Khan academy for abstract algebra

Solution 1:

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

Best you can get i would say! Hope that helps

Solution 2:

Youtube Link MathDoctorBob

This was helpful, he has examples and proves basic theorems. Right now he is up to Galois Theory.

Solution 3:

In case someone stumbles upon this question looking for a really nice introduction to the topics of abstract algebra, Check out the three playlists about group , field and ring theory from ben garside.

https://www.youtube.com/channel/UCu5cg_Jd9XSJL_CHUskgkGw/playlists

Solution 4:

Dr. Gross's lectures are very complete. He also reviews his exams which he acknowledges were too difficult. In his review of the second exam, one of the questions deal with a homomorphism phi from a group where|G|>N! to a group of order N! must have a kernel.He goes on to say there must be mappings of distinct g and g' in G such that map to the same element in G'. Then he says "so that g.(g')^-1 is in the kernel." Why you might ask, as I did. Well since g=g'.Multiply both sides by (g')^-1 and you'll get the right hand side equal e'9the identity in G' and the left is g.(g')^-1 , an element that's in G mapping to the identity so it's in the kernel. I sat for few hours figuring that out the kicked myself. His test contain very tough problems. the remarkable thing about the second exam was that a third of the class got 100+. No wonder Harvard consistently does so well on the Putnam. Speaking of the Putnam ,if you look it up on you Tube you'll see some wonder solutions to apparently tough problems such as ;prove that a triangle in the plane formed by a point(a,b) the x-axis and the line y=x has a minimum perimeter and find that number.