...in both developing and teaching, here's my take:
- Some kind of hardware (microprocessor, etc) course
- Discrete Math: Logic, Sets, Relations
- Algorithms and Complexity
- The Calculus
- Geometry & Trigonometry
- etc... (depending on the industry to which you're attracted)
I really believe that the computational math is strongly supported by an understanding of the practical implementation of stored program computers. This helps both your programming and debugging/troubleshooting, in that you understand the impact of your little creation on the hardware.
Application math is application-dependent, ha-ha. I went for a long time both as a developer and teacher before I encountered advanced statistics or differential calculus; there are more folks out there doing this in aerospace than you might think.
I think the distinction between computational and application math helps to compartmentalize your consideration...