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An Introduction to the History of Algebra: Solving Equations from Mesopotamian Times to the Renaissance (Mathematical World) (Mathematical World, 27)

by Jacques Sesiano (Author)
5.0 5.0 out of 5 stars 6 ratings
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This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. Various examples of problems, with their typical solution methods, are analyzed, and sometimes translated completely. Indeed, it is another aim of this book to ease the reader's access to modern editions of old mathematical texts, or even to the original texts; to this end, some of the problems discussed in the text have been reproduced in the appendices in their original language (Greek, Latin, Arabic, Hebrew, French, German, Provençal, and Italian) with explicative notes.
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  1. ISBN-10
    0821844733
  2. ISBN-13
    978-0821844731
  3. Publisher
    American Mathematical Society
  4. Publication date
    July 9, 2009
  5. Part of series
    Mathematical World
  6. Language
    English
  7. Dimensions
    7 x 0.5 x 9.75 inches
  8. Print length
    174 pages
  9. See all details
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Editorial Reviews

Review

... a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts. ----Warren Van Egmond about the French edition for MathSciNet

Highly Recommended. ---- CHOICE Magazine

Product details

  • Publisher ‏ : ‎ American Mathematical Society (July 9, 2009)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 174 pages
  • ISBN-10 ‏ : ‎ 0821844733
  • ISBN-13 ‏ : ‎ 978-0821844731
  • Item Weight ‏ : ‎ 12.2 ounces
  • Dimensions ‏ : ‎ 7 x 0.5 x 9.75 inches
  • Customer Reviews:
    5.0 5.0 out of 5 stars 6 ratings

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Jacques Sesiano

Jacques Sesiano

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5 out of 5 stars
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Top review from the United States

Sam Adams
5.0 out of 5 stars An Introduction to the History of Algebra
Reviewed in the United States on January 7, 2013
Sesiano discusses and gives examples of solution methods in algebra from Ancient Mesopotamia to Renaissance Italy. Appendices include samples of original language texts in Greek, Latin, Arabic, Hebrew, French, German, Italian, and Provencal.

This is not a comprehensive look at the developments in algebra during this period, nor is there any attempt to place algebra within the larger history of mathematics. What the book offers is an opportunity to see examples of how algebra was done before the use of modern notation and methods. Sesiano does not, however give attention to the evolution of algebraic notation.

For a finely detailed look at the subsequent period, from Cardano to Lagrange, 1545 to 1771, with a brief glance beyond that, see Jaqueline Stedall (2011): From Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra. Of the two books, I find Stedall's book far more interesting, but Sesiano's book is worth spending some time with if you're interested in the history of algebra.

- Contents -
Preface
Chapter 1. Algebra in Mesopotamia
_ 1.1 Introduction
_ 1.2 Linear Systems
_ 1.3 Quadratic Equations and Systems
Chapter 2. Algebra in Ancient Greece
_ 2.1 Introduction
_ 2.2 Common Algebra
_ 2.3 Diophantine Algebra
Chapter 3. Algebra in the Islamic World
_3.1 Introduction
_3.2 Al-Khwarizmi
_3.3 Abu-Kamil
_3.4 The Geometric Construction of Solutions of the Quadratic Equation
_3.5 The Cubic Equation
Chapter 4. Algebra in Medieval Europe
_4.1 Introduction
_4.2 The Liber mahameleth
_4.3 Leonardo Fibonacci
_4.4 Later Developments
Chapter 5. Algebra in the Renaissance
_5.1 The Development of Algebraic Symbolism
_5.2 The Solution of the Cubic and Quartic Equations
_5.3 The Solution of the Cubic Equation in Italy
_5.4 Bombelli and Imaginary Numbers
_5.5 Casus irreducibles
Appendix A Mesopotamian Texts in Translation
Appendix B Greek and Latin Texts
Appendix C Arabic Texts
Appendix D Hebrew Text
Appendix E French, German, Italian, and Provencal Texts
Index
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