Creative Mathematics

How do mathematicians approach a problem, explore the possibilities, and develop an understanding of a whole area around it? The issue is not simply about obtaining 'the answer'; rather, the author explains that a mathematical problem is just one of many related ones that should be simultaneously investigated and discussed at various levels, and that understanding this is a crucial step in becoming a creative mathematician. The title begins with some good advice about procedure, presentation, and organisation that will benefit every mathematician, budding, teaching or practised. In the rest of the title, the author presents a series of simple problems, then, through discussion, consideration of special cases, computer experiments, and so on, the reader is taken through these same problems, but at an increasing level of sophistication and generality. Mathematics is rarely a closed title, and seemingly innocent problems, when examined and explored, can lead to results of significance.

Alan F. Beardon studied at London University and Harvard University, and obtained his Ph.D. from Imperial College, London in 1964. He taught at the University of Maryland (USA) and the University of Kent (UK) before moving to the University of Cambridge in 1968. He is the author of 6 mathematical texts and numerous research papers.