Odds and Ends

Walter Ledermann and the Oliver and Boyd University Mathematical Texts

For about 20 years from the 1940s the Edinburgh publisher Oliver and Boyd published a series of high standard pocket-sized texts in mathematics and mathematical physics entitled ‘University Mathematical Texts.’

Among my favourites, purchased as an undergraduate and still referred to more than forty years later, was ‘Finite Groups’ by Walter Ledermann.

For years Ledermann remained a name on a bookcover for me, until, through the magic of the internet, I chanced upon his reminisces, which begin here, full of warmth and humour.

Ledermann was a German Jew who was lucky enough to emigrate to Britain in the early 1930s, and to be able to follow his chosen career as a mathematician until he was well into his eighties. The account of his PhD student from Afghanistan is particularly humorous and touching.


Magic Squares

A magic square is a square (n x n) array of integers in which each of the integers 1 to n2 appears exactly once, and such that the sum of the integers in each row, each column and each diagonal is the same (the ‘magic number’).

A 3×3 example is shown below.  For this the magic number is 15.

8      1      6

3      5      7

4      9      2

The corresponding blog post here explains what sparked my interest in the topic.

Methods for constructing magic squares for any given n > 2 (there is no square for n = 2) are given on page 148 et seq. of Mathematical Recreations by Maurice Kraitchik (1942). However Kraitchik does not validate the methods he describes, and I set myself this task (see the pdf here).

A side benefit was working out a method of representing ‘clock arithmetic’ that I find more satisfactory than mod notation and equivalence classes.


Long Division Method of Calculating Square Roots

In the 1950s and 1960s schools taught a method of calculating square roots by hand, that resembled long division. Explanations of just why the method works are less frequently encountered. In this pdf, I give my take on the workings of the method.

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