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# Discrete Mathematical Structures 5th Edition by Bernard Kolman Pdf Zipl: A Comprehensive and Accessible Introduction to Discrete Mathematics

## Introduction

In this article, we will introduce you to discrete mathematics, a branch of mathematics that deals with finite and discrete objects and their properties. We will also give you an overview of one of the most popular and widely used textbooks on discrete mathematics, Discrete Mathematical Structures 5th Edition by Bernard Kolman, Robert Busby, and Sharon Ross. Finally, we will show you how to download this book in pdf format using a simple and secure method.

### What is discrete mathematics?

Discrete mathematics is the study of mathematical structures that are discrete, meaning that they are composed of distinct and separate elements. Unlike continuous mathematics, which deals with infinite and continuous objects such as real numbers, functions, and curves, discrete mathematics focuses on finite and countable objects such as integers, graphs, sets, logic, algorithms, and codes.

### Why is discrete mathematics important?

Discrete mathematics is important for several reasons. First, it provides the theoretical foundation for many areas of computer science, such as data structures, algorithms, cryptography, artificial intelligence, and computer networks. Second, it develops the logical and analytical thinking skills that are essential for solving problems and proving results in mathematics and other disciplines. Third, it exposes students to a variety of topics and applications that are relevant and interesting in today's world.

### What are the main topics covered in discrete mathematics?

Some of the main topics covered in discrete mathematics are:

• Logic: The study of formal systems of reasoning and inference, such as propositional logic, predicate logic, proof methods, and Boolean algebra.

• Sets: The study of collections of objects and their properties, such as set operations, relations, functions, cardinality, and countability.

• Combinatorics: The study of counting methods and arrangements of objects, such as permutations, combinations, binomial coefficients, recurrence relations, generating functions, and inclusion-exclusion principle.

• Graphs: The study of structures that consist of vertices (or nodes) and edges (or links) that connect them, such as graph terminology, representations, traversals, connectivity, trees, planarity, coloring, matching, and network flows.

• Algebraic structures: The study of abstract structures that obey certain algebraic rules, such as groups, rings, fields, lattices, and Boolean algebras.

• Coding theory: The study of methods for encoding and transmitting information efficiently and reliably, such as binary codes, Hamming codes, linear codes, and cyclic codes.

• Cryptography: The study of methods for securing and protecting information from unauthorized access or modification, such as classical ciphers, public-key cryptography, RSA algorithm, Diffie-Hellman key exchange, and digital signatures.

## Overview of the book

Now that you have a basic idea of what discrete mathematics is and why it is important, let us introduce you to one of the best books on this subject, Discrete Mathematical Structures 5th Edition by Bernard Kolman, Robert Busby, and Sharon Ross. This book is a comprehensive and accessible introduction to discrete mathematics that covers all the main topics mentioned above and more. It is suitable for undergraduate students of computer science, engineering, and mathematics, as well as for anyone who wants to learn more about discrete mathematics.

### Who are the authors?

The authors of this book are:

• Bernard Kolman: He is a professor emeritus of mathematics at Drexel University. He has a Ph.D. in mathematics from Cornell University and has authored or co-authored several books on linear algebra, discrete mathematics, graph theory, and computer science.

• Robert Busby: He is a professor of mathematics at Drexel University. He has a Ph.D. in mathematics from Temple University and has co-authored several books on discrete mathematics, graph theory, and computer science.

• Sharon Ross: She is an associate professor of mathematics at Drexel University. She has a Ph.D. in mathematics from Temple University and has co-authored several books on discrete mathematics, graph theory, and computer science.

### What are the features of the book?

Some of the features of this book are:

• Clear and concise exposition: The book explains the concepts and techniques of discrete mathematics in a clear and concise manner, with examples, exercises, and applications to illustrate them.

• Student-friendly approach: The book adopts a student-friendly approach that motivates and engages the readers, with pedagogical tools such as learning objectives, summaries, key terms, review questions, historical notes, biographies, and projects.

