then, when you approach a turning intersection, tell them that you are turning right, and the recipient can understand what you should do now.

When you think about it in a normal conversation, for example, the word "because" plays the role of "turn right ahead" in car navigation systems. If the speaker says "because", the receiver can perceive the next story as the "reason" and smoothly understand the "reason" that follows. The same applies to "for example". You can get a smooth understanding of the story by inserting only one math word.

Mathematics words

There are two points in mathematics words. The basic template is "text → mathematics word → text" and making it in short sentences. Let's hold down this point and mathematically convey "Please do not ride in."

There is more than one answer. "Please refrain from rushing ride" → Because → "Because the train delays because of that", "Please stop running rushing" → Because → "Because you may be injured because of that" etc. right. Orient the story with "because" and continue with sentences that match that direction.

What happens if you add the expression "high impact"? "Please refrain from rushing in." → Because → "Because of that, the train will be delayed" → Temporarily → "If the train is delayed for 5 minutes, 5 minutes of all passengers will be robbed" → Further → "That is the commuting time If so, the impact is so socially significant" → Therefore → "Please refrain from rushing in." It is easy to convey and is concisely explained by continuing in a short sentence with four mathematical words in between.

Define mathematically

The representative of "a person who conveys mathematically" is a mathematics teacher. A good mathematics teacher will give a "definition" at the beginning of the lesson. A message that directs the lesson for the day, such as "I will explain how to solve simultaneous equations from now on."

Listeners are reassured and ready to listen when you first give them the definition. The phrase "I will tell you three points from now on" is also part of the definition.

When the author trains, "What do I speak now?" "How much time do I take?" "What kind of posture should I listen to?" "Do I need to take notes?" "Interactive form" I would like to have it", and the "space" of the training is defined. By defining in this way, “comprehension” is created in the communication of training and “discomfort” is eliminated.

Practice to structure

Does "I want to work locally because I have a love for you" pass?

When solving a math sentence problem, the premises of the problem are structured to solve the problem, and the answer is proved to be correct. The essence of mathematics is two "thinking" actions, the first stage "structure grasp" and the second stage "argument".

Here, let's practice "structuring" by using a case that is often found in reality. What do you think about the reason why job hunters often want to work locally because of their attachment?

Structuring this reason using mathematics words, "I like the locals" → therefore → "I want to work locally". If this student's reason for aspiring is really this structure, another content with the same structure should also be a reason for aspiring. "I like Okinawa" → Therefore → "I want to work in Okinawa". "I like Tokyo Disney Resort" → Therefore → "I want to work at Tokyo Disney Resort" has the same structure.

In this way, "I want to work locally because I have a strong attachment" is not a reason to want to join a company that is currently hiring a job or a reason to work locally. If you really want to work locally, it might be more compelling to explain that "I want to set up a base near my parents' home and walk my life as a member of society" for my parents.

Let's define "business"

As another practice of structuring, let's try to structure "business". Consider the sentence "Business is XX" that is included in XX. It is a practice to organize and grasp the structure, and compare it to another.

Based on his experience so far, the authors thought that "business" was from the first stage to the fourth stage. The following is a simple summary of these four steps.

・First stage: Launch

・Second stage: Get on track

・Third stage: eliminate unnecessary things

・Fourth Stage: Assigning work to a third party

When the fourth stage is reached, the person to whom the work is assigned starts a new business and returns to the first stage. The business is to repeat this as a cycle.

Next, I searched for each of these four concepts that had the same structure. The first step is to make a game from scratch, that is, to add. The second step is to put on orbit, multiplication = multiplication. The third stage is a subtraction phase that eliminates things that do not work or are unnecessary. And the fourth stage is division, which divides the work you have. From this point of view, we could define that "business is to continue arithmetic operations".

In this way, various things can be considered mathematically by organizing them and comparing them with the same structure. By all means, try practicing with the materials and themes that are in your daily life.

Life-changing "argument"

"Demonstration" = "convincing" moves people

When solving math problems, think logically about any inconsistencies and fill in the answer sheet. This "demonstration without contradiction" is also a process for you to convince.

A person cannot move unless he is satisfied. For example, "Why do I choose freelancer rather than employment at a well-known company?" → Because → "Because the personal brand is more valuable than the company brand", "Why do I have a drinking party today? "Did you refuse?" → Because → "If you overdo it, it will affect important presentations tomorrow." The more important the situation is, the more convincing people are using math words.

In order to convince a person, he or she must first be convinced. If you are not convinced when giving instructions to your subordinates, you should not be able to convince them.

It is pointed out that there are few people who can act today. The cause may be a lack of convincing skills.

How to produce results that mathematical induction teaches

If you put the dominoes in order without any flaws, defeating the first domino will kill all dominos. Defeat the first = defeat all, this is a mathematical reasoning.

Mathematical induction, for a claim, concludes that:

A: Prove that your starting point is correct.

B: If the last minute is correct, prove that the next is also correct.

We conclude from A and B that the claim is correct in all cases.

If we can prove that only two of A and B are correct, we can conclude that they are correct in all cases. In terms of dominoes, A is "falling down first" and B is "putting all dominoes in order". If even these two things are true, we can conclude that "all dominoes will fall".

Mathematical induction is rarely used in real life, but in fact it gives important attention. It means that if you have a structure where you take a small first step + continue it, you can achieve big results.

If you are convinced by this proof, you may be conscious of "small things and tricks". You can think of a way to make that a habit, or you can take the first step by facing what you have been evading. Believe in mathematically proven facts and take action now.

Recommendation of reading

As I wrote in the review, the summarizer is not very good at math. To be honest, I only have bitter memories, and I'm doubtful that I can still understand simultaneous equations as well as differential integration.

However, when I finished reading this book, my impression on mathematics had changed. In short, "think logically" can be paraphrased as "think mathematically." And, as the author said, "confirming the structure", "demonstrating without inconsistency of 1%" and "explaining clearly" were the three necessary skills for all business people.

Although I could not complete the summary, this book explains how Mr. Takafumi Horie, Shinjiro Koizumi, Osamu Hayashi, etc. can improve the persuasiveness of the remarks by using mathematical words. .. Even the abstractor should be careful not to become a “conversation criminal”, keeping in mind to convey it in a short and easy-to-understand manner.

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