3/ Show how maths prevent the corner case of the intuition
When I study maths alone (even after a course), it's more like:
1/ Understand the technicalities of maths (very tedious because many teacher "leaves the details out"), without bothering much about the subject.
2/ After that huge effort, I try to play with the math to get an intuition of what it does. An intuition == a way to explain what it does in layman's terms, with drawings, physical/real examples, etc.
3/ Revisit the maths, and especially their corner cases (what happens if this denominator goes to zero, what if I cannot invert that matrix ?) and confront that to my intuition. The maths are the safest way to make sure you get your intuition right.
1/ Provide intuition
2/ Show the math
3/ Show how maths prevent the corner case of the intuition
When I study maths alone (even after a course), it's more like:
1/ Understand the technicalities of maths (very tedious because many teacher "leaves the details out"), without bothering much about the subject.
2/ After that huge effort, I try to play with the math to get an intuition of what it does. An intuition == a way to explain what it does in layman's terms, with drawings, physical/real examples, etc.
3/ Revisit the maths, and especially their corner cases (what happens if this denominator goes to zero, what if I cannot invert that matrix ?) and confront that to my intuition. The maths are the safest way to make sure you get your intuition right.