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. The book continually seeks to build upon students’ intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding.

The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.

Features

Approachable for students who have not yet studied mathematics beyond school

Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof

Draws attention to connections with other areas of mathematics

Plenty of exercises for students, both straightforward problems and more in-depth investigations

Introduces many concepts that are required in more advanced topics in mathematics.