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Published online by Cambridge University Press: 16 May 2024
The problems we examine can be roughly classified as follows. Problems A, C, E, and perhaps J, require linear algebra, matrices and so on. The essence of these problems is to realise that the essential features are of a linear character, though not necessarily over the field of real numbers. Elementary cases (where the parameter is small) can be solved by simple matrix computations, while a discussion for larger values of the parameter introduces the idea, and the problems, of finding large matrices on the computer.
Problems B, G and I, which at first sight look elementary, require number theory and, in particular, will develop a good understanding of binary numbers and modular arithmetic.
Problems D, F and H are of a probabilistic nature. Two of these show the power of generating functions, and these go beyond what is normally taught at this level.
Finally, Problem K requires a little real analysis of a practical sort, combined with a critical look at what appears on our computer screen.
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