Discrete Mathematics by Richard Johnsonbaugh: How to Master Introductory Discrete Mathematics with Examples and Exercises (5th Edition PDF)
Discrete Mathematics by Richard Johnsonbaugh: A Review
Discrete mathematics is a branch of mathematics that deals with finite and discrete objects, such as integers, graphs, sets, logic, algorithms, and cryptography. It is often considered as the foundation of computer science, as it provides the tools and techniques for designing and analyzing algorithms, data structures, programming languages, cryptography, and more. In this article, we will review one of the most popular books on discrete mathematics: Discrete Mathematics by Richard Johnsonbaugh. We will discuss what discrete mathematics is and why it is important, who Richard Johnsonbaugh is and what his approach to discrete mathematics is, and how to get the 5th edition of his book in PDF format.
discrete mathematics richard johnsonbaugh 5th ed 2001 pdf
What is discrete mathematics and why is it important?
Discrete mathematics is a broad term that encompasses many subfields, such as combinatorics, graph theory, number theory, logic, set theory, recursion, automata theory, computational geometry, and more. These subfields have many applications in various domains, such as cryptography, coding theory, computer security, artificial intelligence, bioinformatics, network analysis, game theory, and more. Discrete mathematics also helps develop abstract thinking skills, such as reasoning, proof techniques, induction, recursion, and algorithm design.
The main topics and concepts covered in discrete mathematics
Some of the main topics and concepts that are covered in discrete mathematics are:
Logic and proofs: This topic introduces the basic concepts of propositional logic, predicate logic, logical equivalence, logical implication, quantifiers, rules of inference, methods of proof (such as direct proof, proof by contradiction, proof by contrapositive), mathematical induction (such as weak induction, strong induction), recursive definitions (such as factorial function), and recurrence relations (such as Fibonacci sequence).
Algorithms: This topic introduces the concept of an algorithm (a step-by-step procedure for solving a problem), the properties of an algorithm (such as correctness, efficiency), the analysis of an algorithm (such as time complexity, space complexity), the design of an algorithm (such as divide-and-conquer strategy), and some examples of algorithms (such as Euclidean algorithm for finding the greatest common divisor).
Counting methods and the pigeonhole principle: This topic introduces the basic principles of counting (such as product rule, sum rule), permutations (arrangements of objects in a specific order), combinations (selections of objects without regard to order), binomial coefficients (the number of ways to choose k objects from n objects), inclusion-exclusion principle (a method for counting the number of elements in a union of sets), pigeonhole principle (a statement that says that if n items are put into m containers with n > m then at least one container must contain more than one item), and some applications of these principles.
Graph theory: This topic introduces the concept of a graph (a set of vertices and edges), the types of graphs (such as directed, undirected, simple, multigraph, weighted, unweighted), the properties of graphs (such as degree, adjacency, path, cycle, connectedness, Eulerian, Hamiltonian), the representation of graphs (such as adjacency matrix, adjacency list), the traversal of graphs (such as depth-first search, breadth-first search), the algorithms on graphs (such as Dijkstra's algorithm for finding the shortest path, Prim's algorithm for finding the minimum spanning tree, Kruskal's algorithm for finding the minimum spanning tree), and some applications of graphs (such as network models, social networks, map coloring).
Trees: This topic introduces the concept of a tree (a special kind of graph that has no cycles and is connected), the types of trees (such as rooted, unrooted, binary, ordered, complete), the properties of trees (such as height, depth, level, leaf, parent, child, sibling), the representation of trees (such as linked list, array), the traversal of trees (such as preorder, inorder, postorder), the algorithms on trees (such as binary search tree, heap, Huffman coding), and some applications of trees (such as expression evaluation, sorting, compression).
Boolean algebra and combinatorial circuits: This topic introduces the concept of Boolean algebra (a branch of algebra that deals with truth values and logical operations), the laws and properties of Boolean algebra (such as commutative law, associative law, distributive law, De Morgan's laws), the simplification of Boolean expressions (using Karnaugh maps or Quine-McCluskey method), the concept of combinatorial circuits (electronic circuits that perform logical operations on binary inputs and outputs), the types of combinatorial circuits (such as logic gates, adders, subtractors, multiplexers, decoders), and some applications of combinatorial circuits (such as arithmetic circuits).
Automata, grammars, and languages: This topic introduces the concept of automata (abstract machines that can recognize patterns or process information), the types of automata (such as finite-state automata, pushdown automata, Turing machines), the concept of grammars (rules that generate strings from an alphabet), the types of grammars (such as regular grammars, context-free grammars, context-sensitive grammars, unrestricted grammars), the concept of languages (sets of strings generated by a grammar or recognized by an automaton), the types of languages (such as regular languages, context-free languages, context-sensitive languages, recursively enumerable languages), the relationship between automata and languages (such as Chomsky hierarchy), and some applications of automata and languages (such as lexical analysis, parsing, compilation, pattern matching).
