The book you want to learn should be the same as ours. Mathematical Analysis (Volume I and Volume II) is published by the Department of Mathematics of Fudan University, and Advanced Algebra is published by the Department of Mathematics of Peking University. Their publishing houses are all higher education publishing houses. You can buy it, have a good look and study hard. In fact, it is not difficult. We started classes when we were freshmen, and fewer people failed.
In addition, there are several tutors for master students in our college, which is really good. I don't know if you want to continue your PhD and stay as a teacher. If not, in fact, I suggest that you can choose a graduate student in statistics, and it is good to choose Hu or Liu Qiongsun and Professor as your tutor. Professor Liu Qiongsun teaches probability theory, and Professor Zhong Bo teaches mathematical statistics, which is very good. For graduate students, it is all statistics. If you are bent on learning mathematics, Professor Wang Kairong is also very good. Not only can you learn knowledge in his class, but more importantly, you can learn a lot about life. We students all think that it is better to study for ten years than to listen to him.