Название: Mathematical Foundations of Information Sciences
Автор: Esfandiar Haghverdi, Liugen Zhu
Издательство: World Scientific Publishing
Год: 2024
Страниц: 163
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

This is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.

This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.

This book is based on the lecture notes originally prepared by the first author for the course I201-Mathematical Foundations for Informatics at Indiana University Bloomington. Informatics students come from a variety of backgrounds, for example, biology, social sciences, mathematics, and physical sciences, etc. It is not easy to design a course that fits the needs of everybody. These students will pursue different paths in their subsequent years, some will go to graduate school and some others might be joining the work force in industry. In designing this course we tried to understand the needs of such a diverse audience and decided to introduce topics that are vital for a successful completion of the informatics undergraduate program. The book you are reading now is the result of our efforts over the many years that we have been teaching this course.

Here is a brief description of the contents of each chapter. In Chapter 2, we begin our study of the simplest formal system there is, that is propositional logic. We shall study truth tables, truth trees, and some logical puzzles. We will define and analyze validity of arguments in propositional logic. Next we describe a formal system that will allow us to generate proofs for valid arguments. Chapter 3 provides enough background on sets and set identities needed to introduce the more complicated formal system of predicate logic. We will carry an in-depth study of predicate logic, its syntax and semantics, translation from and to English, in Chapter 4. Chapter 5 will discuss the powerful mathematical proof technique, called mathematical induction. We will discuss this proof method in abstract and will provide many worked examples to make its use clear. In Chapter 6, we introduce and discuss the properties of functions and relations, these concepts play a central role in mathematics, Computer Science and all fields of informatics. It is vital that you get a good understanding and a working knowledge of these concepts. Finally, in Chapter 7, we give a brief discussion of graphs and some graph properties using a logical (relation-based) approach.




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