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{i_, j_} /; Abs[i - j] == 1 is a pattern. It matches pairs of expressions the difference of which is 1. /; is Condition. In SparseArray this will put a 1 on the second diagonals, as the difference of the indices of elements on the second diagonals is 1 or -1.


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This functions: params[a] = 5; params[b] = 6; Manipulate[params[a] = n, {n, 10, 100, 1}] In contrast: c = 1; Manipulate[c, {c, 10, 100, 1}] Here, the Manipulate displays the change of the local c. It doesn't change the global c which still has value 1.



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