Truss J.K. Foundations of Mathematical Analysis

Oxford University Press, 1997. - 368 Pages.Foundations of Analysis covers a variety of issues that will interest undergraduates and first-year graduate students studying pure mathematics and philosophy. It covers the development of different number systems and how their consideration leads to specific branches of mathematics.From Preface:Many branches of mathematics originate in questions about the fundamental number systems of mathematical analysis. This book will examine the construction of these number systems in the context of the areas of mathematics for which they provide a starting point. Arising out of this I shall describe a number of central topics in or connected with analysis, particularly from a foundational angle. Many of these questions have important implications for the philosophy of mathematics, such as the concept of "number" itself, problems of categoricity in axiom systems for the real and natural numbers, consistency and completeness, and the nature of proofs suitable for their discussion. The main emphasis, however, will lie in the algebra, analysis, and topology which arise. Inevitably, a survey of such a wide field can only make cursory mention of many topics of great interest. I hope, however, that my exposition will throw them into a new perspective, give pointers to their further development, and encourage readers to follow up topics which they find of particular appeal.