Introduction To 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.
Real Analysis Foundations
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Author : Sergei Ovchinnikov
language : en
Publisher: Springer Nature
Release Date : 2021-02-16
Real Analysis Foundations written by Sergei Ovchinnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-16 with Mathematics categories.
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
An Introduction To Mathematical Thinking
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Author : William J. Gilbert
language : en
Publisher: Pearson
Release Date : 2005
An Introduction To Mathematical Thinking written by William J. Gilbert and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algebraic logic categories.
Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.
The Navy Electricity And Electronics Training Series Module 13 Introduction To Number Systems And Logic
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Author : United States. Navy
language : en
Publisher: Lulu.com
Release Date : 2018-09-16
The Navy Electricity And Electronics Training Series Module 13 Introduction To Number Systems And Logic written by United States. Navy and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-16 with Fiction categories.
Module 13, Introduction to Number Systems and Logic Circuits, presents the fundamental concepts of number systems, Boolean algebra, and logic circuits, all of which pertain to digital computers.The Navy Electricity and Electronics Training Series (NEETS) was developed for use by personnel in many electrical- and electronic-related Navy ratings. Written by, and with the advice of, senior technicians in these ratings, this series provides beginners with fundamental electrical and electronic concepts through self-study. The presentation of this series is not oriented to any specific rating structure, but is divided into modules containing related information organized into traditional paths of instruction.
Foundation Mathematics For Computer Science
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Author : John Vince
language : en
Publisher: Springer
Release Date : 2015-07-27
Foundation Mathematics For Computer Science written by John Vince and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-27 with Computers categories.
John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.
An Experimental Introduction To Number Theory
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Author : Benjamin Hutz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-17
An Experimental Introduction To Number Theory written by Benjamin Hutz 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 2018-04-17 with Mathematics categories.
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Can You Count In Greek
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Author : Judy Leimbach
language : en
Publisher: Taylor & Francis
Release Date : 2023-05-31
Can You Count In Greek written by Judy Leimbach and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Education categories.
Discovering the way people in ancient cultures conducted their lives is fascinating for young people, and learning how these people counted and calculated is a part of understanding these cultures. This book offers a concise, but thorough, introduction to ancient number systems. Students won't just learn to count like the ancient Greeks; they'll learn about the number systems of the Mayans, Babylonians, Egyptians, and Romans, as well as learning Hindu-Arabic cultures and quinary and binary systems. Symbols and rules regarding the use of the symbols in each number system are introduced and demonstrated with examples. Activity pages provide problems for the students to apply their understanding of each system. Can You Count in Greek? is a great resource for math, as well as a supplement for social studies units on ancient civilizations. This valuable resource builds understanding of place value, number theory, and reasoning. It includes everything you need to easily incorporate these units in math or social studies classes. Whether you use all of the units or a select few, your students will gain a better understanding and appreciation of our number system. Grades 5-8