For ease of thinking, take the study of differential equations, recurrence relations etc.

1. Knowledge on the rule – if this, do this then you’ll get the solution

2. Knowledge on the proof – Is it really true that in ALL cases if I follow the rules, I’ll get the solution?

3. Knowledge on the design – How should I design the rules for more complecated cases?

3 or 4. Knowledge on the Big Picture – how the different elements interact? Why the designs are being so?