Recommend a website, Mathematical music （ https://shuxuele.com ）

How to put it? I'm not good at math, but I'm not hopeless. In the pursuit of student career, the basic situation is: good teachers, good grades, bad teachers, poor grades. Unfortunately, I met poor teachers more often.

I didn't feel anything before. When I grow up, who will study mathematics. Later, I encountered some problems in my life. For example, I didn't even understand the concept of interest. I couldn't distinguish between monthly interest rate, annual interest rate, equal principal and interest and equal principal. Then, I was confused about the future. I didn't know how to choose. I saw some popular science articles that explained the uncertain future from the perspective of probability theory. I wanted to see MIT's Introduction to Probability. Only then did I know that the so-called teaching materials were very different. Foreign mathematics textbooks were good. But there is another situation. You know that the textbook is well written, but the mathematics is interlinked, and some foundations you don't know can't go on at all. So I started to turn to the book Thomas Calculus again, and then the problem came again. Because the English foundation is weak, I looked at the tenth version of Thomas Calculus, which is a very awkward translation, After reading many concepts for three or four times, I didn't know what the translation was, so I searched and found this website called Math Music, which was a treasure.

This website is translated from an English website. The explanation of every mathematical concept is of no great detail. It is really broken and broken. It can be said that the concept of logarithm, natural base, radian, inverse function, etc., which was not understood when I was studying in the past, seems to have opened the two channels of supervision. I didn't expect it to be so understood. It suddenly dawned on me that most of the time, you are not stupid, but you have not seen good things. You met a paste teacher who read the book. As a result, you learned to learn how to paste yourself, then gave up, and then found a reason to comfort yourself. If you can't comfort yourself, people will not live.

Of course, talent absolutely exists, and there is a big gap between people. In essence, I don't want to be a mathematician or anything. I just find that I need the basics when I read some books, and then try my best to understand them.

It can be said that the content of this website is suitable for most ordinary people and most people who want to understand the world logically and rationally. If you have children, you can let them have a look at it. No matter from the perspective of illustration or design, it will definitely make them interested in mathematics.

Thank you for the Internet. It's also a pity that if I had such a mentor when I was studying, I might have another life.

Finally, I want to say: whether you want to admit it or not, the world is essentially a group of people who are good at mathematics are cutting the leeks of poor mathematics.

The whole logic building of probability theory is based on these three axioms.

Axiom 1: the probability of any event is between 0 and 1;

Axiom 2: the probability of a necessary event is 1;

Axiom 3: For any incompatible event sequence, the probability of at least one of these events is exactly equal to the sum of their respective probabilities.

The whole edifice of European geometry is based on the following five axioms.

Axiom 1: A straight line can be drawn from one point to another;

Axiom 2: Any line segment can be extended into a straight line indefinitely;

Axiom 3: Given any line segment, one of its endpoints can be used as the center of the circle, and the line segment can be used as the radius to make a circle;

Axiom 4: All right angles are equal;

Axiom 5: If two lines intersect the third line and the sum of the internal angles on the same side is less than two right angles, the two lines must intersect on this side.

What we usually call "feeling" and "intuition" is probably just an expression of "insufficient computing power": the "potential" in Go is hanged in front of Alpha Go, and the "understanding" in Buddhism is likely to be the activation of a certain neural unit. The Pythagorean school's "all things are counted" may be truth. Our brain is designed as "emotion first", which is reasonable, but it is the cerebral cortex that leads human beings out of their rough lives, but it is not easy to control the cerebral cortex and consumes huge energy. The bottom design's physiological happiness of "eating, drinking, whoring, gambling" is like "under the iceberg", and it is often futile to fight against it. But the reason why people are human is that they "live poetically", "this life is not enough, the poetic world", and they don't always look up.

The ambition of remolding thoughts is a middle-aged person's starting again after experiencing chaos. He found that the past is like loose sand and rootless duckweed. The previous words are emotional fragments, dominated by preconceptions, prejudice and emotions, and are a dump. So he wants to change. The beginning of such change should be based on logic, model and mathematical analysis.

Of course, this is very difficult. It is not a natural talent, and time is short. But isn't the pursuit of wisdom a lifelong pursuit?

The edifice of probability theory and Euclidean geometry is deduced from several axioms, which is one direction. On this road, we must first abandon the past, and then like a particle, the point, line and plane are four-dimensional and multi-dimensional to infinity.

Although the road is endless and faraway, I still want to pursue the truth in the world.