Hi! I am posting this to solicit your help in finding out if it's possible to strengthen one's math background during summer vacation.

I am a 1st year MPhil student in an European Econ department. The program itself is quite prestigious, but the problem is it provides very few pure math courses. While the university has some math courses for undergraduates, they are taught in languages other than English, which I cannot manage.

The current workload is not that demanding to me, and I am seriously considering to apply for some more challenging US PhD programs one year later. To strengthen my math background, I would like to take Real Analysis and Measure Theory. But apparently that is not available in here.

In this case, what could I do? I actually audited these courses in my undergraduate institution. But there I cannot register for that nor gain the credits. All I need now is to have the courses somewhere and have them in my transcript, making it more decent/solid for further application. That's why I am considering to have some summer program in math.

I know pretty many such programs are available in US, but I still prefer to have it in mainland or Hong Kong, if possible.

Any advice or information would be highly appreciated! Thanks for your help in advance!