I am a 25 year old high school teacher who wishes to further his understanding of physics to a point where some recent papers on theoretical physics can be read and understood. I graduated with a mathematics degree around 4 years ago and regards myself as fairly talented and able with mathematics, but have unfortunately not spent much time on it in the past few years so am very rusty. I have recently read many popular qualitative accounts of theoretical physics (Lee Smolin, Hawking etc) and wish to properly understand and study some topics, in particular to be able to understand recent attempts at unification (string theory, quantum gravity etc). I have a reasonable knowledge on the following areas of mathematics that could be brushed up fairly quickly: Linear Algebra (pretty comprehensive), Group Thoery (up to Sylow's thoerems), Multi-variable calculus (Green/Stokes theorems), lots of real and complex analysis (spent much of my degree on this), some algebra (simple theorems on fields, rings etc), a little knowledge on differentiable manifolds, early undergrad physics (special relativity, newton's laws, basic quantum mechanics). I skipped a lot of learning about differential equations, perhaps I shall regret that now... I would really like to have a good working knowledge of: General relativity Quantum mechanics The standard model. I would really appreciate advice on the main areas of maths I should learn/brush up on and also which areas other areas of physics I sure explore to help with the above three topics. How would experienced physicists here approach this if they were in my position? Rush to the frontier of the subject and hopefully fill in the blanks later or a slower more careful approach? My aim is to spend around 15-20 hours per week on average, and to be around the stage of a beginning postgrad physics student in a couple of years.