Synopses & Reviews
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics.
Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.
Synopsis
Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
Synopsis
This classic undergraduate text acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many historical figures from the 18th through the mid-20th centuries, it examines the axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and other topics. 1965 second edition.
Table of Contents
Part One: Fundamental Concepts and Methods of Mathematics I. The Axiomatic Method II. Analysis of the Axiomatic Method III Theory of Sets III Theory of Sets IV. Infinite Sets V. Well-Ordered Sets; Ordinal Numbers VI. The Linear Continuum and the Real Number System VII. Groups and Their Significance for the Foundations Part Two: Development of Various Viewpoints on Foundations VIII. The Early Developments IX. The Frege-Russell Thesis: Mathematics an Extension of Logic X. Intuitionism XI. Formal Systems; Mathematical Logic XII. The Cultural Setting of Mathematics Bibliography Index of Symbols Index of Topics and Technical Terms Index of Names