ABSTRACT
This chapter illustrates aspects of problem solving and proof through illustrative examples. At the heart of both pure and applied mathematics, however, are problems: But anyone who has done mathematics knows what comes first – a problem. For a start pupils can usually be solved quite quickly, provided the learner can recognise the technique needed, and the problem usually has just the right amount of information, no more and no less. The growth of mathematics through history has relied upon a symbiotic relationship between pure and applied mathematics. One of the common justifications for the place of mathematics in the curriculum is that it is useful for practical situations in everyday life. Human beings would not live long enough to do the checking themselves so the capacity of the computer to work at high speeds has obviously provided the mathematicians with another potential tool.
