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Table of contents:
From the reviews of the first edition: There are many books on the history of mathematics in which mathematics is subordinated to history. This is a book in which history is definitely subordinated to mathematics. It can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience...we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many. Mathematical Intelligencer The discussion is at a deep enough level that I suspect most trained mathematicians will find much that they do not know, as well as good intuitive explanations of familiar facts. The careful exposition, lightness of touch, and the absence of technicalities should make the book accessible to most senior undergraduates. American Mathematical Monthly
Contents:
The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Revival of Number Theory.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Noneuclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Sets, Logic, and Computation.- Bibliography.- Index.
Brief Description:
A collection of historical essays detailing a large variety of mathematical disciplines and issues. It includes chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. It also includes exercises as well as commentary that helps place the exercises in context.
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