Learn English – Using the word “the” with a university name

The naming of countries is a matter of politics and convention rather than grammar. It is no longer appropriate to say the Ukraine, for example, as the government of that country deprecates it, and some may even be insulted by it.

Ultimately, each country can declare whatever its official and short names will be in English, although it may not always stick in common usage. Holland referring to the Netherlands persisted well into the second half of the 20th century, and Burma remains Burma, perhaps in part to spite the generals who insist on Myanmar.

The article is used where

1. the name of the country includes a common noun, usually indicating the type of state; thus Russia but the Russian Federation, Britain but the UK and the United Kingdom, and the UAE and the United Arab Emirates. Naturally, the formal name of a country almost always entails the article: China but the People's Republic of China (or for stalwarts, the Republic of China), Jordan but the Hashemite Kingdom of Jordan, Gabon but the Gabonese Republic.

   There are exceptions, as always: in Ivory Coast has more than half as many examples as in the Ivory Coast, and it is Vatican City, not the Vatican City— although the latter is also known as the Holy See.

2. the name refers to a geographic or cultural region, a group of islands, or another feature or landmark: The Bahamas, The Gambia, the Comoros, the Netherlands, etc. As far as I can tell, The Gambia and The Bahamas seem to be the only countries which prefer the article always be used and always capitalized. (Among cities, we have The Hague and The Bronx, and a few others.)

The second case is where the has been dropped from many country names; the reference to the country as a region within something larger is taken by some to have colonialist overtones. Thus, what were the Lebanon [mountain], the Argentine [river], the Ukraine [=border region], and the Sudan [desert] a few decades ago are today Lebanon, Argentina, Ukraine, and Sudan properly.

Where a name is imported wholesale from another language, any article in the original language is ignored. Thus, El Salvador, not the Salvador, and likewise subnational entities like Le Havre or Los Angeles.

I have some additional questions on articles and proper nouns linked in the other thread.

Function is a count noun, and it typically appears with a determiner of some sort:

I called a function.
I called this function.
I called the function.
I called two functions.

Lots of determiners work, as you can see above.

You can add the name of the function as an attributive modifier:

I called the printf function.

And in that case, you've made it specific, so the is probably the appropriate determiner (unless you're in an unusual situation where you have more than one printf function to discuss).

But function needs a determiner, so these are ungrammatical:

*I called function.　　　　 　(ungrammatical)
*I called printf function.　(ungrammatical)

By itself, printf doesn't need a determiner. It's a proper noun:

I called printf.

This is fine too, and I think it's probably more common in speech, but I don't have a corpus to check, so that's really just a guess.

In this answer, the * symbol marks an utterance as ungrammatical.