  The topological quantum number Q of a superconducting or chiral insulating
wire counts the number of stable bound states at the end points. We determine Q
from the matrix r of reflection amplitudes from one of the ends, generalizing
the known result in the absence of time-reversal and chiral symmetry to all
five topologically nontrivial symmetry classes. The formula takes the form of
the determinant, Pfaffian, or matrix signature of r, depending on whether r is
a real matrix, a real antisymmetric matrix, or a Hermitian matrix. We apply
this formula to calculate the topological quantum number of N coupled dimerized
polymer chains, including the effects of disorder in the hopping constants. The
scattering theory relates a topological phase transition to a conductance peak,
of quantized height and with a universal (symmetry class independent) line
shape. Two peaks which merge are annihilated in the superconducting symmetry
classes, while they reinforce each other in the chiral symmetry classes.
