The Theory of Functions of a Real Variable and the Theory of Fourier's Series

Abstract

IT is imposible to read Dr. Hobson's book without reflecting on the marvellous change that has come over Cambridge mathematics in the last twenty years. Twenty years ago Cambridge mathematics was a thing standing by itself, and with its own virtues and defects. Pure mathematics in Cambridge meant Cayley and a few disciples; and Cayley (widely as he read) owed little or nothing to anyone but himself. Certainly he never appreciated the most fundamental ideas of modern Continental analysis. It is probable that he could not have defined a function or a limit in a way which would have satisfied Weier-strass or Dr. Hobson: it is certain that he would have been as incapable as any Senior Wrangler of proving any of the less obvious theorems of convergence. The first signs of the absorption of these ideas are td be found, not in Cayley, but in Stokes.

The Theory of Functions of a Real Variable and the Theory of Fourier's Series.

By Dr. E. W. Hobson Pp. xvi + 772. (Cambridge: University Press, 1907.) Price 21s. net.