This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems.

Topics and features:

• Includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary
• Describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann
• Introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices
• Explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory
• Reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking
• Covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving
• Presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus

This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Autorentext

Dr. Gerard O'Regan is a CMMI software process improvement consultant with research interests including software quality and software process improvement, mathematical approaches to software quality, and the history of computing. He is the author of such Springer titles as World of Computing: A Primer Companion for the Digital Age, Concise Guide to Formal Methods, Concise Guide to Software Engineering, Guide to Discrete Mathematics, and Introduction to the History of Computing.

Inhalt

What is a Computer?

Foundations of Computing

Overview of Mathematics in Computing

Introduction to Algorithms

Number Theory

Algebra

Sequences, Series, and Permutations and Combinations

Mathematical Induction and Recursion

Graph Theory

Cryptography

Coding Theory

Language Theory and Semantics

Computability and Decidability

Matrix Theory

A Short History of Logic

Propositional and Predicate Logic

Advanced Topics in Logic

The Nature of Theorem Proving

Software Engineering Mathematics

Software Reliability and Dependability

Overview of Formal Methods

Z Formal Specification Language

Automata Theory

Model Checking

Probability and Statistics

Complex Numbers and Quaternions

Calculus

Epilogue