The Number Systems Foundations Of Algebra And Analysis
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The Number Systems Foundations Of Algebra And Analysis
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Author : Solomon Feferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Number Systems Foundations Of Algebra And Analysis written by Solomon Feferman 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 2003 with Number theory categories.
The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''
Number Systems And The Foundations Of Analysis
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Author : Elliott Mendelson
language : en
Publisher:
Release Date : 1985
Number Systems And The Foundations Of Analysis written by Elliott Mendelson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
The Number Systems Of Analysis
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Author : C H C Little
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-05
The Number Systems Of Analysis written by C H C Little and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-05 with Mathematics categories.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
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
New Foundations In Mathematics
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Author : Garret Sobczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-26
New Foundations In Mathematics written by Garret Sobczyk 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 2012-10-26 with Mathematics categories.
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Number Systems
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Author : Anthony Kay
language : en
Publisher: CRC Press
Release Date : 2021-09-15
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 2021-09-15 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.
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.
Foundations Of Mathematics
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Author : Angela G. Shirley
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-08-26
Foundations Of Mathematics written by Angela G. Shirley and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-26 with categories.
One of the greatest mathematicians of all time is reported to have said, "Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty." Foundations of Mathematics is devoted to awakening such a love for Mathematics among first year university students. It is a two volume series-Volume 1, Sets and Number Systems, introduces the student to concepts in Abstract Algebra, while Volume 2 focuses on Linear Algebra. Sets and Number Systems deals with basic ideas in logic, sets, relations, functions, binary operations, natural numbers, integers, rational, irrational and real numbers. The emphasis is on developing the student's ability to reason mathematically, and on building a solid foundation from which to pursue further studies in Mathematics/Mathematics-related fields and to enhance problem solving skills. The author offers a wealth of experience in teaching introductory mathematics courses. Students are sure to appreciate her detailed notes and many worked-examples and exercises, as well as, the inspiring stories of mathematicians featured at the end of each chapter. The appendix contains material specially designed for the Sets and Number Systems course at the University of the West Indies, where she teaches.
From Numbers To Analysis
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Author : Inder K. Rana
language : en
Publisher: World Scientific
Release Date : 1998
From Numbers To Analysis written by Inder K. Rana and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
"This book is recommended to students and instructors looking for a very well-organized introduction to the foundations of analysis".Acta Sci. Math., 1999
Numbers Sequences And Series
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Author : Keith Hirst
language : en
Publisher: Elsevier
Release Date : 1994-12-08
Numbers Sequences And Series written by Keith Hirst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-08 with Mathematics categories.
Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.