Graduate School Mathematics Preperation

[JordanGo]

Here is my situation:
I am currently finishing my undergraduate physics program and thinking of doing graduate studies. My only concern is that the knowledge of mathematics is fairly weak. My program offers little mathematics, its very general physica. I am interested in doing theoretical physics in the domain of cosmology, quantum mechanics or particle physics (something to that effect). As I am aware, these subjects are heavily based on mathematics.
Here is my question:
I have a good long break coming up and was hoping to get some studying done. Can someone give me a list of mathematical topics/applications I may want to study to enhance my skills in the mathematical side of physics?

 

[Hercuflea]

https://www.amazon.com/dp/0521797071/?tag=pfamazon01-20

 

[ahsanxr]

It depends on what you've already studied. I'll give you reference(s) that covers the material at each level and then you can look at each and fill up the gaps in your knowledge according to that:

Beginning-mid undergrad level:

I would say after the first two or three years of undergrad, most people should be familiar with the topics found in Mary Boas' book:

https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

I haven't read the book myself but it seems like a decent book that covers material beyond calculus.

Advanced undergrad/beginning grad:

Two excellent references are Hassani's "Mathematical Physics: A Modern Introduction to its Foundations" and Stone and Goldbart's "Mathematics for Physics: A guided tour for graduate students".

https://www.amazon.com/dp/0387985794/?tag=pfamazon01-20
https://www.amazon.com/dp/0521854032/?tag=pfamazon01-20

The first one has a pretty good exposition of each topic and is mathematically precise. It states, defines and sometimes proves things clearly. The latter is a somewhat more "down-and-dirty" approach. It can be a bit mathematically sloppy at times but the challenging problems in every chapter (only 10-15 of them, so quality over quantity) make up for it.

Advanced grad/research level:

Nakahara's "Geometry, Topology and Physics". Haven't read a lot of this, but it looks like a good overview of differential geometry, algebraic topology, complex manifolds etc.

 

[JordanGo]

These are great suggestions! Exactly what I was looking for. Thanks so much for your awesome replies!

 

[ahsanxr]

These are great suggestions! Exactly what I was looking for. Thanks so much for your awesome replies!

The book Hercuflea posted is geared towards people who want to graduate school in math, so I wouldn't necessarily start with that. Of course, it's all stuff you're going to have to learn at some point or the other if you want to do theory, but right now you should be learning the topics found in the books I posted.