Tropical Mathematics and Applications to Theoretical Physics and Scientific Computing
Résumé
Tropical Mathematics built on Idempotent Semi-Rings and Dioids permits an extension of the usual Linear methods to Non-Linear problems and provides powerful analyzing and computing in Theoretical Physics and Applied Mathematics. Until recently, solutions in mathematics and physics were organized around algebraic structures such as groups, rings, and fields. These techniques are not well-suited to modeling and solving non-linear problems. This book covers how Idempotent Mathematics when applied appropriately can be a versatile and powerful way to transform non-linear problems into linear ones and can provide solutions to complicated theoretical physics problems.