| What is Abstract Algebra? As the
name indicates, Abstract Algebra involves the study of algebraic equations and the methods used to solve them.
The abstraction refers to the perspective taken in the subject, which is very different from that of high school
algebra courses. Rather than looking for the solutions to a particular problem, we will be interested in such questions
as: When does a solution exist? If a solution does exist, is it unique? What general properties does a solution
possess? Our exploration will go beyond such algebraic structures as the integers and the rationals, and our approach
will be axiomatic. Indeed, working from a fairly small set of axioms one can describe the properties of a wide
range of algebraic structures concisely and elegantly. Focusing on group theory, our study will be motivated by
the desire to describe algebraic structures in a rigorous, concise, and elegant way. As an added bonus, group theory
will also allow us to quantify the various types of symmetries so prevalent in the world around us. |
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