Using a traditional deductive approach, this book looks into the fundamental ideas in discrete mathematics, including graph theory, combinatorics, number theory, coding theory, combinatorial optimization and abstract algebra. It can be approached by anyone with basic competence in arithmetic and experience of simple algebraic manipulations and students of computer science whose curriculum may now allow the study of many ancillary mathematics courses. The main changes to this new edition are to present descriptions of numerous algorithms on a form close to that of a real programming language. The aim is to enable students to develop practical programs from the design of algorithms.