Learn Hardcore Romanian: Cursul de matematică este mai dificil decât alte cursuri. - The math class is more difficult than other classes.

Curs de matematică = a math course / math course (in general)
Cursul de matematică = the math course (a specific one already known from context)

In your sentence, we are talking about a specific course that both speaker and listener know, so Romanian uses cursul (with the definite article -ul stuck to the noun).

What does „de” mean in „cursul de matematică” and why is it used?

„de” literally means „of” and is used to show what kind of course it is.

curs de matematică = course of mathematics = math course
curs de istorie = history course
curs de engleză = English course

This is a very common pattern in Romanian:
curs de + [subject] to mean course in [subject].

Why is it „matematică” without any article (no „matematica”, „o matematică”, etc.)?

Here „matematică” is the name of a school subject / field of study, used in a general, abstract sense, not as a countable thing.

After „curs de …”, the subject is normally bare (no article):
- curs de matematică
- curs de chimie
- curs de literatură

Using „matematica” (with the definite article) would usually refer to mathematics as a field in a more specific or contrastive way, not just as the label of a course in this structure. So here the natural form is just „matematică”.

Why is the adjective „dificil” and not „dificilă”?

Adjectives in Romanian agree with the gender and number of the noun.

cursul is masculine singular
the adjective for masculine singular is dificil
the feminine singular form would be dificilă
the plural form (for both genders) is usually dificili / dificile, depending on context

So:

cursul este dificil (masc. sg.)
materia este dificilă (fem. sg.)
cursurile sunt dificile (plural)

In your sentence, „cursul (de matematică)” is masculine singular, so „dificil” is correct:
Cursul de matematică este mai dificil…

What does „mai dificil” mean exactly, and how does comparison work here?

„mai” is the usual word for forming the comparative of superiority (more… in English).

dificil = difficult
mai dificil = more difficult

So the pattern is:

mai + adjective = more + adjective
- mai mare = bigger
- mai bun = better
- mai interesant = more interesting

In your sentence:
este mai dificil = is more difficult.

Why do we use „decât” after „mai dificil”? Can we use something like „ca” instead?

In Romanian, the standard pattern for saying “more … than …” is:

mai + adjective + decât + [thing you compare to]

So:

mai dificil decât alte cursuri = more difficult than other courses
mai mare decât tine = bigger than you
mai interesant decât filmul = more interesting than the movie

You cannot use „ca” in this pattern.
„ca” appears in other types of comparisons, for example:

la fel de dificil ca = as difficult as
este ca tine = he / she is like you

But for “more … than …”, you must use „decât”.

What does „alte cursuri” mean exactly, and why is it „alte” instead of „alt”?

alt = other / another (masculine singular)
altă = other (feminine singular)
alți / alte = other (plural, agreeing with the noun)

„cursuri” is plural, so you need the plural form of the adjective:

alte cursuri = other courses
alți profesori = other teachers (masc.)
alte materii = other subjects (fem. or neuter plural)

Using „alt cursuri” would be grammatically wrong; the adjective must agree in number and (grammatical) gender with the noun.

Why is it „alte cursuri” and not „celelalte cursuri”? Is there a difference?

Yes, there is a nuance:

alte cursuri = other courses (unspecified; just “different from this one”)
celelalte cursuri = the other courses (a specific set of “the rest of them”)

Your sentence:

Cursul de matematică este mai dificil decât alte cursuri.

means:

The math course is more difficult than other courses (in general / some other ones).

If you said:

Cursul de matematică este mai dificil decât celelalte cursuri.

that would mean:

The math course is more difficult than the other courses (all the rest in a known group).

So „alte” is intentionally more general here.

Why is the plural of „curs” written „cursuri” and not something like „cursi” or „curse”?

„curs” is a neuter noun in Romanian.

Neuter nouns behave like this:

singular: like masculine
plural: like feminine

For many neuter nouns ending in a consonant, the plural is formed with -uri:

un curs → două cursuri
un oraș → două orașe (different ending, same idea of a special plural form)
un exercițiu → două exerciții

So „cursuri” is the regular plural form for „curs”.

Can the word order be changed? For example, can I say „Este cursul de matematică mai dificil decât alte cursuri?” or put „mai dificil” somewhere else?

Yes, word order is fairly flexible for questions and for emphasis.

Statement (neutral):
Cursul de matematică este mai dificil decât alte cursuri.
Yes/no question:
Este cursul de matematică mai dificil decât alte cursuri?
(Is the math course more difficult than other courses?)

Inside the predicate, you generally keep the order:

este mai dificil (verb + „mai” + adjective)

You would not split „mai” from „dificil” or put something in between them.
So forms like „este mai mult dificil” (in this context) would be wrong; the comparative is simply „mai dificil”.