Unknown Quantity:: A Real and Imaginary History of Algebra

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National Academies Press, May 2, 2006 - Science - 16 pages
23 Reviews

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.

  

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Review: Unknown Quantity: A Real and Imaginary History of Algebra

User Review  - Marc Towersap - Goodreads

I did enjoy this book, a bit of a slog, maybe took 2 months to get through it. I worked through much of the math to ensure I understood it. The history was quite interesting, I really enjoyed the way ... Read full review

Review: Unknown Quantity: A Real and Imaginary History of Algebra

User Review  - Nishant Pappireddi - Goodreads

As someone who has already been exposed to many, if not most, of the ideas in this book, I was hoping that it would be more interesting to me than the usual popular math book. "Unknown Quantity ... Read full review

Contents

Numbers and Polynomials
7
The Unknown Quantity
17
Four Thousand Years Ago
19
The Father of Algebra
31
Completion and Reduction
43
Cubic and Quartic Equations
57
Commerce and Competition
65
Relief for the Imagination
81
An Oblong Arrangement of Terms
161
Victorias Brumous Isles
177
Levels of Abstraction
193
Field Theory
195
Pistols at Dawn
206
Lady of the Rings
223
Algebraic Geometry
241
Geometry Makes a Comeback
253

Universal Arithmetic
95
The Lions Claw
97
Roots of Unity
109
The Assault on the Quintic
115
Vector Spaces and Algebras
134
The Leap into the Fourth Dimension
145
Algebraic This Algebraic That
279
From Universal Arithmetic to Universal Algebra
298
Endnotes
321
Picture Credits
353
Index
355
Copyright

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About the author (2006)

Alan Beggs is a psychologist with wide experience at all levels of sporting endeavour. He is the RYA Honorary Sport Psychologist, and has worked with many of Britain's best - known Olympic and international sailors.

John Derbyshire, a former PE teacher, achieved international success as a sailor before he became an RYA Olympic coach, with responsibility for fitness.

John Whitmore has had a long and distinguished career as a racing driver and as a tennis and ski coach, and has taught many performers to master the mental demands of sport at the highest level.

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