Foundations of Mathematical Analysis (Oxford Science Publications) by J. K. Truss (PDF)

Description

Foundations of Mathematical Analysis covers a wide variety of topics that will be of great interest to students of pure mathematics or mathematics and philosophy. Aimed principally at graduate and advanced undergraduate students, its primary goal is to discuss the fundamental number systems,N, Z, Q, R, and C, in the context of the branches of mathematics for which they form a starting point; for example, a study of the natural numbers leads on to logic (via Gödel’s theorems), and of the real numbers (as constructed by Cauchy) to metric spaces and topology. The author offers arefreshingly original and accessible approach, presenting standard material in new ways and incorporating less mainstream topics such as long real and rational lines and the p-adic numbers. With a discussion of constructivism and independence questions, including Suslin’s problem and the continuumhypothesis, the author completes a wide-ranging consideration of the development of mathematics from the very beginning, concentrating on the foundational issues particularly related to analysis.

User’s Reviews

Editorial Reviews: Review “The book can be warmly recommended to students interested to find various connections and intersection of analysis and other braches of classical mathematics and provides a very interesting second reading for virtually everyone.”–European Mathematical Society Newsletter”This book is a remarkable attempt to describe the foundations of mathematical analysis, starting with the logical development and ending with Lebesgue theory and the topology of the real line. . . . [M]any less familiar topics are included and chapters with familiar-sounding titles appear to betreated in novel ways. For instance, the first chapter about natural numbers contains a very well written sketch about coding and the Gödel theorems. . . . The chapters about the integers and the rationals are written with emphasis on their algebraic properties. This makes it possible for the authorto sketch elementary Galois theory and the proof of the fundamental theorem of algebra in his chapter about complex numbers. The three chapters about real numbers, metric spaces and the beginnings of analysis contain many interesting topics . . . The book is written in a brilliant style, perfectlyreadable for persons with some experience in mathematics.”–Mathematical Reviews About the Author John Kenneth Truss is at University of Leeds.

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