Well, your example is a bit special. Let's just say that you definitely have no chance to study mathematics in this college, but have you applied to this school? If it is, then when the applied mathematics and basic mathematics in the school are not full, it is necessary to recruit and adjust in the school first. You are a volunteer applying for the school. As long as your grades are reviewed, you can definitely apply for a transfer to a basic mathematics major or an applied mathematics major. If your score reaches the re-examination score of this college, you are eligible to apply for a transfer to a similar major related to mathematics, regardless of whether your professional performance is in the top ten or the top one hundred. As for the ranking after the second interview, it is not necessarily. Admission is based on the total score ranking.

The role of professional ranking is to arrange your own re-examination and adjustment.

Just like your example, this major enrolls 4 students, and you rank 10, so generally speaking, you don't have a chance to enter the second interview, so you can ask for transfer, and you can contact the admissions office or teachers of the target institution without waiting for the second interview score.

But in your example, the enrollment quota of other majors in the School of Mathematics is not full. Applied mathematics and basic mathematics must continue to recruit, but you said you wouldn't accept adjustment. This is an inappropriate example. If you don't recruit enough, you must adjust. You just need to adjust at school first, or if you are not satisfied, you will announce the need for national adjustment. In this case, you can apply for intra-school transfer, but what is the retest line of the college? The retest line must be reached or exceeded. Assuming that the retest line of a voluntary college is the score of the eighth student in the initial test, you can be sure that you can't participate in the adjustment of the mathematics department of that college. Even if your score is higher than the retest score of higher institutions, you can't apply for adjustment, but you still have the last hope, that is, you can reach and exceed the retest score of other institutions, but you should be a major similar to your major. Cross-category transfers are generally not allowed, but when you are not satisfied with enrollment, universities can set their own requirements for intra-campus transfers and allow some majors to make cross-category transfers. For example, mathematics can be transferred to economics or engineering. These mean that as long as you pass the college re-examination scores, you will have a chance to adjust, especially on campus. As for off-campus transfers, it is definitely possible.