Pure maths for physics undergrads

[Toby_phys]

I am off to start a physics degree in September, with the aim of going into theoretical research. However, for this I feel my pure maths skills need to be better. I know in a physics degree I will learn how to use pure maths (how to solve differential equation, how to use matrices, how to use geometry) however I would also like to know some pure maths (analysis, pure algebra, pure calculus etc). What are good first year books on these topics?

 

[micromass]

https://www.physicsforums.com/threads/micromass-insights-on-how-to-self-study-mathematics.868968/