Introductory Discrete Mathematics (Dover Books on Computer Science) by V. K . Balakrishnan (PDF)

Description

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0–3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material.Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ― the minimal spanning tree problem and the shortest distance problem ― are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.

User’s Reviews

Editorial Reviews: About the Author V. K. Balakrishnan is Professor Emeritus at the University of Maine.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐My dad for some reason wanted this for Christmas so he got it and loved it! I’m happy with that!

⭐The reviews for this text seem to be split between educators with a solid grasp of the material within the text, and frustrated students. As a learning tool for new to discrete math, the average test scores of my class demonstrate this book to be a complete failure. This text may provide concise explanations for those in search of a quick review of concepts, but it sacrifices its effectiveness as a learning tool for new students in exchange for a short page count. Professors choosing this text are setting both themselves and their students up for a semester of frustration.As a student myself, I’ll go over a few of the reasons this text has proven to be a poor choice. Many of the examples within aren’t thoroughly explained. The author prefers to bridge steps in problems by saying “of course” “obviously” “easily” and “thus” rather than provide a step-by-step breakdown. While these problems may be simple to understand and review for those with a solid grasp of the material, these gaps are unforgivable for students attempting to use the text to help guide learning. When I work through homework problems, I use the examples and lecture notes as tools. When the book’s examples use phrases like “of course” and “we easily find” to jump to conclusions I do not easily see, the only result I get is frustration and wasted hours. In addition, problem sets contain errors. On at least 3 different occasions, my professor has had to correct errors found within assigned exercises from the book. As a student, it is my first instinct to assume I did something wrong when my answer does not match that of the author. I judge this text by the disproportionate amount of time I have to spend trying to google better explanations.

⭐once you cross over to non trivial programming, learning this kind of material is the next step. powerful stuff.

⭐As somebody trying to learn these concepts as a complete beginner, I found the explanations needlessly complicated. I found myself having to look up most of the concepts that I came across elsewhere to get a better understanding. For the explanations to make any sense, one should rely on a good understanding of mathematical writing. I think it is safe to say this does not make a good introduction.

⭐This book is full of great examples and loads of practice problems. Its descriptions, for students fairly comfortable with mathematical writing, are concise and no-nonsense, which can be great. It makes a good reference, in that way, but the book doesn’t do much to guide your intuition. It’s also full of tiny mistakes (seemingly due to rushed editing) that should be no problem for an advanced student or someone working closely with another guide to the subject (a teacher, tutor, or other textbook). But for learners who might struggle with the material, these mistakes in the book can really interrupt understanding. (As a result, I chose not to assign this book to my students.)

⭐A good comprehensive tour of the subject. Like all Dover books, the print is rather small. But like all Dover books, it was very affordable.

⭐Definitely a poor introduction. The author seems more concerned with being clever and concise as opposed to educational and helpful. This book is may make a good reference, but is a terrible introduction that I would not recommend. In addition to that the vernacular around graphs may be a tad outdated, although the concepts are the same.

⭐It has all the topics needed for a good introductory stance for discrete structures

⭐I found this book to be extremely useful; last year I took basic courses in Linear Algebra and Calculus. The sections on Recurrence Relations and Graph Theory are particularly good, but I did struggle a little more with the bits on Generating Functions. The book is exceptionally clearly written, and my friend in Discrete Mathematics found it pretty useful for his exams. Highly recommended.

⭐Clear and precise

⭐Lendo o sumário do livro parece ter um conteúdo bastante interessante. Porém a parte didática do livro fica debilitada por ter basicamente somente definição formal, recomendo que use mais como um compêndio e use de outros livros pra pesquisa. Obs: Ainda não terminei o livroI didn’t finish yet, but he Introductory Discrete Mathematics ebook is more insteresting and I love reading this ebook. Thank you so much ! Congratulations to the Author ! Happiness and Infinites realisations !

⭐Uso esse produto em minhas pesquisas, na área em questão.

⭐

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