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Taming the unknown: history of algebra from antiquity to the early twentieth century
Author
Publisher
Princeton University Press
Publication Date
[2014]
Language
English
Description
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Table of Contents
From the Book
Acknowledgments
1. Prelude: What is Algebra?
Why This Book?
Setting and Examining the Historical Parameters
The Task at Hand
2. Egypt and Mesopotamia
Proportions in Egypt
Geometrical Algebra in Mesopotamia
3. The Ancient Greek World
Geometrical Algebra in Euclid's Elements and Data
Geometrical Algebra in Apollonius's Conics
Archimedes and the Solution of a Cubic Equation
4. Later Alexandrian Developments
Diophantine Preliminaries
A Sampling from the Arithmetica: the First Three Greek Books
A Sampling from the Arithmetica: the Arabic Books
A Sampling from the Arithmetica: the Remaining Greek Books
The Reception and Transmission of the Arithmetica
5. Algebraic Thought in Ancient and Medieval China
Proportion and Linear Equations
Polynomial Equations
Indeterminate Analysis
The Chinese Remainder Problem
6. Algebraic Thought in Medieval India
Proportions and Linear Equations
Quadratic Equations
Indeterminte Equations
Linear Congruences and the Pulverizer
The Pell Equation
Sums of Series
7. Algebraic Thought in Medieval Islam
Quadratic Equations
Indeterminate Equations
The Algebra of Polynomials
The Solution of Cubic Equations
8. Transmission, Transplantation, and Diffusion in the Latin West
The Transplantation of Algebraic Thought in the Thirteenth Century
The Diffusion of Algebraic Thought on the Italian Peninsula and Its Environs from the Thirteenth Through the Fifteenth Centuries
The Diffusion of Algebraic Thought and the Development of Algebraic Notation outside of Italy
9. The Growth of Algebraic Thought in Sixteenth-Century Europe
Solutions of General Cubics and Quartics
Toward Algebra as a General Problem-Solving Technique
10. From Analytic Geometry to the Fundamental Theorem of Algebra
Thomas Harriot and the Structure of Equations
Pierre de Fermat and the Introduction to Plane and Solid Loci
Albert Girard and the Fundamental Theorem of Algebra
René Descartes and the Geometry
Johann Hudde and Jan de Witt, Two Commentators on the Geometry
Isaac Newton and the Arithmetica universalis
Colin Maclaurin's Treatise of Algebra
Leonhard Euler and the Fundamental Theorem of Algebra
11. Finding the Roots of Algebraic Equations
The Eighteenth-Century Quest to Solve Higher-Order Equations Algebraically
The Theory of Permutations
Determining Solvable Equations
The Work of Galois and Its Reception
The Many Roots of Group Theory
The Abstract Notion of a Group
12. Understanding Polynomial Equations in n Unknowns
Solving Systems of Linear Equations in n Unknowns
Linearly Transforming Homogeneous Polynomials in n Unknown: Three Contexts
The Evolution of a Theory of Matrices and Linear Transformations
The Evolution of a Theory of Invariants
13. Understanding the Properties of "Numbers"
New Kinds of "Complex" Numbers
New Arithmetics for New "Complex" Numbers
What is Algebra?: the British Debate
An "Algebra" of Vectors
A Theory of Algebras, Plural
14. The Emergence of Modern Algebra
Realizing New Algebraic Structures Axiomatically
The Structural Approach to Algebra
References
Index
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More Details
Contributors
Parshall, Karen Hunger,1955- author
ISBN
9780691149059
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