Description:
The author recommends teaching integration first, and move on to differential calculus only after a sound understanding of integration has been attained. A rationale for teaching integrals before derivatives in a first calculus unit intended primarily for engineering students at the University of Ballarat is presented. It is concluded that students fail to see the connection between getting the right answer and understanding what they are doing. It is noted that the formal manipulations required for high school differential calculus questions are simpler than those for integral calculus.
Description:
We exhibit a non-trivial twisted sum of c0 with a Hilbert space, which is not isomorphic to the example constructed by Johnson and Lindenstrauss in 1974. In fact, no non-separable subspace of either example is isomorphic to any subspace of the other.