ABSTRACT
Modern biology makes use of a variety of discrete and combinatorial methods in order to better understand biological phenomena at both the microscopic and macroscopic levels. This chapter explains how such methods are useful in understanding the structure and properties of the genome (both DNA and RNA structures), gene regulatory networks, the firings of neurons, the classification and evolution of species, as well as competition between species. The chapter also presents a variety of modern algorithms for analyzing biological data. Alignments are a powerful way to compare related DNA or protein sequences. They can be used to capture various facts about the sequences aligned, such as common evolutionary descent or common structural function. Sequence alignment is computationally intensive, with the algorithms requiring an execution time quadratic in the size of the sequences being aligned.
