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Full Description
The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics.
Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian.
The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Contents
Introduction
The 17th and 18th centuries: Introduction: The 17th and 18th centuries
The invention of the calculus
Newton and Leibniz
The development of the calculus
Newtons' $\textit{Principia Mathematica}$
The spread of the calculus
The 18th century
18th-century number theory and geometry
Euler, Lagrange, and 18th-century calculus
18th-century applied mathematics
18th-century celestial mechanics
The 19th century: Introduction: The 19th century
The profession of mathematics
Non-Euclidean geometry
Projective geometry and the axiomatisation of mathematics
The rigorisation of analysis
The foundations of mathematics
Algebra and number theory
Group theory
Applied mathematics
Poincare and celestial mechanics
Coda
Exercises
References
Index
