Learn Hardcore Greek: Στο μάθημα ελληνικών δυσκολεύομαι όταν είμαι κουρασμένος. - In the Greek class I have difficulty when I am tired.

The ending -ομαι shows that this is a middle/passive form in Modern Greek.
Many common verbs in Greek only appear in this -ομαι form and are called “deponent” (they have passive/middle endings but active meaning).

Roughly:

δυσκολεύω = I make something difficult (transitive: I cause difficulty to someone/something)
δυσκολεύομαι = I have difficulty / I find it difficult (intransitive, about myself)

In everyday speech you will almost always see δυσκολεύομαι used to mean:

δυσκολεύομαι στο μάθημα ελληνικών = I struggle in Greek class
δυσκολεύομαι να μιλήσω ελληνικά = I find it hard to speak Greek

Where is the word “I” in this sentence? Why isn’t it written?

Greek normally omits subject pronouns (like “I”, “you”, “he”, etc.) because the verb ending already shows the subject.

δυσκολεύομαι is 1st person singular → it already means “I struggle / I have difficulty.”
So εγώ δυσκολεύομαι is grammatically fine, but in neutral sentences εγώ is usually left out unless you want to emphasize it:
- Εγώ δυσκολεύομαι στο μάθημα ελληνικών.
  = I (as opposed to others) struggle in Greek class.

In your sentence, the subject “I” is contained in the verb form δυσκολεύομαι.

What is the role of στο in Στο μάθημα ελληνικών? Why not just σε?

Στο is a contraction of the preposition σε + the definite article το:

σε + το = στο

You need σε (“in / at / to”) plus the article of the noun:

σε + το μάθημα → στο μάθημα = in/at the lesson/class

So:

σε μάθημα = in a lesson (more general, less common in this context)
στο μάθημα = in the lesson / in the class (specific)

In normal speech, when σε is followed by a definite article, it almost always contracts:

σε + το → στο
σε + τον → στον
σε + την → στη(ν)
σε + τους → στους, etc.

Here, μάθημα is neuter, so the article is το, and we get στο μάθημα.

Why is it μάθημα ελληνικών and not μάθημα ελληνικά?

Ελληνικών here is in the genitive plural, and μάθημα ελληνικών literally means “lesson of Greek (language)”.

ελληνικά (neuter plural nominative/accusative) = “Greek (language)”
ελληνικών (genitive plural) = “of Greek”

In Greek, it’s very common to use the genitive to show what something is about or of:

μάθημα ελληνικών = Greek lesson / Greek class
μάθημα μαθηματικών = math class (lesson of mathematics)
λεξικό αγγλικών = English dictionary (dictionary of English)

So μάθημα ελληνικά would be incorrect in this structure. You need ελληνικών to show “lesson of Greek”.

Is ελληνικών an adjective or a noun here?

Grammatically, ελληνικών is the genitive plural of the adjective ελληνικός, -ή, -ό (“Greek”).
But in Modern Greek, this plural form is often used as a noun meaning “Greek (language)”.

So:

τα ελληνικά = Greek (language)
των ελληνικών / ελληνικών = of Greek (language)

In μάθημα ελληνικών, it functions like a noun in the genitive, expressing what the lesson is about:

μάθημα (των) ελληνικών = lesson of Greek.

The article των is often dropped in this kind of fixed expression, so μάθημα ελληνικών is the usual phrase.

Could I also say στο μάθημα των ελληνικών? Is there any difference?

Yes, στο μάθημα των ελληνικών is grammatically correct and means the same thing: “in the Greek lesson / in Greek class.”

Difference in feel:

στο μάθημα ελληνικών – very natural, a bit more compact; this is what you’ll often hear.
στο μάθημα των ελληνικών – slightly more explicit/formal-sounding, emphasizing “the Greek (subject).”

In everyday speech, στο μάθημα ελληνικών is more common, but both are fine.

What exactly does κουρασμένος mean, and why does it look like an adjective?

Κουρασμένος means “tired”.

It is the masculine singular form of an adjectival participle from the verb κουράζομαι (“I get tired / I get exhausted”).
Forms:
- κουρασμένος (masc. sing.)
- κουρασμένη (fem. sing.)
- κουρασμένο (neut. sing.)

In your sentence:

όταν είμαι κουρασμένος = when I am tired

It behaves just like a normal adjective:

Είμαι κουρασμένος. (masculine speaker)
Είμαι κουρασμένη. (female speaker)
Τα παιδιά είναι κουρασμένα. (the children are tired)

Why is it κουρασμένος and not κουρασμένη or κουρασμένο?

