Rosenberg A.L., Trystram D. Understand Mathematics, Understand Computing: Discrete Mathematics That All Computing Students Should Know

Springer, 3020. — 560 p. — ISBN: 978-3-030-58375-0.In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians.
By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.“Doing” Mathematics: A Toolkit for Mathematical Reasoning
Sets and Their Algebras: The Stem Cells of Mathematics
Numbers I: The Basics of Our Number System
Arithmetic: Putting Numbers to Work
Summation: A Complex Whole from Simple Parts
The Vertigo of Infinity: Handling the Very Large and the Infinite
Numbers II Building the Integers and Building with the Integers
Recurrences: Rendering Complex Structure Manageable
Numbers III: Operational Representations and Their Consequences
The Art of Counting: Combinatorics, with Applications to Probability and Statistics
Graphs I: Representing Relationships Mathematically
Graphs II: Graphs for Computing and Communicating