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fall 2006 course description
fall 2006 syllabus
homework guidelines
instructions for the TI-83
study tips
Abstract algebra is the study of operations, their properties, and the structures that support them. The first operation that you ever learned (probably) was addition of natural numbers. Later you included zero and the negative numbers and started solving integer equations. Given x + 7 = 3, what is x? Abstract algebra asks a higher level question: under what conditions does a solution exist? The first algebraic structure we will study is the group: the simplest setting in which a unique solution to an equation is guaranteed.
From such a simple beginning, it is amazing to realize that algebra can address questions in logic, geometry, linear algebra, function theory, differential equations, chemistry, physics, and other fields. A knowledge of group theory can even help you solve the Rubik's Cube®! But that's why it is called abstract algebra. The same logical structure can apply to many different concrete situations. More on this wide area of study can be found in the algebra section of the Mathematical Atlas and by following the many links in Eric Weisstein's excellent article in MathWorld.
The roots of abstract algebra are found in the late 18th to 19th century, with particular (concrete) investigations into geometry, number theory, and polynomial equations. It was not realized until the second half of the 19th century that several different areas of study all fit under the same umbrella of abstract group theory. The first to take this completely abstract perspective was Arthur Cayley, in 1854. More historical information can be found at the MacTutor History of Math Archive.
fall 2006 course description
fall 2006 syllabus
homework guidelines
instructions for the TI-83
study tips
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