Discrete Mathematics Using a Computer
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However computer science is now a mature topic in its own right, and students of computer science may not have the traditional mathematical background of previous generations. This book is taking this observation into account, and starts at a very elementary mathematical level, even explaining proof techniques, while introducing the first concepts of induction, sets, formal logic, The text is largely self-contained.
All the required concepts and notations are defined, and all the statements are proved in full.
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A computer could be used occasionally to solve the exercises but one can perfectly do without. The text has 31 relatively short chapters, each followed by an itemized summary and about a dozen exercises.
Some of the chapters are related, like for example the ones on probability, but others can be skipped without a problem. The main global topics include formal logic, graphs, automata, and complexity.
The pages have a wide outside margin where all the notes and illustrations are included. To illustrate how the chapters are built up, let's look at the first one which is an illustration of the pigeonhole principle. A simple concept, and yet, it starts with ideas about a mathematical theorem which is all about formulating and proving a general proposition, rather than just a particular case, but it runs up to the fundamental theorem of arithmetic every positive integer is a unique product of prime numbers and the proof that there are infinitely many prime numbers.
Further proof techniques are illustrated with other elementary results from number theory. The book continues with sets, used to introduce relations and functions, and induction lead to countable sets, but also to strings generated from an alphabet using syntax rules. Venn diagrams are an introduction to propositional logic, Boolean algebra, and logic circuits.
Graphs are a major part and return in several chapters. They are first introduced by describing a computer model as a discrete state space machine that executes an algorithm. This is a strange choice to see a graph appear for the first time, but it may be motivating for computer science students.senjouin-renkai.com/wp-content/snapchat/iphone-x-whatsapp-ausspionieren.php
What Are the Applications of Discrete Math? | Sciencing
However, graphs are studied for their own right: directed and undirected graphs, connectivity, trees, and coloring. Previous topics are retraced with finite automata to construct and analyse strings. Two mathematical intermezzos introduce limits, integrals, series, and big-O and small-o notation to define orders of magnitude and another one defines infinite summations and series expansions.
These are prerequisites to deal with counting problems combinatorics , discrete probabilities including conditional probability and Bayes's theorem. Complexity theory might have been another application, but that is not included. To ask other readers questions about Discrete Mathematics Using a Computer , please sign up.
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More filters. Sort order. Aug 01, Cesare De Cal rated it it was amazing. I rented this textbook from my university library without knowing what to expect.
Essential Discrete Mathematics for Computer Science
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