Journey from natural numbers to complex numbers / Nita H. Shah and Thakkar D. Vishnuprasad.

Format:

Book

Author/Creator:

Shah, Nita H., author.

Vishnuprasad, Thakkar D., author.

Series:

CRC focus series

Advances in mathematics and engineering

Language:

English

Subjects (All):

Number theory.

Numbers, Complex.

Physical Description:

1 online resource (95 pages) : illustrations

Edition:

1st.

Place of Publication:

Boca Raton : CRC Press, 2021.

Summary:

"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"-- Provided by publisher.

Contents:

Cover

Half Title

Series Page

Title Page

Copyright Page

Table of Contents

Preface

Author biographies

Chapter 1 Natural Numbers

1.1 Prerequisites

1.1.1 Set Theory

1.1.2 Relation

1.1.3 Function

1.1.4 Cardinality

1.1.5 Algebra

1.2 Positive Integers

1.2.1 Positive Integers in Real Life

1.2.2 Set Theoretic Definition of Natural Numbers

1.2.3 Peano Axioms

1.2.4 Ordering in Natural Numbers

1.2.5 First Principle of Mathematical Induction

1.2.6 Second Principle of Mathematical Induction

1.2.7 Well-Ordering Principle

1.2.8 Limitations of Natural Numbers

1.2.9 Representation of Natural Numbers

1.2.9.1 Hexadecimal System

1.2.10 Number System Used by Computers

1.3 Summary

Chapter 2 Integers

2.1 Informal Introduction of Integers

2.2 Integers as Relation in Ordered Pairs of Natural Numbers

2.3 Ordering in Ordered Pairs

2.4 Operations in Ordered Pairs of Natural Numbers

2.5 Properties of Binary Operations

2.6 Interpretation of Relation and Operations

2.7 Mapping of Ordered Pairs as Extension of Natural Numbers

2.8 Representation of Integers

2.9 Summary

Chapter 3 Rational Numbers

3.1 Informal Introduction of Rational Numbers

3.2 Rational Numbers as Relation in Ordered Pairs of Integers

3.3 Ordering in Ordered Pairs

3.4 Operations in Ordered Pairs

3.5 Properties of Binary Operations

3.6 Interpretation of Relation and Operations

3.7 Mapping of Ordered Pairs as Extension of Integers

3.8 Representation of Rational Numbers

3.9 Limitations of Rational Numbers

3.10 Summary

Chapter 4 Real Numbers

4.1 Least Upper Bound Property

4.2 Rational Cuts

4.3 Dedekind Cuts

4.4 Ordering in Cuts

4.5 Binary Operations in Cuts

4.6 Least Upper Bound Property

4.7 Set of Cuts as Extension of Rational Numbers

4.8 Cardinality of Set of Real Numbers

4.9 Limitations of Real Numbers

4.10 Summary

Chapter 5 Complex Numbers

5.1 Complex Numbers as Ordered Pairs of Real Numbers

5.2 Binary Operations in Complex Numbers

5.3 Introduction of Imaginary Numbers

5.4 Representation of Complex Numbers

5.5 Ordering in Complex numbers

5.6 Cardinality of the Set of Complex Numbers

5.7 Algebraic Numbers

5.8 Summary

Index

Notes:

Description based on print version record.

Includes index.

ISBN:

9781003105244

1003105246

9781000299571

1000299570

9781000299632

1000299635

OCLC:

1184122111

Publisher Number:

401950

9781000299632