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Formal power series in the perturbation parameter can be writtenfor the invariant tori of Hamiltonian systems close to integrable ones.Convergence can be proved only in special cases ( KAM theory or periodicmotions ) : more generally the series have to be summed with suitablesummation rules obtaining nevertheless nontrivial analyticity properties in the ( small ) perturbation parameter . Do n't panic if your first grades are lower than they were in high school ; adjusting takes time . Commons space and study areas continue to be a serious problem.Graduate student enrollment totals 150 , with roughly an equal split between domestic and foreign students . The surreal number line turns to be much richer than the real line , including ( lots of ) numbers further to the right than all the real numbers , and ( lots of ) numbers which , though positive , are less than all the positive real numbers . Towards the end of the term two or three boys caught scarlet fever , and there was much talk of sending them all home in order to escape an epidemic ; but the sufferers were isolated , and since no more were attacked it was supposed that the outbreak was stopped .