# Download PDF by John Tabak: Algebra: Sets, Symbols, and the Language of Thought (The

By John Tabak

ISBN-10: 0816079447

ISBN-13: 9780816079445

Algebra, Revised variation describes the historical past of either strands of algebraic proposal. This up to date source describes the various earliest development in algebra in addition to a few of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early interval. It is going directly to discover the numerous breakthroughs in algebraic ideas in addition to how letters have been used to symbolize numbers. New fabric has been extra to the bankruptcy on "modern" algebra, one of those mathematical examine that maintains to occupy the eye of many mathematicians this present day.

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Extra resources for Algebra: Sets, Symbols, and the Language of Thought (The History of Mathematics)

Sample text

The number 4, for example, was the number of justice and retribution. The number 1 was the number of reason.  . ) They did not recognize negative numbers, the number 0, or any type of fraction as a number. Quantities that we might describe with a fraction they would describe as a ratio between two whole numbers, and although we might not make a distinction between a ratio and a fraction, we need to recognize that they did. They only recognized ratios. To the Pythagoreans the number 1 was the generator of all numbers—by adding 1 to itself often enough they could obtain every number (or at least every number as they understood the concept).

The type of geometry described in Euclid’s textbook— now called Euclidean geometry, though it was not Euclid’s invention—dominated mathematical thought for 2,000 years. We now know that there are other kinds of geometry, but as late as 200 years ago many mathematicians and philosophers insisted that Euclidean geometry was the single true geometry of the universe. It was not until the 19th century that mathematicians began to realize that Euclidean geometry was simply one kind of geometry and that other, equally valid geometries exist.

It was not until the 19th century that mathematicians began to realize that Euclidean geometry was simply one kind of geometry and that other, equally valid geometries exist. The Elements was written in 13 brief books. Of special interest to us is the very brief book II, which lays out the foundations of geometric algebra. In book II we see how thoroughly geometric thinking pervaded all of Greek mathematics including algebra. For example, when we speak of unknowns, x, y, and z, we generally assume that these variables represent numbers.