送交者: mangolasi 于 2006-1-31, 15:27:48:
of mathematics (i.e. mapping the alegbras into objects in space)?
I found myself have deepest understanding of the concepts if the books gave out geometric meanings when I learn them. The application of them is almost instinct. Unfortunately I never met a book using this approach extensively (save those on basic calculus and Fourier series).
This has some bad effect when I am teaching--I use a rule without thinking but it's not very obvious to the students. If I can understand the tools inside out, then things would easier for me to explain the intuition to the students.
Only today I understand what the geometric meaning of the determinant of a matrix though I always know its application (mainly invertibility in econometrics). Once I know it denotes the change of volumn effect of a transformation, the change of variable technique in probability (Jacobian determinant) is suddenly has meaning to me (sadly we learned that as a rule rather than a meaning).