The patterns of variation within a molecular sequence data set result from the interplay between population genetic, molecular evolutionary and macroevolutionary processes-the standard purview of evolutionary biologists. Elucidating these patterns, particularly for large data sets, requires an understanding of the structure, assumptions and limitations of the algorithms used by bioinformatics software-the domain of mathematicians and computer scientists. As a result, bioinformatics often suffers a two-culture problem because of the lack of broad overlapping expertise between these two groups. Collaboration among specialists in different fields has greatly mitigated this problem among active bioinformaticians. However, science education researchers report that much of bioinformatics education does little to bridge the cultural divide, the curriculum too focused on solving narrow problems (e.g. interpreting pre-built phylogenetic trees) rather than on exploring broader ones (e.g. exploring alternative phylogenetic strategies for different kinds of data sets). Herein, we present an introduction to the mathematics of tree enumeration, tree construction, split decomposition and sequence alignment. We also introduce off-line downloadable software tools developed by the BioQUEST Curriculum Consortium to help students learn how to interpret and critically evaluate the results of standard bioinformatics analyses. 