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Understand Mathematics, Understand Computing de Arnold L. Rosenberg

Understand Mathematics, Understand Computing

Autor Arnold L. Rosenberg, Denis Trystram
en Limba Engleză Hardback – 6 dec 2020
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.
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Specificații

ISBN-13: 9783030583750
ISBN-10: 3030583759
Pagini: 580
Ilustrații: XXVII, 550 p. 151 illus., 2 illus. in color.
Dimensiuni: 160 x 241 x 37 mm
Greutate: 0.98 kg
Ediția:1st ed. 2020
Editura: Springer
Locul publicării:Cham, Switzerland

Cuprins

Introduction.- “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.- Summations: Complex Operations from Simple Components.- 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, Probability, and Statistics.- Graphs I: Representing Relationships Mathematically.- Graphs II: Graphs Within Computation and Communication.- Solutions to Exercises.- App. A, Pairing Functions.- App. B, A Deeper Look at the Fibonacci Numbers.- App. C, Two Recurrence-Defined Number Families.- App. D, Signed-Digit Numerals: Carry-Free Addition.- App. E, The Diverse Delights of de Bruijn Networks.- List of Symbols.- References.- Index.

Recenzii

“The text is written in an easy to read format which generously incorporates narratives from the history of mathematics as well as rigorous proofs of the concepts presented. The appendices and references to other texts provide the reader with numerous sources of supplementary information for those wishing to delve into a subject at a deeper level … . chapters are organized and clearly labeled to express which sections are appropriate for a beginning learner, an intermediate learner, or the specialist.” (Tom French, MAA Reviews, October 3, 2021)

“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)

Notă biografică

Arnold L. Rosenberg is a distinguished university professor emeritus at the University of Massachusetts, Amherst. He earlier held full-time positions as a professor at Duke and as a Research Staff member at the IBM Watson Research Center. He has held research positions at Northeastern University and Colorado State University. He has been a visiting professor at the University of Toronto, a Lady Davis visiting professor at the Technion (Israel Inst. of Technology), and a Fulbright Senior Research Scholar at the University of Paris-South. In 1996, he was elected a fellow of the ACM for his work on graph-theoretic models of computation, with a focus on theoretical studies of parallel algorithms and architectures, VLSI design and layout, and data structures. In 1997, he was elected a fellow of the IEEE for his fundamental contributions to theoretical aspects of computer science and engineering.
Lenwood S. Heath is a professor in the Department of Computer Science at Virginia Tech. His research interests include theoretical computer science, algorithms, graph theory, computational biology and bioinformatics, computational genomics, complex networks, and computational epidemiology. He completed a Ph.D. in computer science (1985) at the University of North Carolina, Chapel Hill, an M.S. in mathematics (1976) at the University of Chicago, and a B.S. in mathematics (1975) at the University of North Carolina, Chapel Hill. Before joining the faculty at Virginia Tech in 1987, he was an instructor of applied mathematics and member of the Laboratory of Computer Science at MIT. He is a member of SIAM, a member of the ACM, and a lifetime senior member of the IEEE. He is a managing editor of the Journal of Interconnection Networks

Textul de pe ultima copertă

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.

Caracteristici

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