This 'article is based on the Clay Mathematics Senior Scholar Lecture that was de-livered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture was the tropical approach in mathematics. This approach was in its infancy at that time, but it has since matured and is now an integral part of geometric corn-binatorics and algebraic geometry. It has also expanded into mathematical physics, number theory, symplectic geometry, computational biology, and beyond. We offer an elementary introduction to this subject, touching upon arithmetic, polynomials, curves, phylogenetics, and linear spaces. Each section ends with a suggestion for further re-search. The proposed problems are particularly well suited for undergraduate students. The bibliography contains numerous references for further reading in this field.
展开▼
