Bioinformatics science as an integrated field of science is one of pioneer science and technologies that helped us understand life more and engineer it for our purpose.

Today, virtually all categories of science use mathematical methods and visions as parts of their research process tools. Science has entered a phase of mathematics invading other disciplines. This is because the concepts and visions in all areas of science are growth, and mathematical tools are flexible and generalizable.

With a reality based vision, we can say that the majority of the methods of applied mathematics are used as tools in bioinformatics. So, is there anything peculiar about using mathematical modeling in bioinformatics? Among the tools of applied mathematics some are of special importance, namely probabil-

ity theory and statistics and algorithms in computer science. A large amount of research in bioinformatics uses and combines methods from these two areas. Computer-science algorithms form the technical background for bioinformatics, in the sense that the operation and maintenance of bioinformatic databases require the most up-to-date algorithmic tools. Probability and statistics, besides being a tool for research, also provides a language for formulating results in bioinformatics.

Other mathematical and computational tools, such as optimization techniques with dynamic programming, discrete-mathematics algorithms, and pattern analysis methods, are also of basic importance in ordering bioinformatic data and in modeling biological mechanisms at various levels.

The first part of the book, on mathematical and computational methods is intended to cover the tools used in the book. The presentations of methods in this part are oriented towards their applications in bioinformatics. In the second part of this book, practical uses of these methods are illustrated on the basis of the rather large number of research papers devoted to the analysis of bioinformatic data. Sometimes some further developments of methods are presented, together with the problem they apply to, or some references are given to the derivation of the algorithm. Description of applied mathematical methods is organized into several sections corresponding to logical grouping of methods.

Our presentation of the mathematical approaches is rather descriptive. When discussing mathematical methods we appeal to comprehension and intuitive understanding, to their relations to bioinformatic problems and to cross-applications between items we discuss. This approach allows us to go through a variety of methods and, hopefully, to sketch a picture of bioinformatics. Despite avoiding much of the mathematical formalism we have tried to keep the presentation sufficiently clear and precise. All chapters are accompanied by exercises and problems, which are intended to support understanding of the material and often show further developments. Their levels of difficulty varies, but generally they are rather non trivial.