The title of this book reflects who we are: a computational biologist and an algebraist who share a common interest in statistics. Our collaboration sprang from the desire to find a mathematical language for discussing biological sequence analysis, with the initial impetus being provided by the introductory workshop on Discrete and Computational Geometry at the Mathematical Sciences Research Institute (MSRI) held at Berkeley in August 2003. At that workshop we began exploring the similarities between tropical matrix multiplication and the Viterbi algorithm for hidden Markov models. Our discussions ultimately led to two articles [Pachter and Sturmfels, 2004a,b] which are explained and further developed in various chapters of this book.

In the fall of 2003 we held a graduate seminar on The Mathematics of Phylogenetic Trees. About half of the authors of the second part of this book participated in that seminar. It was based on topics from the books [Felsenstein, 2003, Semple and Steel, 2003] but we also discussed other projects, such as Michael Joswig's polytope propagation on graphs (now Chapter 6). That seminar got us up to speed on research topics in phylogenetics, and led us to participate in the conference on Phylogenetic Combinatorics which was held in July 2004 in Uppsala, Sweden. In Uppsala we were introduced to David Bryant and his statistical models for split systems (now Chapter 17).

Another milestone was the workshop on Computational Algebraic Statistics, held at the American Institute for Mathematics (AIM) at Palo Alto in December 2003.