This is a textbook written for a discrete mathematics course which is central to Freshman/Sophomore university mathematics programs. The authors envision one year of discrete mathematics and one year of calculus as the core mathematics program for all capable students regardless of their majors. The text emphasizes problem solving rather than theory. This interesting book has more material than can be covered in one year, thus allowing instructors a choice of topics.
Chapter 0 introduces standard concepts, notation and operations (e.g. concept of function, set notation, matrix multiplication) used in later chapters. In the next chapter, Chapter 1, some basic ideas of algorithms are developed using several examples. In Chapter 2, a thorough treatment of mathematical induction is given. Some topics in graph theory are discussed in Chapter 3. The topics are used to emphasize various algorithms treated. In Chapter 4 some elementary counting methods are introduced. Chapter 5 covers some ideas of how to model problems using difference equations and then the standard solution methods for linear difference equations. In Chapter 6 several topics in discrete probability are treated and applied in a variety of problems. Topics in propositional calculus are discussed and applied to the verification of algorithm correctness in Chapter 7. Topics in algorithmic linear algebra (Gaussian elimination, vector spaces, eigenvalues, Markov chains) are covered in Chapter 8. In Chapter 9 concepts having to do with infinite processes in discrete mathematics (e.g. limits of sequences, series, generating functions) are discussed.
The book contains many good examples and problems. At the end of the text there are hints and answers to approximately one-half of the problems. Also, there is an instructor solution manual giving answers to all the problems and a student solution manual which gives detailed solutions to the problems that have hints or answers given in the book.