Finite Precision Number Systems and Arithmetic
Finite Precision Number Systems and Arithmetic

Author: Peter Kornerup

Publisher: Cambridge University Press

Published: 2010-09-30

Total Pages: 717

ISBN-13: 113964355X

DOWNLOAD EBOOK

Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.

The New Math
The New Math

Author: Christopher James Phillips

Publisher: University of Chicago Press

Published: 2015

Total Pages: 242

ISBN-13: 022618496X

DOWNLOAD EBOOK

An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. This book examines the rise and fall of the new math as a marker of the period's political and social ferment.

Advanced Topics in the Arithmetic of Elliptic Curves
Advanced Topics in the Arithmetic of Elliptic Curves

Author: Joseph H. Silverman

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 482

ISBN-13: 1461208513

DOWNLOAD EBOOK

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

Capitalism and Arithmetic
Capitalism and Arithmetic

Author: Frank J. Swetz

Publisher: Open Court Publishing

Published: 1987

Total Pages: 372

ISBN-13: 9780812690149

DOWNLOAD EBOOK

"The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in vernacular Venetian and published in Treviso, Italy in 1478. The Treviso Arithmetic is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science. The Treviso Arithmetic is a practical book intended for self study and for use in Venetian trade. It is written in vernacular Venetian and communicated knowledge to a large population. It helped to end the monopoly on mathematical knowledge and gave important information to the middle class. It was not written for a large audience, but was intended to teach mathematics of everyday currency. The Treviso became one of the first mathematics books written for the expansion of human knowledge. It provided an opportunity for the common person, rather than only a privileged few, to learn the art of computation. The Treviso Arithmetic provided an early example of the Hindu-Arabic numeral system computational algorithms."--Wikipedia.

Digital Arithmetic
Digital Arithmetic

Author: Milos D. Ercegovac

Publisher: Elsevier

Published: 2004

Total Pages: 736

ISBN-13: 1558607986

DOWNLOAD EBOOK

The authoritative reference on the theory and design practice of computer arithmetic.

Arithmetic
Arithmetic

Author: Paul Lockhart

Publisher: Belknap Press

Published: 2019-07-15

Total Pages: 232

ISBN-13: 067423751X

DOWNLOAD EBOOK

“Inspiring and informative...deserves to be widely read.” —Wall Street Journal “This fun book offers a philosophical take on number systems and revels in the beauty of math.” —Science News Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart presents arithmetic not as rote manipulation of numbers—a practical if mundane branch of knowledge best suited for filling out tax forms—but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher. “A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education...Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.” —Jonathon Keats, New Scientist “What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story...A wonderful book.” —Keith Devlin, author of Finding Fibonacci

The Number System
The Number System

Author: H. A. Thurston

Publisher: Courier Corporation

Published: 2012-10-23

Total Pages: 146

ISBN-13: 0486154947

DOWNLOAD EBOOK

This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.

The Arithmetic of Dynamical Systems
The Arithmetic of Dynamical Systems

Author: J.H. Silverman

Publisher: Springer Science & Business Media

Published: 2007-06-06

Total Pages: 518

ISBN-13: 0387699031

DOWNLOAD EBOOK

This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.