Neutrices and External Numbers: A Flexible Number System: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Autor Bruno Dinis, Imme van den Bergen Limba Engleză Hardback – 24 iun 2019
Features
- Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system.
- Outlines complete algebraic rules for the neutrices and external numbers
- Conducts operational analysis of convergence and integration of functions known up to orders of magnitude
- Formalises a calculus of error propagation, covariant with algebraic operations
- Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox
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Specificații
ISBN-13: 9781498772679
ISBN-10: 1498772676
Pagini: 360
Ilustrații: 4 Illustrations, black and white
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.64 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics
ISBN-10: 1498772676
Pagini: 360
Ilustrații: 4 Illustrations, black and white
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.64 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Cuprins
1 Introduction to Elementary Nonstandard Analysis
2 Some models and calculations involving imprecisions.
3 Neutrices and external numbers
4 Advanced properties
5 Sequences. Convergence up to a neutrix
6 Functions of external numbers
7 Integration of functions of external numbers
8 Flexible systems of linear equations
9 Applications in asymptotics
10 Applications in other fields
11 External numbers as a complete arithmetical solid
A Background on Nonstandard Analysis
B Solutions to selected exercises
2 Some models and calculations involving imprecisions.
3 Neutrices and external numbers
4 Advanced properties
5 Sequences. Convergence up to a neutrix
6 Functions of external numbers
7 Integration of functions of external numbers
8 Flexible systems of linear equations
9 Applications in asymptotics
10 Applications in other fields
11 External numbers as a complete arithmetical solid
A Background on Nonstandard Analysis
B Solutions to selected exercises
Recenzii
The book Neutrices and External numbers: A Flexible Number System by Bruno Dinis and Imme van den Berg provides a remarkable presentation of the system of external numbers. It is a rigorous and convenient mathematical theory that provides a strong foundation for a complete doctrine of orders of magnitude — the art of neglecting—so present in the scientific approach. This subject is exposed in a pedagogical and comprehensive way by multiplying the points of view and the applications.
—Retired Professor Guy Wallet, La Rochelle University, France
[. . .] The latest addition to the outstanding CRC Press 'Monographs and Research Notes In Mathematics' series, Neutrices and External Numbers: A Flexible Number System by Bruno Dinis and Imme van den Berg (who is an Associated Professor in Mathematics at the University of Evora, Portugal and whose main area of interest lies in non-standard analysis) is enhanced for academia with an informative five page Foreword, as well as the inclusion of a twelve page Bibliography and a four page Index -- making is a significant and unreservedly recommended addition to professional, college, and university library Advanced Mathematics collections and supplemental curriculum lists. It should be noted for students, academia, and non-specialist readers with an interest in the subject that "Neutrices and External Numbers" is also available in a digital book format
—Midwest Book Review
—Retired Professor Guy Wallet, La Rochelle University, France
[. . .] The latest addition to the outstanding CRC Press 'Monographs and Research Notes In Mathematics' series, Neutrices and External Numbers: A Flexible Number System by Bruno Dinis and Imme van den Berg (who is an Associated Professor in Mathematics at the University of Evora, Portugal and whose main area of interest lies in non-standard analysis) is enhanced for academia with an informative five page Foreword, as well as the inclusion of a twelve page Bibliography and a four page Index -- making is a significant and unreservedly recommended addition to professional, college, and university library Advanced Mathematics collections and supplemental curriculum lists. It should be noted for students, academia, and non-specialist readers with an interest in the subject that "Neutrices and External Numbers" is also available in a digital book format
—Midwest Book Review
Notă biografică
Bruno Dinis is a postdoc at the Faculdade de Ciências, University of Lisbon, whose main area of interest is Mathematical Logic, Proof Theory, Nonstandard Analysis, and Philosophy of Mathematics.
Imme van den Berg is Associated Professor in Mathematics at the University of Évora, Portugal. His main area of interest lies in non-standard analysis. He is the author / co-author of 4 books and over 20 articles in the area of non-standard analysis.
Imme van den Berg is Associated Professor in Mathematics at the University of Évora, Portugal. His main area of interest lies in non-standard analysis. He is the author / co-author of 4 books and over 20 articles in the area of non-standard analysis.
Descriere
The book introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations.