Some links and resources, Ph.D. qualifying exams
The current winner of the global AI contest is the United States. Computing power is probably the most concern among the major nations on the globe. The students, international students, can only learn something like the tip of an iceberg in most fields of study. One reason is that all nations need to keep some of the information confidential. Colleges and universities need to make profits from the students, especially international students and yet will not let them having access to any really confidential information. So a student cannot expect to get a Ph.D. degree in AI or a related field and be the most competitive in the job market. A reality is, in many good universities, CS Ph.D. students may have much stronger math backgrounds than Ph.D. students majoring in mathematics.
To be successful, a top student must know something most other people do not know, have original discoveries and keep some information, confidential. On the other hand, it is not easy to learn the many advanced theories, solve many problems that are known to the public. The percentage of people who can understand advanced "public information" is already very low, although still much higher than those a nation like the USA must depend on.
For those who are not familiar with AI, here is a link:
Competitions and prizes in artificial intelligence:
Wait! Have you passed your qualify exams yet?? If not or this does not apply to you, you can always look at the resources:
Ph.D. qualifying exams: https://math.stackexchange.com/questions/267554/phd-qualifying-exams