Taming the Unknown by Parshall, Karen Hunger, Katz, Victor J. -- Read -- Imperial Library of Trantor

Index

Cover Page Title Page Copyright Page Dedication Page Contents 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

4 Later Alexandrian Developments

5 Algebraic Thought in Ancient and Medieval China

Proportions and Linear Equations Polynomial Equations Indeterminate Analysis The Chinese Remainder Problem

6 Algebraic Thought in Medieval India

Proportions and Linear Equations Quadratic Equations Indeterminate 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

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

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

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