x PREFACE methods from classical discrete mathematics,with a primary focus on devel- oping basic concepts and techniques.They set the stage for Chapter 5,which is pivotal,as it covers analytic combinatorics,a calculus for the study of large discrete structures that has emerged from these classical methods to help solve the modern problems that now face researchers because of the emergence of computers and computational models.Chapters 6 through 9 move the fo- cus back toward computer science,as they cover properties of combinatorial structures,their relationships to fundamental algorithms,and analytic results. Though the book is intended to be self-contained,this structure sup- ports differences in emphasis when teaching the material,depending on the background and experience of students and instructor.One approach,more mathematically oriented,would be to emphasize the theorems and proofs in the first part of the book,with applications drawn from Chapters 6 through 9. Another approach,more oriented towards computer science,would be to briefly cover the major mathematical tools in Chapters 2 through 5 and em- phasize the algorithmic material in the second half of the book.But our primary intention is that most students should be able to learn new mate- rial from both mathematics and computer science in an interesting context by working carefully all the way through the book. Supplementing the text are lists of references and several hundred ex- ercises,to encourage readers to examine original sources and to consider the material in the text in more depth. Our experience in teaching this material has shown that there are nu- merous opportunities for instructors to supplement lecture and reading ma- terial with computation-based laboratories and homework assignments.The material covered here is an ideal framework for students to develop exper- tise in a symbolic manipulation system such as Mathematica,MAPLE,or SAGE.More important,the experience of validating the mathematical stud- ies by comparing them against empirical studies is an opportunity to provide valuable insights for students that should not be missed. Booksite.An important feature of the book is its relationship to the booksite aofa.cs.princeton.edu.This site is freely available and contains supple- mentary material about the analysis of algorithms,including a complete set of lecture slides and links to related material,including similar sites for A/go- rithms and Analytic Combinatorics.These resources are suitable both for use by any instructor teaching the material and for self-study. www.it-ebooks.infox P Ş ő Œ ō ŏ ő methods from classical discrete mathematics, with a primary focus on devel￾oping basic concepts and techniques. Ļey set the stage for Chapter 5, which is pivotal, as it covers analytic combinatorics, a calculus for the study of large discrete structures that has emerged from these classical methods to help solve the modern problems that now face researchers because of the emergence of computers and computational models. Chapters 6 through 9 move the fo￾cus back toward computer science, as they cover properties of combinatorial structures, their relationships to fundamental algorithms, and analytic results. Ļough the book is intended to be self-contained, this structure sup￾ports differences in emphasis when teaching the material, depending on the background and experience of students and instructor. One approach, more mathematically oriented, would be to emphasize the theorems and proofs in the ŀrst part of the book, with applications drawn from Chapters 6 through 9. Another approach, more oriented towards computer science, would be to brieły cover the major mathematical tools in Chapters 2 through 5 and em￾phasize the algorithmic material in the second half of the book. But our primary intention is that most students should be able to learn new mate￾rial from both mathematics and computer science in an interesting context by working carefully all the way through the book. Supplementing the text are lists of references and several hundred ex￾ercises, to encourage readers to examine original sources and to consider the material in the text in more depth. Our experience in teaching this material has shown that there are nu￾merous opportunities for instructors to supplement lecture and reading ma￾terial with computation-based laboratories and homework assignments. Ļe material covered here is an ideal framework for students to develop exper￾tise in a symbolic manipulation system such as Mathematica, MAPLE, or SAGE. More important, the experience of validating the mathematical stud￾ies by comparing them against empirical studies is an opportunity to provide valuable insights for students that should not be missed. Booksite. An important feature of the book is its relationship to the booksite aofa.cs.princeton.edu. Ļis site is freely available and contains supple￾mentary material about the analysis of algorithms, including a complete set of lecture slides and links to related material, including similar sites for Algo￾rithms and Analytic Combinatorics. Ļese resources are suitable both for use by any instructor teaching the material and for self-study. www.it-ebooks.info