• Comprehensive coverage: The book covers all the main topics of discrete mathematics in depth and breadth, with additional topics such as languages, automata, computability, complexity, number theory, and discrete probability.

• Flexible organization: The book is organized into 11 chapters that can be taught in various sequences and combinations, depending on the instructor's preference and the course objectives.

• Online resources: The book comes with online resources such as instructor's solutions manual, test bank, PowerPoint slides, and companion website that provide additional support for teaching and learning.

### How is the book organized?

The book is organized into 11 chapters as follows:

Chapter

Title

Main Topics

1

Fundamentals

Sets, logic, proofs, algorithms, complexity

2

Logic

Propositional logic, predicate logic, proof methods, Boolean algebra

3

Counting

Permutations, combinations, binomial coefficients, recurrence relations, generating functions, inclusion-exclusion principle

4

Relations And Digraphs

Relations, properties of relations, equivalence relations, partial orderings, digraphs, matrix representations, transitive closure, Warshall's algorithm

5

Functions And Matrices

Functions, one-to-one functions, onto functions, inverse functions, composition of functions, cardinality of sets, matrices, operations on matrices, special matrices

6

Lattices And Boolean AlgebrasLattices, properties of lattices, sublattices, distributive lattices, complemented lattices, Boolean algebras, homomorphisms of Boolean algebras,7 >Coding Theory >Coding theory basics, binary codes, Hamming codes, linear codes,cyclic codes,

Chapter

Title

Main Topics

8

Group Theory And Cryptography

Groups, subgroups, cyclic groups, cosets, Lagrange's theorem, homomorphisms, isomorphisms, cryptography basics, classical ciphers, public-key cryptography, RSA algorithm, Diffie-Hellman key exchange, digital signatures

9

Graph Theory And Its ApplicationsGraphs, terminology and representations, graph isomorphism, connectivity and paths, Euler and Hamilton paths and circuits, shortest-path problems, planar graphs, graph coloring, matching and covering,network flows,

Chapter

Title

Main Topics

10

Languages And Finite-State MachinesLanguages, grammars, Chomsky hierarchy, regular languages, regular expressions, finite-state machines, deterministic and nondeterministic finite-state machines,equivalence of regular expressions and finite-state machines,

Chapter

Title

Main Topics

11

## Computability And ComplexityComputability, Turing machines, Church-Turing thesis, decidability, undecidability, reducibility, complexity, time complexity, space complexity,P and NP classes, NP-completeness,</td How to download the book in pdf format?

If you are interested in reading this book and learning more about discrete mathematics, you might be wondering how to download it in pdf format. Pdf format is a convenient and portable way of accessing digital books, as it preserves the original layout, fonts, images, and hyperlinks of the book. You can also easily view, print, and share pdf files using various devices and platforms.

• High quality: You can download the book in pdf format with high resolution and clarity, without any loss of quality or distortion.

• Easy access: You can download the book in pdf format with a simple click of a button, without any hassle or delay.

• Offline availability: You can download the book in pdf format and save it on your device, without needing an internet connection or online access.

• Flexible usage: You can download the book in pdf format and use it for various purposes, such as studying, teaching, researching, or referencing.

Before you download the book in pdf format, you need to make sure that you have the following requirements:

• A device: You need a device such as a computer, laptop, tablet, or smartphone that can connect to the internet and store files.

• An internet connection: You need an internet connection that is fast and reliable, to ensure a smooth and quick download process.

• A browser: You need a browser such as Chrome, Firefox, Safari, or Edge that can access and display web pages.

• Select a location: Select a location on your device where you want to save the file and click on "Save" or "OK". The file name should be "Discrete Mathematical Structures 5th Edition by Bernard Kolman.pdf.zip".

• Extract the file: Locate the file on your device and right-click on it. Choose "Extract All" or "Unzip" and follow the instructions to extract the file. The extracted file name should be "Discrete Mathematical Structures 5th Edition by Bernard Kolman.pdf".

