This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation.
The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.
Enrique A. Gonzalez-Velasco is a professor of mathematics at the University of Massachusetts at Lowell. His specialty is the history of math. He has also published a textbook on Fourier analysis and boundary value problems with a historical focus.
Preface.- 1 TRIGONOMETRY.- 1.1 The Hellenic Period.- 1.2 Ptolemy's Table of Chords.- 1.3 The Indian Contribution.- 1.4 Trigonometry in the IslamicWorld.- 1.5 Trigonometry in Europe.- 1.6 From Viete to Pitiscus.- 2 LOGARITHMS.- 2.1 Napier's First Three Tables.- 2.2 Napier's Logarithms.- 2.3 Briggs' Logarithms.- 2.4 Hyperbolic Logarithms.- 2.5 Newton's Binomial Series.- 2.6 The Logarithm According to Euler.- 3 COMPLEX NUMBERS.- 3.1 The Depressed Cubic.- 3.2 Cardano's Contribution.- 3.3 The Birth of Complex Numbers.- 3.4 Higher-Order Roots of Complex Numbers.- 3.5 The Logarithms of Complex Numbers.- 3.6 CasparWessel's Breakthrough.- 3.7 Gauss and Hamilton Have the FinalWord.- 4 INFINITE SERIES.- 4.1 The Origins.- 4.2 The Summation of Series.- 4.3 The Expansion of Functions.- 4.4 The Taylor and Maclaurin Series.- 5 THE CALCULUS.- 5.1 The Origins.- 5.2 Fermat's Method of Maxima and Minima.- 5.3 Fermat's Treatise on Quadratures.- 5.4 Gregory's Contributions.- 5.5 Barrow's Geometric Calculus.- 5.6 From Tangents to Quadratures.- 5.7 Newton's Method of Infinite Series.- 5.8 Newton's Method of Fluxions.- 5.9 Was Newton's Tangent Method Original?.- 5.10 Newton's First and Last Ratios.- 5.11 Newton's Last Version of the Calculus.- 5.12 Leibniz' Calculus: 1673-1675.- 5.13 Leibniz' Calculus: 1676-1680.- 5.14 The Arithmetical Quadrature.- 5.15 Leibniz' Publications.- 5.16 The Aftermath.- 6 CONVERGENCE.- 6.1 To the Limit.- 6.2 The Vibrating String MakesWaves.- 6.3 Fourier Puts on the Heat.- 6.4 The Convergence of Series.- 6.5 The Difference Quotient.- 6.6 The Derivative.- 6.7 Cauchy's Integral Calculus.- 6.8 Uniform Convergence.- BIBLIOGRAPHY.- Index