From a

mathematical point of view, it is at least as interesting to study the random variable MaxPlateau, which assigns to each Motzkin path the maximal plateau length.

IBAS said: "From a

mathematical point of view, the two predictions included in the double are not 'independent' by virtue of the fact that they involve the same match."If predictions are not independent, they are necessarily related, regardless of how little bearing a person may believe the outcome of either one of the predictions has upon the probability of the other."

From a

mathematical point of view, the problems are difficult to understand, and the story and illustrations do not provide clues to solve the problems.

Additionally, while the higher-SES students seemed to approach the real world problems with an eye toward the larger, abstract, mathematical ideas, the lower-SES students often missed the intended

mathematical point. An examination of sociological literature revealed ways in which these patterns in the data could be related to more than individual differences in temperament or achievement among the children.

And for those of a nervous disposition, there was the added bonus of being safe in the knowledge that 41 points now leaves the club all but a single

mathematical point away from guaranteed Premiership security.

A spokesman said: "If you look at it from a

mathematical point of view, the Millennium would start on January 1, 2001, but because of the public wish to celebrate the start of the year 2000, that seems to have become the date to capture the public's imagination."

From a

mathematical point of view, the matrices with exactly one pair of zero-sum eigenvalues form a codimension 1 manifold in the space of all matrices, defined by (for example) the condition that the determinant of the biproduct matrix is zero.

"Being able to move from a simple knot to a composite is--from a

mathematical point of view--a real step."

This is a fascinating collection, an intellectual feast for anyone interested in the continuum - whether from a philosophical or historical or purely

mathematical point of view.

It is a

mathematical point. Too many subsidies mean that government cannot help anyone.

From this it would seem to follow that the

mathematical point cannot be identified with the painter's mark.

"From a

mathematical point of view, this type of morphing is a primitive example of a homotopy, or a time-dependent geometric deformation," says Francis.