• Open the file: Locate the extracted file on your device and double-click on it. The file should open with your default pdf reader. You can also choose to open it with another pdf reader of your choice.

## Conclusion

In this article, we have introduced you to discrete mathematics, a branch of mathematics that deals with finite and discrete objects and their properties. We have also given you an overview of one of the best books on discrete mathematics, Discrete Mathematical Structures 5th Edition by Bernard Kolman, Robert Busby, and Sharon Ross. Finally, we have shown you how to download this book in pdf format using a simple and secure method.

### Summary of the main points

To summarize, here are the main points we have covered in this article:

• Discrete mathematics: It is the study of mathematical structures that are discrete, such as integers, graphs, sets, logic, algorithms, and codes.

• Importance of discrete mathematics: It provides the theoretical foundation for many areas of computer science, such as data structures, algorithms, cryptography, artificial intelligence, and computer networks. It also develops the logical and analytical thinking skills that are essential for solving problems and proving results in mathematics and other disciplines.

• Topics covered in discrete mathematics: Some of the main topics covered in discrete mathematics are logic, sets, combinatorics, graphs, algebraic structures, coding theory, and cryptography.

• Discrete Mathematical Structures 5th Edition by Bernard Kolman, Robert Busby, and Sharon Ross: It is a comprehensive and accessible introduction to discrete mathematics that covers all the main topics mentioned above and more. It is suitable for undergraduate students of computer science, engineering, and mathematics, as well as for anyone who wants to learn more about discrete mathematics.

### Call to action

What is the difference between discrete mathematics and continuous mathematics?

• Discrete mathematics deals with finite and discrete objects and their properties, such as integers, graphs, sets, logic, algorithms, and codes. Continuous mathematics deals with infinite and continuous objects and their properties, such as real numbers, functions, and curves.

What are some examples of applications of discrete mathematics?

Some examples of applications of discrete mathematics are:

• Data structures: Discrete mathematics helps to design and analyze data structures such as arrays, lists, stacks, queues, trees, and graphs that store and manipulate data efficiently.

• Algorithms: Discrete mathematics helps to design and analyze algorithms such as sorting, searching, recursion, dynamic programming, and greedy algorithms that solve problems optimally.

• Cryptography: Discrete mathematics helps to create and break codes that secure and protect information from unauthorized access or modification.

• Artificial intelligence: Discrete mathematics helps to model and reason about intelligent agents, knowledge bases, logic programming, and machine learning that simulate human intelligence.

• Computer networks: Discrete mathematics helps to model and optimize network topologies, routing protocols, error detection and correction, and network security that enable communication among computers.

What are some prerequisites for reading this book?

• This book assumes that the reader has some background in high school algebra and calculus and some familiarity with basic concepts of computer science such as variables, data types, and loops. However, the book also provides sufficient review and explanation of these concepts as needed.

How long does it take to read this book?

• This book has 11 chapters and each chapter has about 40 pages on average. The time it takes to read this book depends on the reader's pace and level of interest. However, a reasonable estimate is that it takes about 20 hours to read this book thoroughly and complete all the exercises and projects.

Where can I find more resources on discrete mathematics?

Some of the resources you can find on discrete mathematics are:

• Websites: There are many websites that offer online courses tutorials videos and quizzes on discrete mathematics such as Khan Academy Coursera edX MIT OpenCourseWare and YouTube.

• Books: There are many books that cover discrete mathematics in depth and breadth such as Discrete Mathematics and Its Applications by Kenneth Rosen Introduction to Discrete Mathematics by Susanna Epp Graham, Donald Knuth, and Oren Patashnik and Elements of Discrete Mathematics by C.L. Liu and D.P. Mohapatra.

• Forums: There are many forums that offer discussions questions answers and tips on discrete mathematics such as Stack Exchange Reddit Quora and MathOverflow.

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