Symmetry might be fearful in a Tiger as William Blake alludes to in his poem,The Tyger, but in mathematics it is wholly a thing of beauty. Symmetry can often be used as a tool to cut a simple, elegant, path through a labyrinth of mathematical obstacles. Abstractly, a mathematical object displays the property of symmetry if it is invariant to parametric change.

1. 1.

   This generalizes the summation found in equation (4.36)which counted the number of times an inner loop was executed in a nested set of for loops.

2. 2.

   Selecting initial points to start the algorithm is often an art rather than a science. It is not uncommon to perform a set of experiments with a variety of initial points.

Authors and Affiliations

1. (Home address), Beverly, MA, USA

   Randolph Nelson

Reprints and permissions

© 2020 Springer Nature Switzerland AG

Policies and ethics