Vk Balakrishnan Discrete Mathematics Pdf

[Gaynelle Beltramo]

DiscreteMathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math and computer science majors. The book is especially well-suited for courses that incorporate inquiry-based learning. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at more than 200 colleges and universities around the world (see the partial adoptions list). The text is endorsed by the American Institute of Mathematics' Open Textbook Initiative and is well reviewed on the Open Textbook Library.

This 3rd edition brings many improvements, including nearly 100 new exercises (including many interactive exercises providing instant feedback), a new section on trees in the graph theory chapter, and improved exposition throughout. Previous editions will continue to be available indefinitely. A few times a year, the text is updated with a new "printing" to correct errors. See the errata list for more information.

Online homework sets are available through Runestone Academy (free), Edfinity (inexpensive) or as WeBWorK sets from the author (the WeBWorK exercises are available in the Contrib folder of the OPL as well).

Please contact the author with feedback and suggestions, or if you are decide to use the book in a course you are teaching. You can also easily submit feedback about an error or typo by creating a GitHub issue.

The entire book is available for free as an interactive online ebook. This should work well on all screen sizes, including smart phones, and work will with screen readers for visually impaired students. Hints and solutions to examples and exercises are hidden but easily revealed by clicking on their links. Some exercises also allow you to enter and check your work, so you can try multiple times without spoiling the answer.

For offline use, a free pdf version, suitable for reading on a tablet or computer, is available for download. This should be searchable and easy to navigate using embedded links. Hints and solutions (when available) can be accessed by clicking on the exercise number, and clicking on the number of the hint or solution will bring you back to the exercise.

If you prefer a physical copy, an inexpensive print version of the text is available on Amazon. This should be cheaper than printing the entire book and binding it yourself. Page numbers match the pdf version. There is also a cheap Kindle version available; it works great on Android tablets; unfortunately it seems the math does not render well on Amazon's e-ink readers.

There are a number of videos instructors have made for classes they taught using the book. Check out the playlists below. If you make videos or know of others, please share them.Mathematical Visual Proofs. Beautifully animated videos illustrating ideas from the book.Dr. Trevor Bazett's Course. A complete course that uses the textbook as a basis for the videos.

If you are using the book in a class you are teaching, instructor resources are available by request. Just contact the author. You can also request WeBWorK homework sets if you have access to a WeBWorK server.

The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proofs" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Originally designed to support future math teachers, the text has a friendly and informal tone, and puts an emphasis on understanding the included concepts, rather than simply memorizing procedures. The book has also been successfully used in courses catering to computer science students, who also benefit from the deeper understanding it promotes.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.

Oscar Levin is a professor at the University of Northern Colorado. He has taught mathematics and computer science at the college level for over 15 years and received multiple teaching awards. He received his Ph.D. in mathematical logic from the University of Connecticut in 2009.

Discrete Mathematics: An Open Introduction by Oscar Levin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. You are free to download, use, print, and even sell this work as you wish to. You can also modify the text as much as you like (create a custom edition for your students, for example), as long as you attribute the parts of the text you use to the author.

Introductory Discrete Mathematics is a concise text for a discrete mathematics course at an introductory level for undergraduate students in computer science and mathematics. The essential components of any beginning level discrete mathematics curriculum are combinatorics, graph theory with applications to some standard network optimization problems, and algorithms to solve these problems. In this book the stress is on these core components. Both the Association for Computing Machinery and the Committee for the Undergraduate Program in Mathematics recognize the vital role of an undergraduate course in discrete methods that introduces the student to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics.

The material in Chapter 0 serves as an introduction to the fundamental operations involving sets and the principle of mathematical induction. For those students familiar with the topics discussed here, this is essentially a chapter for review.

The standard topics in combinatorics in any course on discrete mathematics are covered in Chapters 1, 2, and 3. These topics include basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. The role of applications is emphasized wherever possible. There are more than 200 exercises at the end of these chapters. Each counting problem requires its own special insight, and it is advantageous for the student to work out several of these problems.

In the next three chapters is a survey of graphs and digraphs. We begin with treating graphs and digraphs as models of real-world phenomena by giving several examples. The connectedness properties of graphs and digraphs are studied. Basic results and applications of graph coloring and of Eulerian and Hamiltonian graphs are presented with a stress on applications to coding and other related problems. Two important problems in network optimization are the minimal spanning tree problem and the shortest distance problem; they are covered in the last two chapters. The approach to compute the complexity of algorithms in these chapters is more or less informal.

It is possible to cover the topics presented in this book as a one-semester course by skipping some sections if necessary. Of course it is for the instructor to decide which sections she or he may skip.

My chief acknowledgment is to the students who have studied discrete mathematics with me at the University of Maine during the past decade. They taught me how to teach. Their contributions and encouragement are implicit on every page. In particular, I would like to mention the names of Rajesh and Thananchayan. My scientific indebtedness in this project encompasses many sources including the articles and books listed in the bibliography. If there are errors or misleading results, the blame of course falls entirely on my shoulders. Finally, it goes without saying that I owe a great deal to the interest and encouragement my family has shown at every stage of this work.

The concept of a set plays a very significant role in all branches of modern mathematics. In recent years set theory has become an important area of investigation because of the way in which it permeates so much of contemporary mathematical thought. A genuine understanding of any branch of modern mathematics requires a knowledge of the theory of sets for it is the common foundation of the diverse areas of mathematics. Sets are used to group distinct objects together. It is necessary that the objects which belong to a set are well-defined in the sense that there should be no ambiguity in deciding whether a particular object belongs to a set or not. Thus, given an object, either it belongs to a given set or it does not belong to it. For example, the first five letters of the English alphabet constitute a set which may be represented symbolically as the set a, b, c, d, e. An arbitrary object belongs to this set if and only if it is one of these five letters. These five distinct objects can appear in any order in this representation. In other words, this set can also be represented by d, b, a, e, c. The objects that belong to a set need not possess a common property. Thus the number 4, the letter x, and the word book can constitute a set S which may be represented as S = x, book, 4. A particular day may be cold for one person and not cold for another, so the collection of cold days in a month is not a clearly defined set. Similarly, the collection of large numbers and the collection of tall men are also not sets.

Thus a set is a collection of distinct objects. The objects in a set are called the elements or members of the set. If x is an element of a set A, we say that x belongs to A, and this is expressed symbolically as x A. The notation denotes that y is not an element of the set A.

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