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Having recently read a review that expounded on the rigour and depth of books by 'earlier' British mathematicians (mainly analysts) I would like to know more. My own research yielded the following tentative list, which I believe to be relatively incomplete and shallow:

  • G. H. Hardy, A Course of Pure Mathematics.
  • G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers.
  • E. C. Titchmarsh, The Theory of Functions.
  • E. W. Hobson, The Theory of Functions of a Real Variable and the Theory of Fourier's Series (2 vols.).
  • E. T. Copson, An Introduction to the Theory of Functions of a Complex Variable.
  • Alfred North Whitehead, Bertrand Russell, Principia Mathematica.
  • G. S. Carr, Synopsis of Pure Mathematics (2 vols.).

I'm certain that there are many other classics, concentrated most probably in the early or mid-20th century. Any suggestions would be greatly appreciated.

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    $\begingroup$ There is also en.wikipedia.org/wiki/A_Course_of_Modern_Analysis. $\endgroup$
    – lhf
    Commented Mar 17, 2016 at 10:51
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    $\begingroup$ Do all the authors have to be British? The book Inequalities by Hardy, Littlewood and Pólya, for example, is also a classic, 2/3 of the authors of which are British. I can also suggest Baker's Transcendental Number Theory and Ingham's Distribution of Prime Numbers, although of course it depends on exactly what you call a "classic". $\endgroup$
    – Gro-Tsen
    Commented Mar 17, 2016 at 13:16
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    $\begingroup$ Especially influential were Whittaker's 1902 (1st edition) A Course of Modern Analysis (Watson joined as co-author with the 1915 2nd edition) and Bromwich's 1908 (1st edition) An Introduction to the Theory of Infinite Series. (moments later) I see that @lhf has cited Whittaker also. $\endgroup$
    – Dave L Renfro
    Commented Mar 17, 2016 at 15:33
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    $\begingroup$ As a very rough guess, maybe around 1500 math books, plus or minus 2 or 3 hundred. Keep in mind that I've been accumulating them for about 45 years. On the other hand, the number of journal pages that I've photocopied over the last 25-30 years is probably some kind of record (a number well into 6 digits). See my comments here, for instance. And in the past 10 years I've digitally accumulated from google-books nearly 1000 19th century books and full runs of 25 to 30 19th century journals. $\endgroup$
    – Dave L Renfro
    Commented Mar 17, 2016 at 21:33
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    $\begingroup$ Basically you want cambridge.org/us/academic/subjects/mathematics/… $\endgroup$
    – Marcus Johnson
    Commented Mar 19, 2016 at 12:14

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You really want a list of British early 20th century books in mathematics? What for? It will be too long, of course.

Two classical books by Titchmarsh are missing in your list:

Riemann zeta function,

and Eigenfunction expansions associated with second-order differential equations.

Another notable omission in your list are the books of Watson,

Bessel functions, and

Course of Modern Analysis, joint with Whittaker.

The last book deserves an entry in the Guinnes book of records as a textbook continuously in print for more than 100 years. Perhaps unique in all sciences.

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