Computational geometry: This topic introduces the concept of computational geometry (the study of algorithms and data structures for geometric problems), the types of geometric objects (such as points, lines, segments, polygons, circles), the properties and operations on geometric objects (such as distance, angle, intersection, convexity), the algorithms and data structures for computational geometry (such as Graham scan for finding the convex hull, Jarvis march for finding the convex hull, sweep line algorithm for finding intersections, quadtree for spatial partitioning), and some applications of computational geometry (such as computer graphics, computer vision, robotics, geographic information systems).
The benefits and challenges of learning discrete mathematics
Learning discrete mathematics has many benefits for students who are interested in computer science or related fields. Some of these benefits are:
It provides a solid foundation for advanced topics: Discrete mathematics covers many fundamental concepts and techniques that are essential for understanding and mastering more advanced topics in computer science, such as algorithms analysis and design, data structures implementation and optimization, programming languages theory and design, cryptography theory and practice, artificial intelligence theory and applications, and more.
It develops critical thinking and problem-solving skills: Discrete mathematics teaches students how to think abstractly and logically about discrete objects and structures. It also teaches students how to formulate precise questions and hypotheses, how to construct rigorous proofs and arguments using various methods and strategies. It also teaches students how to solve complex problems using discrete mathematics tools and techniques.
It enhances creativity and imagination: Discrete mathematics exposes students to many interesting and challenging problems that require creativity and imagination to solve. It also encourages students to explore different approaches and perspectives to solve a problem. It also inspires students to create new problems or variations based on existing ones.
Who is Richard Johnsonbaugh and what is his approach to discrete mathematics?
Richard Johnsonbaugh is a professor of computer science at DePaul University in Chicago. He has a Ph.D. in mathematics from the University of Oregon and has taught discrete mathematics, computer science, and mathematics for over 25 years. He has also written several textbooks on discrete mathematics, computer science, and mathematics, such as Discrete Mathematics (8th edition), Foundations of Mathematical Analysis, and Applications of Discrete Mathematics.
The author's background and qualifications
Richard Johnsonbaugh has a strong background and qualifications in both mathematics and computer science. He has a bachelor's degree in mathematics from Morehouse College, a master's degree in mathematics from the University of Oregon, and a Ph.D. in mathematics from the University of Oregon. He has also done postdoctoral work in computer science at the University of Chicago and the University of Illinois at Chicago. He has received several awards and honors for his teaching and research, such as the Excellence in Teaching Award from DePaul University, the Distinguished Alumni Award from Morehouse College, and the Outstanding Contribution Award from the Association for Computing Machinery.
The features and structure of the book
Discrete Mathematics by Richard Johnsonbaugh is one of the most popular and widely used textbooks on discrete mathematics. It provides an accessible and comprehensive introduction to discrete mathematics through an algorithmic approach that focuses on problem-solving techniques. The book has the following features and structure:
It covers all the main topics and concepts of discrete mathematics: The book covers all the main topics and concepts that are typically taught in a one- or two-semester course on discrete mathematics, such as logic and proofs, algorithms, counting methods and the pigeonhole principle, recurrence relations, graph theory, trees, network models, Boolean algebra and combinatorial circuits, automata, grammars, and languages, computational geometry, and more.
It integrates the techniques of proofs throughout the text: The book integrates the techniques of proofs as a running theme throughout the text. It introduces the basic concepts and methods of proofs in the first chapter and then reinforces them in subsequent chapters with examples and exercises. It also provides tips and hints for writing clear and correct proofs.
It emphasizes algorithmic thinking and problem-solving skills: The book emphasizes algorithmic thinking and problem-solving skills by presenting algorithms as pseudocode or flowcharts, analyzing their correctness and efficiency, designing new algorithms using various strategies, implementing algorithms using programming languages (such as C++, Java, or Python), applying algorithms to solve real-world problems (such as encryption, compression, or routing), and comparing different algorithms for solving the same problem.
It includes many examples and exercises: The book includes many examples and exercises that illustrate and reinforce the concepts and techniques covered in each chapter. The examples are carefully chosen to show how discrete mathematics can be applied to various domains (such as computer science, engineering, biology, cryptography, or game theory). The exercises are graded by difficulty level (from easy to challenging) and by type (such as review questions, conceptual questions, algorithmic questions, programming questions, or writing questions). The book also provides answers or hints to selected exercises at the end of each chapter.
It offers online resources and supplements: The book offers online resources and supplements that enhance the learning experience for both students and instructors. These include an online study guide that provides additional examples, exercises, and quizzes for each chapter; an online instructor's manual that provides solutions to all exercises, lecture notes, and test bank questions for each chapter; an online companion website that provides links to relevant websites, videos, and software tools for each chapter; and an online student solutions manual that provides complete solutions to selected exercises for each chapter.
The strengths and weaknesses of the book
Another possible source and method to obtain a PDF version of the book is to search for legal and ethical online sources that offer a PDF version of the book for free or for a low price. These sources may include online libraries, archives, repositories, or platforms that have the permission or authorization from the author, publisher, or distributor to host or share the PDF version of the book. They may also include online communities, forums, or groups that have the consent or approval from the author, publisher, or distributor to exchange or recommend the PDF version of the book. However, these sources may not be reliable or authentic, so they should be verified and checked before downloading or using the PDF version of the book.
