Most software engineering degrees require you to take the following:
- Calculus I
- Calculus II
- Calculus III
- Linear Algebra
- Discrete Mathematics
- Differential Equations
And usually another higher level math course such as Probability Theory. But, these degrees and their requirements change from school to school. Check out the curriculum for the school you're thinking about attending.
A lot! By the end of your degree you would a couple of courses away from having a minor in math.