Welcome to Professor Holdener's
Abstract Algebra II Webpage!

Section: Math 435-00

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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Dec. 30, 2001