Conclusion
In conclusion, discrete mathematics is a branch of mathematics that deals with finite and discrete objects and structures. It is often considered as the foundation of computer science, as it provides the tools and techniques for designing and analyzing algorithms, data structures, programming languages, cryptography, and more. Discrete Mathematics by Richard Johnsonbaugh is one of the most popular and widely used textbooks on discrete mathematics. It provides an accessible and comprehensive introduction to discrete mathematics through an algorithmic approach that focuses on problem-solving techniques. However, it is not easy to get the 5th edition of the book in PDF format. There are some advantages and disadvantages of using a PDF version of the book, some legal and ethical issues of downloading a PDF version of the book, and some best sources and methods to obtain a PDF version of the book.
If you are interested in learning more about discrete mathematics or getting a copy of Discrete Mathematics by Richard Johnsonbaugh in PDF format, here are some actions you can take:
Visit the official website or online platform of the author, publisher, or distributor of the book: You can find more information about the book, such as its features, structure, contents, reviews, and supplements. You can also find a PDF version of the book for free or for a low price as a sample, an ebook, or an online access code.
Contact your educational institution or organization that uses or recommends the book: You can ask them if they have a PDF version of the book available for their students or instructors as part of their library services, course materials, or online learning systems. You can also ask them if they have permission or authorization from the author, publisher, or distributor to use or share the PDF version of the book.
Search for legal and ethical online sources that offer a PDF version of the book: You can look for online libraries, archives, repositories, or platforms that have the permission or authorization from the author, publisher, or distributor to host or share the PDF version of the book. You can also look for online communities, forums, or groups that have the consent or approval from the author, publisher, or distributor to exchange or recommend the PDF version of the book. However, you should verify and check these sources before downloading or using the PDF version of the book.
FAQs
Here are some frequently asked questions (FAQs) about discrete mathematics and Discrete Mathematics by Richard Johnsonbaugh:
What is discrete mathematics?
Discrete mathematics is a branch of mathematics that deals with finite and discrete objects and structures, such as integers, graphs, sets, logic, algorithms, and cryptography.
Why is discrete mathematics important?
Discrete mathematics is important because it is often considered as the foundation of computer science, as it provides the tools and techniques for designing and analyzing algorithms, data structures, programming languages, cryptography, and more. It also helps develop abstract thinking skills, such as reasoning, proof techniques, induction, recursion, and algorithm design.
Who is Richard Johnsonbaugh?
Richard Johnsonbaugh is a professor of computer science at DePaul University in Chicago. He has a Ph.D. in mathematics from the University of Oregon and has taught discrete mathematics, computer science, and mathematics for over 25 years. He has also written several textbooks on discrete mathematics, computer science, and mathematics, such as Discrete Mathematics (8th edition), Foundations of Mathematical Analysis, and Applications of Discrete Mathematics.
What is Discrete Mathematics by Richard Johnsonbaugh?
Discrete Mathematics by Richard Johnsonbaugh is one of the most popular and widely used textbooks on discrete mathematics. It provides an accessible and comprehensive introduction to discrete mathematics through an algorithmic approach that focuses on problem-solving techniques. It covers all the main topics and concepts of discrete mathematics that are relevant and important for computer science and related fields. It also includes some recent developments and applications of discrete mathematics, such as computational geometry, cryptography, bioinformatics, and network analysis.
How to get the 5th edition of Discrete Mathematics by Richard Johnsonbaugh in PDF format?
The 5th edition of Discrete Mathematics by Richard Johnsonbaugh was published in 2001 by Prentice Hall. It is an updated version of the previous editions that includes new topics (such as computational geometry), new examples and exercises, new online resources and supplements, and new design and layout. However, it is not easy to get the 5th edition of the book in PDF format. There are some advantages and disadvantages of using a PDF version of the book, some legal and ethical issues of downloading a PDF version of the book, and some best sources and methods to obtain a PDF version of the book.
What are the advantages and disadvantages of using a PDF version of the book?
Using a PDF version of the book has some advantages and disadvantages compared to using a physical copy of the book. Some of these are:
Advantages:
A PDF version of the book is more convenient and portable. It can be easily stored, accessed, searched, copied, printed, or shared using a computer or a mobile device. It can also be zoomed in or out, highlighted, annotated, or bookmarked using a PDF reader or editor.
A PDF version of the book is more durable and eco-friendly. It does not wear out, tear, fade, or get lost or damaged by water, fire, insects, or other factors. It also does not consume paper, ink, or energy to produce or distribute.
A PDF version of the book is more affordable and available. It usually costs less or nothing to download or view online compared to buying or renting a physical copy of the book. It also does not depend on the availability or location of a bookstore, library, or seller to obtain.
Disadvantages:
A PDF version of the book is less authentic and reliable. It may not be an exact replica of the origin