Mathematical Explorations
AIMS Library of Mathematical Sciences Series

Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.

Preface; How to use this book; 1. Paying for parking; 2. Lengths and angles; 3. Magic squares; 4. Intersecting chords; 5. Crossing squares; 6. Repeated vector products; 7. A rolling disc; 8. Sums of powers of digits; 9. The metric dimension; 10. Primes and irreducible elements; 11. The symmetries of a quadrilateral; 12. Removing a vertex; 13. Squares within squares; 14. Catalan numbers; References; Index.

Alan F. Beardon studied at the University of London and Harvard University, and obtained his PhD from Imperial College London in 1964. He taught at the University of Maryland and the University of Kent before moving to the University of Cambridge in 1968, where he is now an Emeritus Professor. He is the author of six mathematical texts and numerous research papers.