専門職グループ

公開·42名のメンバー

2023年6月10日

How Discrete Mathematics 7th Edition by Richard Johnsonbaugh Can Help You Master Computer Science

# Discrete Mathematics 7th Edition by Richard Johnsonbaugh: A Comprehensive Review ## Introduction - What is discrete mathematics and why is it important for computer science? - Who is Richard Johnsonbaugh and what are his credentials? - What are the main features and benefits of the 7th edition of his book? ## Chapter 1: Sets and Logic - What are sets, subsets, operations, and cardinality? - What are propositions, truth tables, logical equivalence, and implication? - How to use quantifiers, predicates, and arguments? ## Chapter 2: Proofs - What are direct proofs, proof by contrapositive, and proof by contradiction? - How to use mathematical induction and strong induction? - What are recursive definitions and structural induction? ## Chapter 3: Algorithms - What are algorithms, pseudocode, and flowcharts? - How to analyze the time and space complexity of algorithms? - What are some common algorithm design techniques? ## Chapter 4: Number Theory - What are divisibility, primes, greatest common divisors, and Euclidean algorithm? - How to use modular arithmetic, congruences, and inverse modulo? - What are some applications of number theory in cryptography? ## Chapter 5: Relations - What are relations, properties, matrices, and digraphs? - How to use equivalence relations, partitions, and equivalence classes? - How to use partial orders, lattices, and Boolean algebras? ## Chapter 6: Functions - What are functions, domains, codomains, ranges, and compositions? - How to use one-to-one, onto, and invertible functions? - How to use growth of functions, asymptotic notation, and big-O notation? ## Chapter 7: Counting - What are the basic counting principles: sum rule, product rule, and inclusion-exclusion principle? - How to use permutations, combinations, binomial coefficients, and Pascal's triangle? - How to use the pigeonhole principle and generalized permutations and combinations? ## Chapter 8: Probability - What are experiments, outcomes, sample spaces, events, and probabilities? - How to use conditional probability, independence, Bayes' theorem, and odds? - How to use discrete random variables, expected value, variance, and standard deviation? ## Chapter 9: Recurrence Relations - What are recurrence relations and how to solve them using iteration method? - How to use characteristic equation method and generating function method? - How to use recurrence relations to model algorithms and combinatorial problems? ## Chapter 10: Graphs - What are graphs, vertices, edges, paths, cycles, and degrees? Some possible continuations for the outline are: ## Chapter 10: Graphs (continued) - How to use adjacency matrices, adjacency lists, and incidence matrices to represent graphs? - How to use graph traversals, connected components, and Eulerian paths and circuits? - How to use Hamiltonian paths and circuits, traveling salesman problem, and shortest path algorithms? ## Chapter 11: Trees - What are trees, rooted trees, and binary trees? - How to use tree traversals, spanning trees, and minimum spanning trees? - How to use binary search trees, heaps, and Huffman coding? ## Chapter 12: Boolean Algebra - What are Boolean expressions, Boolean functions, and Boolean circuits? - How to use truth tables, canonical forms, and Karnaugh maps to simplify Boolean expressions? - How to use De Morgan's laws, duality principle, and NAND and NOR gates? ## Conclusion - Summarize the main topics covered in the book and how they relate to computer science. - Highlight the strengths and weaknesses of the book and its pedagogical approach. - Provide some recommendations for further reading or learning resources. ## FAQs ### Q1: Who is the target audience of this book? ### A1: This book is intended for undergraduate students who are taking a one- or two-term introductory course in discrete mathematics. It assumes some familiarity with basic algebra and calculus. ### Q2: What are the prerequisites for reading this book? ### A2: The book does not require any specific prerequisites, but it helps to have some background in logic, proofs, and algorithms. The book provides some review and examples of these topics in the first few chapters. ### Q3: How is the 7th edition different from the previous editions? ### A3: The 7th edition reflects user and reviewer feedback on both content and organization. It has more exercises, examples, and applications, as well as improved clarity and readability. It also has some new topics, such as cryptography, Huffman coding, and big-O notation. ### Q4: What are the supplementary materials available for this book? ### A4: The book comes with an instructor's manual, a student solutions manual, and a companion website that contains additional resources, such as slides, quizzes, and online labs. ### Q5: How can I get a copy of this book? ### A5: You can buy this book from various online or offline retailers, such as Amazon, Google Books, or your local bookstore. You can also check if your library has a copy of this book or request one through interlibrary loan.