In high school, we study elementary mathematics, and advanced mathematics is a compulsory course for freshmen in science universities, and it is also the most important course for the whole freshman. Advanced mathematics can be regarded as the transition from high school to university.

The content is elementary mathematics: sequence (bounded, convergent, limit) and function (continuous, convergent, limit). Here, we should pay attention to the definition of concepts, and some proof methods must be clearly remembered. If you insist on looking ahead, just look at the contents above.

Advanced Mathematics: Differential. The first volume of Basic Calculus, except for the first two chapters to consolidate some concepts in elementary mathematics, is all around this theme. Differential things will not be explained here, because there are too many. Besides, you don't need to look at college knowledge so critically now. I think calculus is easy to learn in freshman year (PS: not to mention the water in our school, I am from China University of Science and Technology).

Here are some other suggestions for you.

At present, universities start school earlier and earlier. After the college entrance examination, this holiday is the longest holiday in a person's life, and there is no test pressure. So we must cherish it, look around and experience the feeling of relaxation, because after all, students in China have spent too much time and energy on the college entrance examination.

The second one is about college, which is different from high school. Learning is only one aspect of college life. When I first went to college four years ago, our elder brother told me that in college, we should learn to be a man first, and then learn to be a scholar. Meaning depends on our personal understanding. Anyway, don't think too idealistically about the university, and don't think too hard about the university courses. Many things happen. As long as you study hard, you can learn well in high school without being so tired.

Third, students who dare to apply for mathematics majors should be psychologically prepared to study hard, because mathematics is still very boring compared with other pure engineering courses. Moreover, as a basic subject, the only field that mathematics can be used and used is scientific research. If you want to apply what you have learned and make achievements in other industries, you must think about its application value. One of the common applications of mathematics major is computer. If you offer courses in C++ or other programming languages, don't miss them. The other is to transfer to finance. In fact, finance is a science, and the difficulty and quantity of many calculations are beyond the ability of economics students.

In short, although mathematics can not be directly applied to practical work, it is a necessary and important foundation for any science and engineering discipline.

I hope I can help you.