Should I take abstract algebra?

[jaejoon89]

How hard is Artin's Algebra book to understand? For a student who has not had any upper level (proof based) math classes beyond calculus, is it doable if you are sufficiently motivated?

 

[rubrix]

it's recommended (and most likely mandatory) to have some short of proof based course (even be it just an introductory course) before taking Abstract Algebra.

for basic (first course) in abstract algebra, you'll need following:

- mathematical induction (along with proof by contradiction)
- basic properties of integers: well ordering principle, division algorithm, notion of gcd, fundamental theorem of arithmetic
- understanding of
- modular mathematics
- equivalence relations (along with partition)
- functions/mapping

if you are not familiar with 1/2 of the listed above, take a introductory proof based course first.

https://www.amazon.com/dp/0521597188/?tag=pfamazon01-20 is a good book for selective self-study as well as detailed reading.

 

[jambaugh]

I suggest you take a Linear Algebra class and then Abstract Algebra. The linear algebra class has more concrete application and introduces some of the more abstract ideas such as non-commutative multiplication (AB not equal to BA). Also you'll get some experience with proofs. I'd recommend you take them back to back.