Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar
This is a book that covers various topics in discrete mathematics, such as sets, relations, functions, logic, graphs, algebraic structures, and languages. The book aims to provide a rigorous and comprehensive treatment of these topics, with applications to computer science and related fields. The book was first published in 1975 by McGraw-Hill as part of their computer science series[^2^]. It has been widely used as a textbook for undergraduate courses in discrete mathematics and theoretical computer science.
The book is divided into six parts: Part I introduces the basic concepts of sets, relations, and functions; Part II deals with propositional and predicate logic, proof techniques, and recursion; Part III explores graphs, trees, and combinatorics; Part IV covers algebraic structures such as groups, rings, fields, and lattices; Part V discusses languages, grammars, automata, and Turing machines; and Part VI presents some advanced topics such as computability, complexity, and cryptography. Each chapter contains numerous examples, exercises, and problems to reinforce the concepts and skills learned.
The book is written in a clear and concise style, with an emphasis on mathematical rigor and abstraction. The authors also provide historical notes and biographical sketches of some prominent mathematicians who contributed to the development of discrete mathematics. The book is suitable for students who have some background in calculus and linear algebra, and who are interested in learning more about the mathematical foundations of computer science.Some of the applications of discrete mathematics to computer science that the book covers are: data structures, algorithms, cryptography, coding theory, logic programming, artificial intelligence, formal languages, and computability theory. The book also shows how discrete mathematics can be used to model and solve real-world problems such as encryption, error detection and correction, graph coloring, scheduling, and optimization.
The book has received positive reviews from both students and instructors who have used it as a textbook or a reference. Some of the strengths of the book are: its comprehensive coverage of topics, its clear and rigorous presentation of concepts and proofs, its abundance of examples and exercises, its historical and biographical notes, and its relevance to computer science. Some of the drawbacks of the book are: its outdated notation and terminology, its lack of color illustrations and diagrams, its occasional errors and typos, and its high level of difficulty for some readers.
Overall, Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar is a classic and influential book in the field of discrete mathematics and computer science. It is a valuable resource for anyone who wants to learn more about the theoretical aspects of computing and the mathematical tools that underlie them. 061ffe29dd