By John Stillwell

Algebra is summary arithmetic - allow us to make no bones approximately it - but it's also utilized arithmetic in its most sensible and purest shape. it's not abstraction for its personal sake, yet abstraction for the sake of potency, strength and perception. Algebra emerged from the fight to resolve concrete, actual difficulties in geometry, and succeeded after 2000 years of failure through different kinds of arithmetic. It did this by means of exposing the mathematical constitution of geometry, and via supplying the instruments to examine it. this is often regular of how algebra is utilized; it's the most sensible and purest kind of program since it unearths the easiest and so much common mathematical buildings. the current publication goals to foster a formal appreciation of algebra via displaying abstraction at paintings on concrete difficulties, the classical difficulties of development by way of straightedge and compass. those difficulties originated in the course of Euclid, while geometry and quantity thought have been paramount, and weren't solved till th the nineteen century, with the arrival of summary algebra. As we now comprehend, alge­ bra brings a few unification of geometry, quantity conception and certainly so much branches of arithmetic. this isn't particularly mind-blowing whilst one has a historic figuring out of the topic, which I additionally wish to impart.

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Elements of Algebra: Geometry, Numbers, Equations (Undergraduate Texts in Mathematics) by John Stillwell

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