Unknown Quantity A Real and Imaginary History of Algebra First Edition by John Derbyshire ISBN 030909657X 978-0309096577

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Product details: 

ISBN 10: 030909657X 

ISBN 13: 978-0309096577

Author: John Derbyshire

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages—and it promises to be just what his die-hard fans have been waiting for. “Here is the story of algebra.” With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel’s proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics—it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

Table of contents: 

Part 1
The Unknown Quantity

Four Thousand Years Ago

The Father of Algebra

Completion and Reduction
Math Primer: Cubic and Quartic Equations

Commerce and Competition

Relief for the Imagination

Part 2
Universal Arithmetic

The Lion’s Claw
Math Primer: Roots of Unity

The Assault on the Quintic
Math Primer: Vector Spaces and Algebras

The Leap into the Fourth Dimension

Part 3
Levels of Abstraction

Math Primer: Field Theory

An Oblong Arrangement of Terms

Victoria’s Brumous Isles

Pistols at Dawn

Lady of the Rings
Math Primer: Algebraic Geometry

Geometry Makes a Comeback

Algebraic This, Algebraic That

From Universal Arithmetic to Universal Algebra

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Tags: John Derbyshire, Unknown Quantity, A Real, Imaginary History