# A Complete Review of Elements of Discrete Mathematics by C.L. Liu (PDF Download)

## Elements of Discrete Mathematics by C.L. Liu: A Comprehensive Guide

If you are looking for a book that covers all the essential topics of discrete mathematics in a clear, concise, and rigorous way, then Elements of Discrete Mathematics by C.L. Liu is the book for you. This book is widely used as a textbook for undergraduate courses in discrete mathematics, as well as a reference book for researchers and professionals who need to apply discrete mathematics in their work. In this article, we will give you an overview of what discrete mathematics is, who C.L. Liu is, what are the main topics covered in his book, how to use his book effectively, and how to download his book for free in PDF format.

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## What is discrete mathematics and why is it important?

Discrete mathematics is the branch of mathematics that deals with finite or countable structures, such as sets, logic, relations, functions, combinatorics, graphs, algorithms, algebraic structures, and coding theory. Unlike continuous mathematics, which studies smooth and continuous phenomena, such as calculus and analysis, discrete mathematics focuses on discrete and discrete phenomena, such as integers, binary digits, truth values, permutations, trees, encryption schemes, etc.

Discrete mathematics is important because it provides the theoretical foundation for many fields of science and engineering, especially computer science and information technology. Discrete mathematics helps us to model and analyze various aspects of computation, such as data structures, algorithms, complexity, cryptography, artificial intelligence, logic programming, database systems, network protocols, coding theory, etc. Discrete mathematics also helps us to develop abstract thinking skills and logical reasoning abilities that are essential for solving problems and proving theorems.

## Who is C.L. Liu and what are his contributions to discrete mathematics?

C.L. Liu (Chung Laung Liu) is a distinguished professor emeritus of computer science at the University of Illinois at Urbana-Champaign. He was born in Taiwan in 1934 and received his B.S. degree from National Cheng Kung University in Taiwan in 1956 and his M.S., E.E., and Sc.D. degrees from Massachusetts Institute of Technology in 1960 and 1962. He was a faculty member at MIT from 1962 to 1971 and at UIUC from 1971 to 1998. He was also a visiting professor at Tokyo University in Japan, National Central University in Taiwan, National Tsing Hua University in Taiwan, etc.

C.L. Liu is a renowned scholar and researcher in the fields of discrete mathematics, computer science, and electrical engineering. He has authored or co-authored eight books and more than 200 technical papers on topics such as set theory, logic, relations, functions, combinatorics, recurrence relations, graph theory, algorithms, algebraic structures, coding theory, scheduling theory, optimization methods, computer architecture, operating systems, real-time systems, distributed computing, etc. He is a fellow of the Institute of Electrical and Electronics Engineers (IEEE) and the Association for Computing Machinery (ACM). He has received many awards and honors for his academic achievements and contributions, such as the IEEE Computer Society Technical Achievement Award, the IEEE Computer Society Harry H. Goode Memorial Award, the ACM Karl V. Karlstrom Outstanding Educator Award, the IEEE Circuits and Systems Society Education Award, the IEEE Computer Society Taylor L. Booth Education Award, etc.

## What are the main topics covered in Elements of Discrete Mathematics?

### Set theory and logic

The first chapter of the book introduces the basic concepts and notations of set theory, such as sets, subsets, operations, cardinality, power sets, partitions, etc. The second chapter covers the fundamentals of logic, such as propositional logic, truth tables, logical equivalence, tautologies, contradictions, normal forms, etc. The third chapter extends the logic to predicate logic, which involves quantifiers, predicates, variables, domains, etc. The fourth chapter discusses various methods of proof, such as direct proof, indirect proof, proof by contradiction, proof by cases, proof by induction, etc.

