After work, I feel that high school mathematics is actually quite simple, but it is still difficult to deal with the problem of high mathematics. Of course, the exam passed smoothly at that time because there were routine questions. Now I understand, I didn't study at that time, but I definitely studied in high school, and I will still do it after almost 20 years.
Theoretical physics and mathematics are closely related to feelings. Theoretical physicists must be excellent mathematicians, and the feeling of physics and mathematics is the real genius field. This field is not made up by diligence, and you can't get in without talent. Mathematics in our junior and middle schools is actually simple arithmetic, plus Euclid geometry, as well as basic reciprocal and most basic function calculation. It belongs to the category that ordinary people can understand, and college advanced mathematics is the real mathematical foundation, which needs a lot of things. In fact, it is very important to be diligent in mathematics in the college entrance examination. I have done a lot of exercises and found out the routine of the examination questions, and the scores are generally not low. To put it bluntly, experience can make up for the lack of talent. However, math doesn't wait for me to take the exam, and math doesn't mean doing problems. Therefore, it is very unreliable to judge math ability with good grades.
At least the requirements of advanced mathematics are much simpler than those of high school, and basically no skills are needed, so it is not difficult to solve problems. The exam questions are similar to the homework at the back of the textbook. Because of carelessness, I didn't get full marks in the advanced mathematics exam. The high school exam, that's because I can't, and I can't afford to break my head. Later, I specially asked Jimmy Dovich's high math problem set to do it. That's it. It's rare for high school students to encounter so many problems that they can't do. I feel that college mathematics only talks about calculus, but the content is relatively simple, not as extensive as high school.
The latter probability theory and linear algebra are simpler and cannot be compared with calculus. As for college chemistry and college physics, it's just another study of chemistry and physics in high school. Physical chemistry, which is independent from chemistry, covers all reactions and substances in a completely accurate quantitative way from a brand-new angle, which is rare. Almost need to learn from scratch, there are no old books to eat, otherwise it is a gobbledygook. College electrical engineering, electronics, mechanics, which are independent from physics, will also feel difficult in an instant.
Many people don't understand what talent is until they get to college. Learning well in high school is more about understanding and proficiency in content. Good grades in college exams are a prerequisite for talent, but they are not necessarily talented. The big coffee in mathematics has established its own school when we were in college, such as Newton, who invented calculus when he went home to herd cattle. Galois talked about group theory at the age of 22, and it took decades to understand it. Gauss, riemann sum Fermat. These people, I believe, are really talented. More than 90% of us basically have nothing to do with the word talent. At most, I am proficient in something, and I know it a little earlier than others, that's all. The world is so big that you have nothing to do.
The learning thinking of universities has completely subverted the thinking of primary schools in senior high schools. It takes hundreds of times to train a formula in high school to understand the method, and it is probably exhausting to learn a lot of new knowledge in college. The more solid high school students are, the worse they learn. On the contrary, when you go to high school, take a course of study, and enter a university, you can easily learn university knowledge. Learning depends not on hard work, but on analogy. Life is full of learning. You should play with middle school instead of blindly strengthening useless things. Learning new knowledge will lead to negative migration in the future.
The difference between high school mathematics and university is that the knowledge points in high school are not so difficult to understand, but even if you understand everything in the book, you will do the exercises and exercises in the book, but many times you will not do the exam questions. In college, it is abstract to understand knowledge points when time is tight, but as long as the knowledge points understand the exam, it is easy to do the questions. Examination is also the level of speaking exercise questions, and it is much more difficult to do two questions for one question.
Most of my science subjects are self-taught, and I can feel that the difficult courses of college mathematics are very different, but there is continuity between them. Almost every section is the key point. I have fallen behind in the front, and my grades in the back will definitely not be much better. Mathematics before and after high school is basically basic, with little continuity, and the actual focus is rarely described. The contents of three senior math books may actually be equal to the contents of the previous 10 math book, so your understanding ability is poor. You can recite high school mathematics, but you need to understand advanced mathematics, otherwise you will have a hard time in the next class.
Any basic research is difficult, not only mathematics and physics, but also a Chinese character. If you trace back to the source, not everyone who scored 700 points in the college entrance examination can do it. Therefore, universities should decide their future direction. If you study to make money, you should change your major as soon as possible. If you are studying for academic purposes, you should stop thinking about making money as soon as possible and change yourself to a stupid direction, so that you will not be stupid enough to enter the academic field.