Hello all, I'm currently planning to apply to Cambridge Math Part III. My questions: (1) What should I do to improve my chance to be admitted? (Basic information attached below) (2) How helpful would this program be for application to PhD programs? (I'm aiming for top US programs, you know, Princeton, Harvard, etc.) (3) Is it a good idea to graduate in three years and go to Cambridge before applying for PhD programs? Basic Information: UC Berkeley sophomore: physics and pure math double major Overall GPA: 3.95 Math GPA: 4.00 (with multiple A+, but our school count A+ as 4.00) Physics GPA: 4.00 (with almost all A+) Brief list of relevant courses I have taken so far: (1) Math: (Apart from lower-division undergraduate classes) two classes in analysis (real and complex), one in linear algebra, two in abstract algebra, one in topology (graduate), one in general algebraic structures (graduate), one in probability (2) Physics: (Apart from lower-division undergraduate classes) two in classical mechanics (one of them graduate class), three in quantum mechanics (actually skipped one of them by convincing the dean, and another is a graduate class), one in thermodynamics, two in electrodynamics (one of them graduate class) Classes that I would take before the end of junior year: another class in topology, a class in differential geometry, a class in stochastic process, a class in general relativity, a class in elementary quantum field. I know it's a bit long for one single thread, but I really really want to assess my chance of being admitted. I really love Cambridge, since I have visited there as a tourist. And needless to say, I am extremely dedicated to studying theoretical physics. (In advance) Thank you all for helping!!!