What is abstract algebra, what are some of its applications, and what are some nice books about it?
First, a quick disclaimer. Any abstract algebra course you take will be 95% formal proof writing at the very least. Most universities will require students to take a prerequisite course, usually called something like “transition to formal mathematics” which teaches you how to construct formal proofs. You’ll want to have a firm grasp on writing proofs, especially those involving set theory. So, if you don’t have those prerequisites, you may want to consider a different math course. Abstract algebra is the study of algebraic structures, which are sets together with one or more binary operations (like addition, multiplication, function composition, matrix multiplication, etc.), usually with some additional properties. The first algebraic structure you will learn about in any abstract algebra course is a group: http://en.wikipedia.org/wiki/Group_(math… A group is a set of objects with one binary operation used to
