history of algebra

I enjoyed Lewis Carroll in Numberland: His Fantastical Mathematical Life by Robin Wilson (we liked Wilson's little book on sudokus awhile back). A book review and a podcast (scroll down a bit) from +Plus magazine (more here).

Wilson presents biographical information on Carroll (really Charles Dodgson) whose upper-middle class family homeschooled with tutors. There are brief forays into mathematics. For example, Wilson gives a quick overview of the algebraic geometry of the plane and three-dimensional space along and then some of the mathematics of Dodgson's determinents and 'Method of Condensation'.

This integration of math, biography and concise explanation is a rich mix for whole learning (akin to whole foods) that preserves context, reduces the emphasis on over-processed and highly-refined literacy, and is just more fun. Wilson is witty and the book is well-illustrated. There are many mathematics puzzles and oddities. I think many learners will respond to this integrated approach, a favorite of mine.

A similar method, less complex,  is used in a straight history book on algebra by another English author, John Derbyshire, in his Unknown Quantity: A Real and Imaginary History of Algebra. Again, added to a history of algebra are math breakouts on numbers and polynomials, cubic and quartic equations, roots of unity, vector spaces and algebras, field theory, and algebraic geometry.

To the ever-vexing question, just what is algebra?, the author, in workmanlike fashion, defines it as the part of mathematics that is not calculus and moves onto a discussion of algebra as abstraction. I prefer the wikipedia definition.

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