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Journey from Natural Numbers to Complex Numbers [Kietas viršelis]

2.00/5 (1 ratings by Goodreads)
(Gujarat University, India), (Gujarat University, India)
  • Formatas: Hardback, 80 pages, aukštis x plotis: 216x138 mm, weight: 222 g, 2 Tables, black and white; 2 Illustrations, black and white
  • Serija: Advances in Mathematics and Engineering
  • Išleidimo metai: 04-Dec-2020
  • Leidėjas: CRC Press
  • ISBN-10: 0367613328
  • ISBN-13: 9780367613327
Kitos knygos pagal šią temą:
Journey from Natural Numbers to Complex NumbersDidesnis paveikslėlis
  • Formatas: Hardback, 80 pages, aukštis x plotis: 216x138 mm, weight: 222 g, 2 Tables, black and white; 2 Illustrations, black and white
  • Serija: Advances in Mathematics and Engineering
  • Išleidimo metai: 04-Dec-2020
  • Leidėjas: CRC Press
  • ISBN-10: 0367613328
  • ISBN-13: 9780367613327
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780367613327.html
Raktažodžiai:
"This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way"--

This book is for those interested in number systems, abstract algebra, and analysis. It provides an understanding of negative and fractional numbers with theoretical background and explains rationale of irrational and complex numbers in an easy to understand format.This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way.
Preface vii
Author biographies xiii
1 Natural Numbers
1(30)
1.1 Prerequisites
1(13)
1.1.3 Set Theory
1(2)
1.1.3 Relation
3(3)
1.1.3 Function
6(2)
1.1.3 Cardinality
8(2)
1.1.3 Algebra
10(4)
1.2 Positive Integers
14(15)
1.2.3 Positive Integers in Real Life
14(2)
1.2.3 Set Theoretic Definition of Natural Numbers
16(1)
1.2.3 Peano Axioms
17(2)
1.2.3 Ordering in Natural Numbers
19(1)
1.2.3 First Principle of Mathematical Induction
20(1)
1.2.3 Second Principle of Mathematical Induction
20(1)
1.2.3 Well-Ordering Principle
21(1)
1.2.3 Limitations of Natural Numbers
21(1)
1.2.3 Representation of Natural Numbers
21(2)
1.2.9.1 Hexadecimal System
23(3)
1.2.3 Number System Used by Computers
26(3)
1.3 Summary
29(2)
2 Integers
31(16)
2.1 Informal Introduction of Integers
31(4)
2.2 Integers as Relation in Ordered Pairs of Natural Numbers
35(1)
2.3 Ordering in Ordered Pairs
36(1)
2.4 Operations in Ordered Pairs of Natural Numbers
36(1)
2.5 Properties of Binary Operations
37(2)
2.6 Interpretation of Relation and Operations
39(3)
2.7 Mapping of Ordered Pairs as Extension of Natural Numbers
42(1)
2.8 Representation of Integers
43(2)
2.9 Summary
45(2)
3 Rational Numbers
47(14)
3.1 Informal Introduction of Rational Numbers
47(2)
3.2 Rational Numbers as Relation in Ordered Pairs of Integers
49(1)
3.3 Ordering in Ordered Pairs
50(1)
3.4 Operations in Ordered Pairs
50(1)
3.5 Properties of Binary Operations
50(1)
3.6 Interpretation of Relation and Operations
51(1)
3.7 Mapping of Ordered Pairs as Extension of Integers
52(1)
3.8 Representation of Rational Numbers
53(5)
3.9 Limitations of Rational Numbers
58(1)
3.10 Summary
59(2)
4 Real Numbers
61(10)
4.1 Least Upper Bound Property
62(1)
4.2 Rational Cuts
62(1)
4.3 Dedekind Cuts
63(1)
4.4 Ordering in Cuts
64(1)
4.5 Binary Operations in Cuts
65(1)
4.6 Least Upper Bound Property
66(1)
4.7 Set of Cuts as Extension of Rational Numbers
66(1)
4.8 Cardinality of Set of Real Numbers
67(2)
4.9 Limitations of Real Numbers
69(1)
4.10 Summary
69(2)
5 Complex Numbers
71(8)
5.1 Complex Numbers as Ordered Pairs of Real Numbers
71(1)
5.2 Binary Operations in Complex Numbers
71(1)
5.3 Introduction of Imaginary Numbers
72(1)
5.4 Representation of Complex Numbers
73(3)
5.5 Ordering in Complex numbers
76(1)
5.6 Cardinality of the Set of Complex Numbers
76(1)
5.7 Algebraic Numbers
77(1)
5.8 Summary
77(2)
Index 79
Nita H. Shah received her PhD in Statistics from Gujarat University in 1994. From February 1990 till now she is HOD of Department of Mathematics in Gujarat University, India. She is post-doctoral visiting research fellow of University of New Brunswick, Canada. Prof. Nita's research interests include inventory modeling in supply chain, robotic modeling, mathematical modeling of infectious diseases, image processing, dynamical systems and its applications etc. Prof. Nita has published 13 monograph, 5 textbooks, and 475+ peer-reviewed research papers. Four edited books were prepared for IGI-Global and Springer with a coeditor. Her papers are published in high impact Elsevier, Inderscience and Taylor and Francis journals. She is the author of 14 books.

Vishnuprasad D. Thakkar did his Masters in Mathematics from Gujarat University, India and was recipient of the National Merit Scholarship during his post-graduation study. The study was followed by 35+ years experience in Information Technology in the area of application solution design, development and implementation including ERP implementation and real-time process monitoring. After retirement from industry, he completed his Ph.D. in Mathematics under guidance of Prof. (Dr.) Nita H. Shah.