Synopses & Reviews
"This book presents a concise unified view of mathematics and its historical development. It is aimed at senior undergraduates - or other mathematicians - who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole. Reasons for the emergence of the main fields of modern mathematics are identified, and connections between them are explained, by tracing the course of a few mathematical themes from ancient times down to the 20th century. The emphasis is on history as a method for unifying and motivating mathematics, rather than as an end in iteself, and there is more mathematical detail than in other general histories. No historical expertise is assumed, and classical mathematics is rephrased in modern terms whenever it seems desirable. Nevertheless, there are copious references to original sources, and readers wishing to explore the classics for themselves will find it a useful guide. An advantage of the unified approach is that it ties up loose ends and fills gaps in the standard undergraudate curriculum. Thus, readers can expect to add to their mathematical knowledge as well as gaining a new perspective on what they already know."
Review
"The author presents the mathematics of the past in modern notation and explains it by using modern concepts and results. This has the risk that the students obtain a biased impression of the content and form of classical sources. On the other hand this presentation makes it much easier to grasp the main ideas. This book is highly recommended as the basis for courses, especially for students who want to become teachers at secondary schools. MATHEMATICAL REVIEWS"
Description
Includes bibliographical references (p. [333]-362) and index.
Table of Contents
1 The Theorem of Pythagoras
2 Greek Geometry
3 Greek Number Theory
4 Infinity in Greek Mathematics
5 Polynomial Equations
6 Analytic Geometry
7 Projective Geometry
8 Calculus
9 Infinite Series
10 The Revival of Number Theory
11 Elliptic Functions
12 Mechanics
13 Complex Numbers in Algebra
14 Complex Numbers and Curves
15 Complex Numbers and Functions
16 Differntial Geometry
17 Noneuclidean Geometry
18 Group Theory
19 Topology
20 Sets, Logic, and Computation