# Discrete Mathematical Structures By Tremblay And Manohar Pdf

## Discrete Mathematical Structures by Tremblay and Manohar: A Review

Discrete mathematics is the study of finite and discrete objects, such as integers, graphs, sets, logic, and algorithms. It is an essential foundation for computer science, as it provides the tools and techniques for designing and analyzing software, hardware, cryptography, and artificial intelligence. Discrete mathematics also has applications in other fields, such as combinatorics, number theory, coding theory, and cryptography.

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One of the classic textbooks on discrete mathematics is Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar. This book was first published in 1975 and has been widely used by students and instructors of computer science and mathematics. The book covers various topics in discrete mathematics, such as sets, relations, functions, algebraic structures, Boolean algebra, logic, proof techniques, recursion, induction, counting, combinatorics, graphs, trees, languages, automata, and computability.

The book is divided into six parts: Part I introduces the basic concepts of sets, relations, functions, and algebraic structures. Part II deals with Boolean algebra and logic, including propositional logic, predicate logic, normal forms, resolution, and logic programming. Part III presents the methods of proof and mathematical reasoning, such as direct proof, proof by contradiction, proof by contrapositive, proof by cases, mathematical induction, recursion, and recursive definitions. Part IV explores the topics of counting and combinatorics, such as permutations, combinations, binomial coefficients, generating functions, recurrence relations, inclusion-exclusion principle, pigeonhole principle, and Ramsey theory. Part V focuses on graphs and trees, such as graph terminology, graph representations, graph algorithms (such as traversal, shortest path, spanning tree), Eulerian and Hamiltonian graphs, planar graphs (such as Euler's formula), coloring problems (such as chromatic number and chromatic polynomial), directed graphs (such as digraphs and tournaments), trees (such as binary trees and tree traversal), and applications of graphs and trees (such as Huffman coding and game trees). Part VI covers the theory of languages, automata, and computability (such as regular languages (such as regular expressions and finite automata), context-free languages (such as context-free grammars and pushdown automata), Turing machines (such as Turing-recognizable languages and Turing-decidable languages), undecidability (such as the halting problem and Rice's theorem), and complexity theory (such as time complexity and NP-completeness)).

The book is well-written and organized. It provides clear definitions, examples, exercises, and theorems for each topic. It also includes historical notes, biographical sketches, and references for further reading. The book is suitable for both undergraduate and graduate students who want to learn the fundamentals of discrete mathematics and its applications to computer science. The book assumes some background in elementary mathematics, such as algebra, calculus, and set theory.

The book is available in both print and digital formats. The print version can be purchased from various online or offline bookstores. The digital version can be downloaded for free from some websites or accessed through some libraries. However, the digital version may not be the latest edition or may have some errors or missing pages. Therefore, it is advisable to check the quality of the digital version before using it.

In conclusion, Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar is a comprehensive and classic textbook on discrete mathematics that covers a wide range of topics and applications relevant to computer science. It is a valuable resource for students and instructors who want to learn or teach discrete mathematics in a rigorous and engaging way.

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Like any other textbook, Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar has its own advantages and disadvantages. Some of the advantages are:

The book covers a wide range of topics in discrete mathematics, from basic concepts to advanced topics, such as computability and complexity theory. The book provides a comprehensive overview of the field and its applications to computer science.

The book is well-structured and organized. Each chapter begins with an introduction, followed by definitions, examples, exercises, and theorems. Each chapter ends with a summary, historical notes, biographical sketches, and references. The book also has appendices that provide additional information on topics such as matrices, algebra, logic, and set theory.

The book is well-written and clear. The language is simple and precise. The explanations are concise and easy to follow. The examples are relevant and illustrative. The exercises are challenging and diverse. The theorems are rigorous and proven.

The book is engaging and interesting. The book uses a variety of examples from computer science, such as cryptography, artificial intelligence, logic programming, coding theory, and game theory. The book also includes historical notes and biographical sketches that provide context and background for the topics and concepts. The book also uses humor and anecdotes to make the reading more enjoyable.

Some of the disadvantages are:

The book is outdated and obsolete. The book was first published in 1975 and has not been updated since then. The book does not reflect the current state of the art and research in discrete mathematics and computer science. The book does not cover some of the newer topics and developments in the field, such as quantum computing, cryptography, graph theory, complexity theory, and algorithm design.

The book is too dense and difficult. The book covers too many topics in too much detail. The book assumes a high level of mathematical maturity and background from the readers. The book does not provide enough motivation or intuition for some of the topics and concepts. The book does not provide enough examples or applications for some of the topics and concepts.

The book is too expensive and inaccessible. The print version of the book is hard to find and costly to buy. The digital version of the book is not widely available or reliable. The digital version may have errors or missing pages. The digital version may not be compatible with some devices or formats.

In conclusion, Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar is a classic textbook on discrete mathematics that has many advantages but also some disadvantages. It is a valuable resource for students and instructors who want to learn or teach discrete mathematics in a rigorous and engaging way, but it may also require some supplementation or adaptation to suit the needs and preferences of modern readers.

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Since Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar is an old and outdated textbook, some readers may want to look for alternatives or supplements to the book. Some of the alternatives or supplements are:

Discrete Mathematics and Its Applications by Kenneth H. Rosen. This is a popular and modern textbook on discrete mathematics that covers most of the topics in Tremblay and Manohar's book, as well as some additional topics, such as cryptography, number theory, algorithm analysis, and complexity theory. The book is well-written and organized, with clear explanations, examples, exercises, and applications. The book also has online resources, such as videos, slides, and software.

Discrete Mathematics with Applications by Susanna S. Epp. This is another popular and modern textbook on discrete mathematics that focuses on the applications of discrete mathematics to computer science. The book covers some of the topics in Tremblay and Manohar's book, such as logic, proof techniques, sets, functions, relations, algebraic structures, combinatorics, graphs, trees, languages, and automata. The book is well-written and organized, with clear explanations, examples, exercises, and applications. The book also has online resources, such as videos, slides, and software.

Concrete Mathematics: A Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. This is a classic and influential textbook on discrete mathematics that emphasizes the concrete aspects of mathematics, such as manipulation of formulas, solving recurrences, summation notation, generating functions, asymptotic analysis, and binomial coefficients. The book covers some of the topics in Tremblay and Manohar's book, such as counting and combinatorics, recursion and induction, graphs and trees, languages and automata. The book is well-written and organized, with clear explanations, examples, exercises, and applications. The book also has online resources, such as videos, slides, and software.

Introduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. This is a comprehensive and authoritative textbook on algorithms that