If you want to teach mathematics and applied mathematics in the future, you will be a normal major! Generally, which major is arranged in advance by the school according to your wishes, but you can change your major after you go to school, but the process may be a bit troublesome!
Teaching in a university is not only determined by academic qualifications, but also depends on your personal wishes. You probably won't be able to teach in a university after graduating from a master's degree. It should be no problem to study for a doctorate!
In fact, it is not bad to go to a scientific research unit and take an examination of civil servants. It is more convenient for people with high academic qualifications to find jobs!
There are some differences. If you want to be a teacher, of course, you should choose Normal University first. They are still a little different. Teachers should be more professional. And it may be more convenient to find a job in the future!
No famous school is unattainable! First-class schools have first-class teachers, the academic atmosphere of the school should be strong, and you should have more opportunities!