Prof Benedict Gross is one of the best Algebra professors I have seen – he can explain so well the abstract concepts, without injecting fear and confusion to the students.
As Prof Gross had brilliantly said in the beginning of this Lecture 1:
Algebra is the language of Math.
Since Math is the language of science,
therefore any serious Science needs to speak in Algebra language.
Today, if you read a research paper on any math (or Computer Science, Mathematical Physics…) topic, hardly you can avoid these “basic” algebraic lingoes: Group, Ring, Field, Vector Spaces, Quotient Group, Ideal, …
I strongly recommend to anyone who likes to study Modern Algebra but afraid of the abstractness, this is the course (free) for you. I can guarantee you by the halfway (15th lecture) you will have a solid foundation, and by the last lecture you will be able to follow high-level math lectures — because you understand the language of Math.
Bon courage ! 加油
(Go to YouTube to follow the whole series of lectures by Prof Gross; or check Harvard Online website to download the videos and lecture notes.)
Note: Spend one of two nights per week of 1.5 hours to attend the lectures. You can complete the whole course in 6 months.