I am an undergrad senior math major taking a gap year looking to become an actuary. However, I still want to continue learning pure math. I've been looking for a relatively high level text to self study for the next few months. I'm already a good chunk through the first chapter and everything is flowing nicely. However, I have not done any of the exercises. Also, there are a lot of topological examples and things not purely algebraic which I would need to review (I have access to Munkres). In the end, I want to learn a lot of math (which could possibly help with my thesis) and solve a lot of problems. For background, my algebra class sophomore year used Artin's Algebra and I have also taken a seminar on algebraic combinatorics. Are there other texts (within or outside abstract algebra) better-suited for what I'm looking for? And finally, is the Companion to Lang's a supplement/fleshing out of the material, or more of a guide to getting at the solutions?

I am an undergrad senior math major taking a gap year looking to become an actuary. However, I still want to continue learning pure math. I've been looking for a relatively high level text to self study for the next few months. I'm already a good chunk through the first chapter of Lang's "Algebra" and everything is flowing nicely. However, I have not done any of the exercises. Also, there are a lot of topological examples and things not purely algebraic which I would need to review (I have access to Munkres). In the end, I want to learn a lot of math (which could possibly help with my thesis) and solve a lot of problems. For background, my algebra class sophomore year used Artin's Algebra and I have also taken a seminar on algebraic combinatorics. Are there other texts (within or outside abstract algebra) better-suited for what I'm looking for? And finally, is the Companion to Lang's a supplement/fleshing out of the material, or more of a guide to getting at the solutions?