I am currently pursuing a Bachelor+Master program in mathematics and physics. While the material is very interesting, I feel it sometimes is lacking in the mathematical rigour necessary for Phd studies in mathematics.
A while ago, I discovered the one-year Master program (part III of the tripos) in mathematics at Cambridge University, and it seemed to feature a lot of highly interesting material. I think it would be a nice complement to my current program, and I am very interested in taking the course.
My only concern is, that at the time of graduating from my current program, I will be 26 years old. Would this be much too old for taking the part III course, and also, would I, upon (hopefully) completing the course, be too old for pursuing a Phd at a good university?