Is there a course in Mauritius that is USA recognised?

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Try UTM/UOM. Basically for any degree/Dip you have you need to pass tests to enter an American University.

The better choice would be to see what institutions does Britain accept. There's a great chance that America too would accept it. Try the MIE at reduit as I've found that it offers Distance Learning.

But, if you have the money, going to America to study would remain the best choice.

Universities in the United States of America require that you sit the following exams:

TOEFL - Test of English as a Foreign Language

SAT - a test of critical reading, mathematics, writing

SAT Subject Tests – tests measuring knowledge or skills in a particular subject or ability to apply that knowledge.

Contact the TEC and ask them which institutions in Mauritius have sent more students to America.

For the Air Hostess course, you can check FlyMates which is an approved IATA training centre. The certificate is internationally recognised which means you won't have any problems in the USA or elsewhere in the world.

For the Health & Safety course, I'm not too sure because different countries have different rules and regulations in that respect. So it would be difficult in my opinion to offer a specific USA approved course when you're currently residing in Mauritius and dealing with its local laws.

Seems that you've already chosen your country. So it might be a good idea to find out which jobs are mostly in demand in the USA first, then try to acquire the qualifications for them. A working visa is difficult to get when trying your luck abroad but like people have suggested to you, studying in the country first makes this process easier.