The adjective must agree with the gender, number, and case of the subject.

Here, the subject is “I” (implicit εγώ), and the sentence seems to assume a male speaker, so:

Masculine 1sg: κουρασμένος
If the speaker is female, it should be:
- Στο μάθημα ελληνικών δυσκολεύομαι όταν είμαι κουρασμένη.

So:

masculine “I” → είμαι κουρασμένος
feminine “I” → είμαι κουρασμένη
neuter/abstract subject → είναι κουρασμένο

Can I drop είμαι and say όταν κουρασμένος?

No, in standard Modern Greek you cannot drop είμαι here.

You must say:

όταν είμαι κουρασμένος = when I am tired

Possible alternatives:

όταν κουράζομαι = when I get tired / when I become tired
όταν αισθάνομαι κουρασμένος = when I feel tired

But you can’t say όταν κουρασμένος by itself. Greek requires either a form of “to be” (είμαι) or a full verb to connect to the adjective.

Is the word order fixed? Could I say Δυσκολεύομαι στο μάθημα ελληνικών όταν είμαι κουρασμένος?

The word order is flexible in Greek, and your alternative is perfectly natural:

Στο μάθημα ελληνικών δυσκολεύομαι όταν είμαι κουρασμένος.
Δυσκολεύομαι στο μάθημα ελληνικών όταν είμαι κουρασμένος.

Both mean the same thing. The differences are just slight shifts in emphasis:

Starting with Στο μάθημα ελληνικών emphasizes the place / context (“In Greek class…”).
Starting with Δυσκολεύομαι emphasizes the difficulty/struggle.

All of these are acceptable:

Όταν είμαι κουρασμένος, δυσκολεύομαι στο μάθημα ελληνικών.
Δυσκολεύομαι, όταν είμαι κουρασμένος, στο μάθημα ελληνικών. (more marked, added emphasis)

Could I say Έχω δυσκολία στο μάθημα ελληνικών instead of δυσκολεύομαι? Is there a difference?

Yes, you can say:

Έχω δυσκολία στο μάθημα ελληνικών όταν είμαι κουρασμένος.
= I have difficulty in Greek class when I’m tired.

Both δυσκολεύομαι and έχω δυσκολία are correct, but:

δυσκολεύομαι is more natural and common in everyday speech.
έχω δυσκολία sounds slightly more formal or “bookish”, and is often used with a more precise object:
- Έχω δυσκολία στην προφορά. = I have difficulty with pronunciation.
- Έχω δυσκολία στην κατανόηση κειμένων. = I have difficulty understanding texts.

For a general “I struggle in class”, δυσκολεύομαι στο μάθημα ελληνικών is the most natural choice.

What tense is δυσκολεύομαι, and does it describe a habit?

Δυσκολεύομαι is present tense, 1st person singular.

In Greek, the present tense can express:

Right now:
- Τώρα δυσκολεύομαι στο μάθημα. = Right now I’m struggling in class.
Habitual / general truth, which is what your sentence does:
- Στο μάθημα ελληνικών δυσκολεύομαι όταν είμαι κουρασμένος.
  = In Greek class I (tend to) struggle when I’m tired.

So yes, here it describes a repeated or typical situation, not just a one-time event.

How do you pronounce δυσκολεύομαι and where is the stress?

δυσκολεύομαι has 5 syllables:
δυ-σκο-λέ-vo-μαι

The stress is on the second-to-last syllable: -λεύ-
Rough pronunciation (Latin letters): this-ko-LÉ-vo-me

Breakdown:

δυς- (dis-) like “this” but with a softer “th/d” (actually “th” as in “this” is close)
-κο- like “ko” in “coffee”
-λεύ-: “LEV” (ε like “e” in “get”)
-ο- “o” as in “not”
-μαι like “me” but with a short “e” (meh)

The key is to keep the stress on -λεύ-: δυσκολεύομαι.

What exactly does μάθημα mean here: “lesson”, “class”, or “course”?

Μάθημα can correspond to several English words, depending on context:

a single class session / lesson
- Έχουμε μάθημα στις 9. = We have class at 9.
a subject (school subject)
- Το αγαπημένο μου μάθημα είναι τα ελληνικά. = My favorite subject is Greek.
a course (in some contexts)
- Παρακολουθώ ένα μάθημα ελληνικών. = I’m taking a Greek course.

In Στο μάθημα ελληνικών δυσκολεύομαι όταν είμαι κουρασμένος, it most naturally means:

“In Greek class / in the Greek lesson” (the actual class time / class environment).