New PDF release: Elements of Algebra: Geometry, Numbers, Equations

By John Stillwell

Algebra is summary arithmetic - allow us to make no bones approximately it - but it's also utilized arithmetic in its top and purest shape. it's not abstraction for its personal sake, yet abstraction for the sake of potency, energy and perception. Algebra emerged from the fight to unravel concrete, actual difficulties in geometry, and succeeded after 2000 years of failure by way of different kinds of arithmetic. It did this by means of exposing the mathematical constitution of geometry, and via delivering the instruments to examine it. this is often common of ways algebra is utilized; it's the top and purest kind of program since it unearths the best and such a lot common mathematical buildings. the current ebook goals to foster a formal appreciation of algebra via exhibiting abstraction at paintings on concrete difficulties, the classical difficulties of building 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 until eventually th the nineteen century, with the arrival of summary algebra. As we now comprehend, alge­ bra brings a few unification of geometry, quantity concept and certainly such a lot branches of arithmetic. this isn't quite spectacular while one has a ancient 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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