Number Systems
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The Number System
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Author : H. A. Thurston
language : en
Publisher: Courier Corporation
Release Date : 2012-10-23
The Number System written by H. A. Thurston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-23 with Mathematics categories.
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.
Number Systems
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Author : Sergeĭ Ovchinnikov
language : en
Publisher:
Release Date : 2015
Number Systems written by Sergeĭ Ovchinnikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students
The Real Number System
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Author : John M. H. Olmsted
language : en
Publisher: Courier Dover Publications
Release Date : 2018-09-12
The Real Number System written by John M. H. Olmsted and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-12 with Mathematics categories.
Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises—more than 300, all with answers provided—make this a particularly valuable book for self-study. The first two chapters examine fields and ordered fields, followed by an introduction to natural numbers and mathematical induction. Subsequent chapters explore composite and prime numbers, integers and rational numbers, congruences and finite fields, and polynomials and rational functions. Additional topics include intervals and absolute value, the axiom of completeness, roots and rational exponents, exponents and logarithms, and decimal expansions. A helpful Appendix concludes the text.
Number Systems And The Foundations Of Analysis
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Author : Elliott Mendelson
language : en
Publisher: Dover Books on Mathematics
Release Date : 2008
Number Systems And The Foundations Of Analysis written by Elliott Mendelson and has been published by Dover Books on Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.
Number Systems
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Author : Sergei Ovchinnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-26
Number Systems written by Sergei Ovchinnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-26 with Mathematics categories.
This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
Number Systems
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Author : Anthony Kay
language : en
Publisher: CRC Press
Release Date : 2021-09-14
Number Systems written by Anthony Kay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-14 with Mathematics categories.
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs. The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems. Features Approachable for students who have not yet studied mathematics beyond school Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematics.
Residue Number Systems
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Author : P.V. Ananda Mohan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-30
Residue Number Systems written by P.V. Ananda Mohan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-30 with Computers categories.
This text is an excellent reference for both professional and academic researchers in the field of VLSI using residue number systems. It is also of interest to those working in the general fields of VLSI design, DSP design, and cryptography. Topics covered include choice of moduli; architectures for conversion from binary to RNS; RNS to binary conversion techniques; quadratic RNS; and applications. Numerous examples illustrate the ideas developed. The area and computational requirements are highlighted for all designs, so the selection of a particular architecture is facilitated. Some of the topics covered have application in cryptography. The book includes a comprehensive bibliography in this area.Residue Number Systems: Algorithms and Architectures is also suitable for a graduate-level course as part of a VLSI curriculum.
Residue Number Systems
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Author : Amos R. Omondi
language : en
Publisher: Imperial College Press
Release Date : 2007
Residue Number Systems written by Amos R. Omondi and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today. This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.
Cultural Number Systems
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Author : Karenleigh A. Overmann
language : en
Publisher: Springer Nature
Release Date : 2025-04-26
Cultural Number Systems written by Karenleigh A. Overmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-26 with Social Science categories.
This sourcebook presents an extensive look at cultural number systems in numeracy and writing systems. Based on a decade of research by the author, the work examines topics such as why Xerxes the First counted his army by having his men march through an enclosure big enough to hold 10,000 of them at a time, why the Hawaiian word for "twenty" means “nine and two,” why an ancient Greek mathematician was driven mad by irrational numbers, and how old counting might be and how we might know this. Along the way, the author describes topics such as dactylonomy, the ancient art of expressing and calculating numbers with the fingers; specified counting, the use of different counting sequences to count different types of objects; and the ephemeral abacus, strategies for counting that involve people and goods but not an actual device. The chapters are organized into six geographical areas (the ancient Near East, Africa, Europe, Asia/India, Oceania, and the Americas).
Number Systems For Deep Neural Network Architectures
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Author : Ghada Alsuhli
language : en
Publisher: Springer Nature
Release Date : 2023-09-01
Number Systems For Deep Neural Network Architectures written by Ghada Alsuhli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-01 with Technology & Engineering categories.
This book provides readers a comprehensive introduction to alternative number systems for more efficient representations of Deep Neural Network (DNN) data. Various number systems (conventional/unconventional) exploited for DNNs are discussed, including Floating Point (FP), Fixed Point (FXP), Logarithmic Number System (LNS), Residue Number System (RNS), Block Floating Point Number System (BFP), Dynamic Fixed-Point Number System (DFXP) and Posit Number System (PNS). The authors explore the impact of these number systems on the performance and hardware design of DNNs, highlighting the challenges associated with each number system and various solutions that are proposed for addressing them.