Overview
- Endows the reader with an operational conceptual and methodological understanding of discrete mathematics for computing
- Suitable for advanced undergraduate and graduate students, and self-study by researchers and professionals
- Authors' ambition is that the reader will truly understand the elements of computing rather than just know them
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“Each chapter comes with several exercises from easy to difficult, the latter with complete solutions in the appendix. To accommodate the book to readers with different backgrounds and goals, the authors provide a guide which gives paths through the book for several courses. The exposition is always clear and motivating, no prerequisites are presumed, all terms and concepts are defined precisely, and there are many look-and-see proofs.” (Dieter Riebesehl, zbMATH 1465.68004, 2021)
“The breadth of today's technology is so wide and the variety of programming languages so large, that we can easily feel far removed from the foundations that support the modern technical edifice that is computing. For example, when we write code we create and invoke methods. Increasingly, we build solutions by combining and calling cloud microservices. We query databases. We search and filter information using online services. In utilizing different technologies these regular tasks appear to be quite dissimilar, but in fact they are fundamentally alike. They are all instances of mathematical functions, that is: mappings between sets. It turns out that when we have a mathematical grounding in the concept of sets we are empowered to discover unifying abstractions and powerful simplifications in our solutions. [This] is a wonderful guide to the mathematical connections that underpin computing and it shows you where to look.” (Peter Rodgers, Founder, 1060 Research)
“This book is a must-read for anyone who wishes to understand the mathematical foundations of the modern computing enterprise. The book is exceptionally accessible to a diverse audience of students, practitioners, scientists, hardware designers, and software professionals. It uses the most powerful techniques for teaching by approaching each topic in multiple different ways and connecting abstract math with concrete applications. The authors accomplish the rare feat of complementing mathematical rigor with intuitive explanations and visual examples. The result is a true joy to read with its conversational prose and interesting historical asides that bring the topics to life.” (Ramesh K. Sitaraman, UMass Amherst)
Authors and Affiliations
About the authors
Prof. Arnold Rosenberg is a distinguished university professor emeritus at the University of Massachusetts, Amherst. He also held research positions at Northeastern University and Colorado State University, a professorship at Duke University, and a staff research position at IBM Watson Research Center. He was elected a fellow of the ACM in 1996 for his work on graph-theoretic models of compuation, emphasizing theoretical studies of parallel algorithms and architectures, VLSI design and layout, and data structures. In 1997, he was elected as a fellow of the IEEE for fundamental contributions to theoretical aspects of computer science and engineering.
Prof. Denis Trystram is a distinguished professor at the Grenoble Institute of Engineering, an honorary member of the Institut Universitaire de France (IUF), and he works at the Laboratoire d'Informatique de Grenoble (LIG) in the team-project DataMove-INRIA. His research interestst include the design and analysis of efficient algorithms for optimizing resource use in parallel and distributed systems, approximation algorithms for scheduling and packing problems, and algorithms for data analytics. Both authors have considerable teaching and practical experience in the application of discrete mathematics approaches to computing tasks.
Bibliographic Information
Book Title: Understand Mathematics, Understand Computing
Book Subtitle: Discrete Mathematics That All Computing Students Should Know
Authors: Arnold L. Rosenberg, Denis Trystram
DOI: https://doi.org/10.1007/978-3-030-58376-7
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-58375-0Published: 06 December 2020
Softcover ISBN: 978-3-030-58378-1Published: 07 December 2021
eBook ISBN: 978-3-030-58376-7Published: 05 December 2020
Edition Number: 1
Number of Pages: XXVII, 550
Number of Illustrations: 149 b/w illustrations, 2 illustrations in colour
Topics: Mathematics of Computing, History of Mathematical Sciences, History of Computing, Theory of Computation