### Relations and functions

The fifth chapter defines and explores the properties of relations, such as reflexivity, symmetry, transitivity, equivalence relations, partial orders, etc. The sixth chapter introduces the concept of functions and their types, such as one-to-one functions, onto functions, bijections, inverse functions, composition of functions, etc. The seventh chapter deals with some special functions and sequences that are important in discrete mathematics and computer science, such as factorial function, binomial coefficients, Fibonacci sequence, recurrence relations, generating functions, etc.

### Combinatorics and recurrence relations

The eighth chapter studies the techniques and principles of counting and enumeration, such as the sum rule, the product rule, the inclusion-exclusion principle, permutations, combinations, arrangements, etc. The ninth chapter applies the counting techniques to various problems involving discrete probability and statistics, such as sample spaces, events, probability axioms and rules, conditional probability, Bayes' theorem, expected value, variance, standard deviation, etc. The tenth chapter revisits the topic of recurrence relations and shows how to solve them using different methods, such as iteration method, characteristic equation method, generating function method, etc.

### Graph theory and algorithms

The eleventh chapter introduces the basic concepts and terminology of graph theory, such as graphs, vertices, edges, degrees, paths, cycles, connectedness, components, etc. The twelfth chapter explores some special types of graphs and their properties, such as trees, rooted trees, spanning trees, binary trees, Eulerian graphs, Hamiltonian graphs, planar graphs, etc. The thirteenth chapter discusses some algorithms and applications of graph theory in computer science and engineering, such as graph traversal algorithms (breadth-first search and depth-first search), shortest path algorithms (Dijkstra's algorithm and Floyd-Warshall algorithm), minimum spanning tree algorithms (Prim's algorithm and Kruskal's algorithm), network flow algorithms (Ford-Fulkerson algorithm and Edmonds-Karp algorithm), etc.

### Algebraic structures and coding theory

The fourteenth chapter introduces the concept of algebraic structures and their examples in discrete mathematics and computer science, such as groups, subgroups, cyclic groups, permutation groups, cosets, normal subgroups, quotient groups, rings, subrings, ideals, quotient rings, fields, vector spaces, matrices, etc. The fifteenth chapter applies the algebraic structures to the field of coding theory, which deals with the design and analysis of codes for data transmission and storage, such as binary codes, Hamming distance, Hamming weight, error detection, error correction, linear codes, Hamming codes, cyclic codes, Reed-Solomon codes, etc.

## How to use Elements of Discrete Mathematics as a textbook or a reference book?

### Features and benefits of the book

### Elements of Discrete Mathematics is a comprehensive book that covers all the major topics of discrete mathematics in a clear, concise, and rigorous way. The book has many features and benefits that make it suitable for both students and instructors, such as: - The book is organized into 15 chapters that follow a logical sequence and cover all the essential topics of discrete mathematics. - The book provides clear definitions, examples, theorems, proofs, and exercises for each topic. - The book uses a computer-oriented approach that emphasizes the applications and relevance of discrete mathematics to computer science and engineering. - The book includes many solved examples and exercises that illustrate the concepts and techniques of discrete mathematics. - The book offers hints and solutions to selected exercises at the end of each chapter. - The book provides supplementary materials, such as slides, lecture notes, and online resources, for instructors and students. Tips and tricks for studying and solving problems

Elements of Discrete Mathematics is a book that requires active reading and problem-solving skills. Here are some tips and tricks for studying and solving problems using this book: - Read the chapter carefully and understand the definitions, examples, theorems, and proofs. Try to follow the logic and reasoning behind each statement and proof. - Review the solved examples and exercises at the end of each section. Try to solve them by yourself before looking at the solutions. Compare your solutions with the given ones and identify your mistakes and gaps in understanding. - Practice more exercises from the book or from other sources. Try to solve different types of problems that test your knowledge and skills in discrete mathematics. - Use online tools and calculators to check your answers and verify your calculations. For example, you can use Wolfram Alpha to compute set operations, truth tables, binomial coefficients, recurrence relations, etc. - Seek help from your instructor, tutor, or peers if you have any doubts or difficulties in understanding or solving problems. Discuss your ideas and solutions with others and learn from their feedback and suggestions.

