# Discrete Mathematics for Computer Science: A Review of Kolman's 5th Edition

## Discrete Mathematical Structures 5th Edition by Bernard Kolman PDF Zip Checked

## Introduction

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, cryptography, coding theory and many other areas. Discrete mathematics also helps to develop abstract thinking, logical reasoning and problem-solving skills that are essential for computer scientists.

## discrete mathematical structures 5th edition by bernard kolman pdf zip checked

One of the most popular and comprehensive books on discrete mathematics is Discrete Mathematical Structures by Bernard Kolman, Robert C. Busby and Sharon Cutler Ross. The fifth edition of this book was published in 2003 by Prentice Hall and covers a wide range of topics such as sets, logic, relations, functions, graphs, trees, counting, algorithms and applications. The book is designed for undergraduate students of computer science and related fields, and provides numerous exercises, examples, proofs and applications to illustrate the concepts.

In this article, we will show you how to download the fifth edition of Discrete Mathematical Structures by Bernard Kolman in PDF format and check its validity. We will also give you an overview of the book and its contents, as well as some reasons why you should learn discrete mathematics for computer science.

## Discrete Mathematics and Computer Science

Discrete mathematics is a vast and diverse field that encompasses many topics and subfields. Some of the most important ones are:

Sets: A set is a collection of distinct objects that share some common property. Sets are used to represent data types, collections, categories and classes in computer science. For example, a set can represent a group of students, a list of numbers or a set of keywords.

Logic: Logic is the study of valid reasoning and inference. Logic is used to construct formal languages, systems and proofs in computer science. For example, logic can be used to define syntax and semantics of programming languages, design circuits and hardware devices or verify software correctness.

Relations: A relation is a set of ordered pairs that express some connection or association between two sets. Relations are used to model data structures, operations, functions and properties in computer science. For example, a relation can represent a database table, a graph edge or a function mapping.

Functions: A function is a special type of relation that assigns a unique output to each input from a given domain. Functions are used to describe computations, transformations, algorithms and processes in computer science. For example, a function can represent a mathematical formula, a program subroutine or a hash function.

Graphs: A graph is a set of vertices and edges that connect them. Graphs are used to represent networks, structures, systems and problems in computer science. For example, a graph can represent a social network, a web page, a circuit or a traveling salesman problem.

Trees: A tree is a special type of graph that has no cycles and has a unique root vertex. Trees are used to represent hierarchies, organizations, classifications and algorithms in computer science. For example, a tree can represent a file system, a family tree, a decision tree or a binary search tree.

Counting: Counting is the study of enumeration and combinatorics. Counting is used to calculate probabilities, complexities, efficiencies and optimizations in computer science. For example, counting can be used to estimate the number of possible passwords, the running time of an algorithm or the optimal solution of a problem.

Algorithms: An algorithm is a finite sequence of steps that solves a specific problem or performs a specific task. Algorithms are the core of computer science, as they provide the methods and techniques for designing and implementing software and hardware systems. For example, an algorithm can be used to sort a list of numbers, encrypt a message or find the shortest path in a graph.

These are just some of the topics that discrete mathematics covers and that are relevant for computer science. By learning discrete mathematics, you will be able to understand the concepts and principles behind many computer science applications and domains such as cryptography, coding theory, data structures, complexity theory, artificial intelligence and more. You will also be able to develop your abstract thinking, logical reasoning and problem-solving skills that are essential for computer scientists.

## Discrete Mathematical Structures 5th Edition by Bernard Kolman

Discrete Mathematical Structures by Bernard Kolman, Robert C. Busby and Sharon Cutler Ross is one of the most popular and comprehensive books on discrete mathematics for computer science students. The fifth edition of this book was published in 2003 by Prentice Hall and has 528 pages. The book is divided into 11 chapters that cover the following topics:

Fundamentals: This chapter introduces the basic concepts of sets, logic and proofs.

Logic: This chapter covers propositional logic, predicate logic, logical equivalences and methods of proof.

Counting: This chapter covers the basic principles of counting such as permutations, combinations, binomial coefficients and inclusion-exclusion.

Relations and Digraphs: This chapter covers relations, digraphs, matrices, equivalence relations, partial orderings and lattices.

Functions: This chapter covers functions, one-to-one functions, onto functions, inverse functions, composition of functions and growth of functions.

Order Relations and Structures: This chapter covers order relations, ordered sets, bounds, extremal elements, well-ordered sets and recursive definitions.

Trees: This chapter covers trees, rooted trees, binary trees, spanning trees and traversal algorithms.

Topics in Graph Theory: This chapter covers graphs, Euler paths and circuits, Hamilton paths and circuits, planar graphs and graph coloring.

Semigroups and Groups: This chapter covers semigroups, groups, subgroups, cyclic groups and permutation groups.

