Number Systems - A Path Into Rigorous Mathematics

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.

List of contents

Preface and Acknowledgements 1 Introduction: The Purpose of This Book 2 Sets and Relations 3 Natural Numbers 4 Integers, Z 5 Foundations of Number Theory 6 Rational Numbers, Q 7 Real Numbers, R 8 Quadratic Extensions: General Concepts and Extensions of Z and Q 9 Complex Numbers, C: A Quadratic Extension of R 10 Yet More Number Systems 11 Where Do We Go from Here? A How to Read Proofs: The Self-Explanation" Strategy Solutions to Exercises and Hints for Investigations Bibliography Index

About the author

Anthony Kay was a Lecturer in Mathematical Sciences at Loughborough University for 32 years up to his retirement in 2020. Although his research has been in applications of mathematics, he has taught a wide range of topics in pure and applied mathematics to students at all levels, from first year to postgraduate.

Product details

• Authors: Anthony Kay
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Release: 29.08.2025
• EAN: 9781032988238
• ISBN: 978-1-0-3298823-8
• No. of pages: 384
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / General, MATHEMATICS / Applied, MATHEMATICS / Number Theory, Philosophy of Mathematics, Number Theory, Calculus & mathematical analysis, Applied mathematics, Mathematical foundations, Calculus and mathematical analysis