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.
Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application.
This book was written in an attempt to make available an introductory treatment of the foundations of mathematics and of concepts that are basic to mathematical knowledge.
This book provides an introduction to axiomatic set theory and descriptive set theory.
Introduction to the Foundations of Mathematics
The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics.
This series of books, Mathematics and Its Applications, is devoted to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathematical and/or scientific specialized areas; ...
This book provides an introduction to mathematical logic and the foundations of mathematics.
This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level.
An introductory guide for pre-service primary teachers covering the principles of effective pedagogy and explaining the core content of the primary mathematics curriculum.