Number Systems

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.

Autorentext

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.

Klappentext

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.

Inhalt

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