My professors are already scaring us into shifting out of Math telling us that the Abstract Algebra series will kill us all. What excatly makes this algebra 'abstrat'?
I just really disagree with that statement!
The current cohort of students, most of whom are proficient with complicated computer came, should find abstract algebra a lot of fun. One must conquer a set of very complicated rules to play most games. Well in abstract algebra we have a set of rules, they are called definitions & axioms. Then we have a set tasks to perform, they are called theorems, which are performed in accord with the definitions & axioms. A correct performing of a task is called a proof of a theorem. Abstract algebra is a great course for teaching proofs to a beginning serious student.
Now why is it called abstract algebra? I think the answer is: It is possible to teach an entire course in abstract algebra without using any of the operations seen before the course. That is, we can use abstract operations, abstract sets, and abstract applications. That having been said, most good texts/instructors will relate these abstractions to concrete structures familiar to the students; such as: real & complex numbers, set of matrices, a set or polynomials, etc.
i wasn't being completely serious. nevertheless, in my defense i shall say this: abstract math is a different animal from elementary math, and it is a difficult world to grasp for many students (even "serious" ones). do i agree with what the professors say? or even with what i said in my first post? NO! it was a poor attempt at humor.
i'm not good with things that have a lot of rules . not good at video games either
An Introduction to Abstract Algebra might be a challenge to some students who are not so good in abstract/formal proofs. But it is not that bad. Most of it is spend on learning the definitions and some basic theorems.
However, Field/Galois Theory is truly difficult. Not only is it a complete abstraction there are so many things (definitions and concepts) to know. But out of all the things I learned I think Field theory is the most beautiful area in mathematics (it has a super strong connection to number theory). But Luckily for you that is a Graduate course. The Field theory exposed in an Undergraduate course is not much difficult.