A long time ago, when younger and rasher mathematicians, we both momentarily harboured the ambition that one day, older and wiser, we might write a multivolume treatise titled “On the Mathematical Foundations of Numerical Analysis”. And then it dawned that such a creation already exists: it is called ‘a mathematics library’. Indeed, it is almost impossible to identify a mathematical theme, no matter how ‘pure’, that has never influenced numerical reasoning: analysis of all kinds, of course, but also algebra, graph theory, number theory, probability theory, differential geometry, combinatorial topology, category theory . . . The mainspring of numerical analysis is, indeed, the entire aquifer of mathematics, pure and applied, and this is an enduring attraction of the discipline. Good luck to those content to spend their entire mathematical existence toiling in a narrow specialism; our choice is an activity that borrows eclectically, indeed with abandon, from all across the mathematical landscape.
Text contains essays covering computational mathematics. Topics include geometric integration and its applications, linear programming and condition numbers under the real number computation model, and chaos in finite difference scheme.