This book, Foundations of Constructive Analysis, founded the field of constructive analysis because it proved most of the important theorems in real analysis by constructive methods. The author, Errett Albert Bishop, born July 10, 1928, was an American mathematician known for his work on analysis. In the later part of his life Bishop was seen as the leading mathematician in the area of Constructive mathematics. From 1965 until his death, he was professor at the University of California at San Diego.

Importance.--Expression.--Understanding.--Perspective.--Forms of process.--Civilized universe.--Nature lifeless.--Nature alive.--The aim of philosophy.

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

Suitable for advanced undergraduates and graduate students from diverse fields and varying backgrounds, this self-contained course in mathematical logic features numerous exercises that vary in difficulty. The author is a Professor of Mathematics at the University of Wisconsin.

Introduction I. The Aim: Defining Whitehead's Categories of Existence Ontology is the study of being or beings. But what is being? Which are the beings? ...

Order and Organism shows how Alfred North Whitehead's thought can reconcile some of the most insistent demands of common sense with the esoteric results of modern physics and mathematics.