Languages: This chapter covers languages, alphabets, strings, operations on languages, grammars, finite-state machines and Turing machines .

Finite-State Machines: This chapter covers finite-state machines, Moore machines, Mealy machines, equivalence and minimization of finite-state machines.

The book also has four appendices that cover mathematical systems, matrices, the algebra of sets and proof techniques . The book provides numerous exercises, examples, applications and proofs to illustrate the concepts and help the students practice their skills. The book also has some features that make it stand out from other similar books such as:

The book uses an informal tone and a conversational style to engage the reader and make the material more accessible and enjoyable.

The book emphasizes the applications of discrete mathematics to computer science and shows how the theory can be used to solve real-world problems.

## Downloading and Checking the Book in PDF Format

If you want to download the fifth edition of Discrete Mathematical Structures by Bernard Kolman in PDF format, you can use the following link:

https://openlibrary.org/books/OL9286558M/Discrete_Mathematical_Structures_Fifth_Edition

This link will take you to the Open Library website, where you can borrow the book for free for 14 days. You will need to create an account and sign in to access the book. Once you have borrowed the book, you can download it as a PDF file or read it online.

The file name of the book is discrete-mathematical-structures-5th-edition-by-bernard-kolman-pdf.zip. The file size is 16.4 MB. The file contains 528 pages. The edition is the fifth edition. The ISBN number is 9780130457974.

To unzip the file and open it with a PDF reader, you can follow these steps:

Locate the file on your computer and right-click on it.

Select "Extract All" from the menu and choose a destination folder for the extracted files.

Open the destination folder and double-click on the file discrete-mathematical-structures-5th-edition-by-bernard-kolman.pdf.

The file will open with your default PDF reader. You can also use any other PDF reader of your choice.

To check the validity of the file, you can compare its size, pages, edition and ISBN number with the information provided on the Open Library website or on other reliable sources such as Amazon or Google Books. You can also scan the file with an antivirus software to make sure it is free of malware or viruses.

## Conclusion

In this article, we have shown you how to download the fifth edition of Discrete Mathematical Structures by Bernard Kolman in PDF format and check its validity. We have also given you an overview of the book and its contents, as well as some reasons why you should learn discrete mathematics for computer science.

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, cryptography, coding theory and many other areas. Discrete mathematics also helps to develop abstract thinking, logical reasoning and problem-solving skills that are essential for computer scientists.

Discrete Mathematical Structures by Bernard Kolman, Robert C. Busby and Sharon Cutler Ross is one of the most popular and comprehensive books on discrete mathematics for computer science students. The fifth edition of this book was published in 2003 by Prentice Hall and covers a wide range of topics such as sets, logic, relations, functions, graphs, trees, counting, algorithms and applications. The book is designed for undergraduate students of computer science and related fields, and provides numerous exercises, examples, proofs and applications to illustrate the concepts.

We hope that this article has inspired you to explore more about discrete mathematics and computer science. If you want to learn more about this topic, you can check out some of these additional resources or references:

Introduction to Discrete Mathematics for Computer Science by Gennady Pekhimenko

Discrete Mathematics Course by Victor Adamchik

Discrete Mathematics Video Lectures by Shai Simonson

Discrete Mathematics with Applications by Susanna S. Epp

Concrete Mathematics: A Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth and Oren Patashnik

Thank you for reading this article and we hope you have enjoyed it. If you have any questions or feedback, please feel free to leave a comment below. Happy learning!

## FAQs

What is discrete mathematics?

Discrete mathematics is a branch of mathematics that deals with finite and discrete objects and structures.

Why is discrete mathematics important for computer science?

Discrete mathematics is important for computer science because it provides the tools and techniques for designing and analyzing algorithms, data structures, cryptography, coding theory and many other areas. It also helps to develop abstract thinking, logical reasoning and problem-solving skills that are essential for computer scientists.

What are the main topics covered in Discrete Mathematical Structures 5th Edition by Bernard Kolman?

The main topics covered in Discrete Mathematical Structures 5th Edition by Bernard Kolman are sets, logic, relations, functions, graphs, trees, counting, algorithms and applications.

How to download Discrete Mathematical Structures 5th Edition by Bernard Kolman in PDF format?

You can download Discrete Mathematical Structures 5th Edition by Bernard Kolman in PDF format from the Open Library website. You will need to create an account and sign in to access the book. You can borrow the book for free for 14 days and download it as a PDF file or read it online.

How to check the validity of Discrete Mathematical Structures 5th Edition by Bernard Kolman PDF file?

You can check the validity of Discrete Mathematical Structures 5th Edition by Bernard Kolman PDF file by comparing its size, pages, edition and ISBN number with the information provided on the Open Library website or on other reliable sources. You can also scan the file with an antivirus software to make sure it is free of malware or viruses.

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