### Additional resources and supplements

Elements of Discrete Mathematics is a book that provides a comprehensive coverage of discrete mathematics. However, you may also want to use some additional resources and supplements to enhance your learning experience, such as: - Other books on discrete mathematics that offer different perspectives, approaches, and levels of difficulty. For example, you can use Discrete Mathematics and Its Applications by Kenneth H. Rosen or Discrete Mathematics with Applications by Susanna S. Epp as complementary books. - Online courses and videos on discrete mathematics that explain the concepts and techniques in an interactive and visual way. For example, you can use MIT OpenCourseWare or Khan Academy as online learning platforms. - Online forums and communities on discrete mathematics that allow you to ask questions, share ideas, and interact with other learners and experts. For example, you can use Stack Exchange or Reddit as online discussion platforms.

## How to download Elements of Discrete Mathematics for free in PDF format?

### Legal and ethical issues of downloading books online

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### Sources and links for downloading the book

If you still want to download Elements of Discrete Mathematics for free in PDF format, you may find some sources and links that offer such a service online. However, you should be careful and cautious when using these sources and links, as they may not be reliable, safe, or legal. Some of these sources and links may require you to register, sign up, or provide personal information, which may compromise your privacy and security. Some of these sources and links may also contain ads, pop-ups, or redirects, which may annoy you or lead you to unwanted sites. Some of these sources and links may also provide incomplete, inaccurate, or outdated versions of the book, which may affect your learning quality and experience.

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### Alternatives and options for accessing the book

If you do not want to download Elements of Discrete Mathematics for free in PDF format, you may have some alternatives and options for accessing the book in other ways, such as: - Buying the book from online or offline bookstores that sell new or used copies of the book. For example, you can buy the book from Amazon or Flipkart. - Borrowing the book from libraries or friends that have the book. For example, you can borrow the book from your college library or your classmate. - Renting the book from online or offline rental services that offer the book for a limited period of time. For example, you can rent the book from Chegg or BookRenter. - Accessing the book from online or offline subscription services that offer the book as part of their collection. For example, you can access the book from Scribd or Kindle Unlimited.

## Conclusion

In this article, we have given you an overview of what discrete mathematics is, who C.L. Liu is, what are the main topics covered in his book Elements of Discrete Mathematics, how to use his book effectively, and how to download his book for free in PDF format. We hope that this article has helped you to learn more about discrete mathematics and appreciate its applications and relevance to computer science and engineering. We also hope that this article has inspired you to read Elements of Discrete Mathematics by C.L. Liu and enhance your knowledge and skills in discrete mathematics.

## FAQs

Here are some frequently asked questions and answers about Elements of Discrete Mathematics by C.L. Liu: Q: What is the difference between the 2nd edition and the 3rd edition of the book? A: The 2nd edition of the book was published in 1985 and the 3rd edition was published in 2012. The 3rd edition has been revised and updated to reflect the changes and developments in discrete mathematics and computer science. The 3rd edition also has a co-author, Durga Prasad Mohapatra, who is a professor of computer science at National Institute of Technology Rourkela in India. Q: Is Elements of Discrete Mathematics by C.L. Liu suitable for beginners or advanced learners? A: Elements of Discrete Mathematics by C.L. Liu is suitable for both beginners and advanced learners of discrete mathematics. The book covers all the essential topics of discrete mathematics in a clear, concise, and rigorous way. The book also provides many examples and exercises that cater to different levels of difficulty and complexity. Q: How long does it take to read Elements of Discrete Mathematics by C.L. Liu? A: The length of time it takes to read Elements of Discrete Mathematics by C.L. Liu depends on your reading speed, comprehension level, and interest level. The book has about 280 pages and 15 chapters. If you read one chapter per day, it may take you about two weeks to finish the book. If you read two chapters per day, it may take you about one week to finish the book. 71b2f0854b