Number Systems A Path into Rigorous Mathematics 1st Edition by Anthony Kay 9780429602245 0429602243

Number Systems A Path into Rigorous Mathematics 1st Edition Anthony Kay – Ebook Instant Download/Delivery ISBN(s): 9780367180652, 0367180650, 9780429602245, 0429602243

Product details:

• ISBN 10: 0429602243
• ISBN 13: 9780429602245
• Author:  Anthony Kay 

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.

Table contents:

1 Introduction: The Purpose of This Book

2 Sets and Relations

3 Natural Numbers, ℕ

4 Integers, ℤ

5 Foundations of Number Theory

6 Rational Numbers, ℚ

7 Real Numbers, ℝ

8 Quadratic Extensions I: General Concepts and Extensions of ℤ and ℚ

9 Quadratic Extensions II: Complex Numbers, ℂ

10 Yet More Number Systems

11 Where Do We Go from Here?

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