Learn Hardcore German: Am Schluss der Vorlesung stellt die Dozentin unsere Hausarbeit vor. - At the end of the lecture the lecturer presents our term paper.

am Schluss literally = an dem Schluss (at the end)
It’s the idiomatic way to say at the end (of something).
im Schluss is not idiomatic and would sound wrong in this context.
You can also say am Ende (at the end); am Schluss and am Ende are very close in meaning.
- am Schluss often sounds a bit more like “finally / in the final part”
- am Ende is more neutral “at the end”

You cannot normally drop the preposition and just say Schluss der Vorlesung stellt die Dozentin …; you need am (or zum, am Ende, etc.).

What case is used in Am Schluss der Vorlesung, and why?

There are actually two things going on:

am Schluss
- am = an + dem → dative case
- Schluss is masculine, so dative singular: dem Schluss → contracts to am Schluss.
  This is a time expression: “at the end”.
der Vorlesung
- This is genitive singular of die Vorlesung (feminine).
- Pattern: der Schluss der Vorlesung = “the end of the lecture”.

So, structurally:

am Schluss → dative (fixed time expression)
der Vorlesung → genitive, showing “of the lecture”

Fun complication: der Vorlesung looks the same in dative and genitive singular feminine, but here it functions as genitive (end of the lecture).

Why is the verb split into stellt … vor? What’s going on with vorstellen?

vorstellen is a separable verb (trennbares Verb):

infinitive: vorstellen
prefix: vor-
main verb: stellen

In a main clause in simple present, the finite verb must be in second position. With separable verbs:

The conjugated part goes to verb position 2.
The prefix goes to the end of the clause.

So:

infinitive: vorstellen
main-clause present: Die Dozentin stellt unsere Hausarbeit vor.

Here: stellt (position 2) … vor (at the end).

How does vorstellen behave in other tenses or in subordinate clauses?

With separable verbs like vorstellen, where the parts go depends on the structure:

Simple past, main clause
- Die Dozentin stellte unsere Hausarbeit vor.
  (same pattern: finite verb 2nd, prefix at the end)
Present perfect (with haben)
- Die Dozentin hat unsere Hausarbeit vorgestellt.
  Here the pieces are joined: vorgestellt (past participle) goes to the end.
Subordinate clause (e.g. with weil)
- … weil die Dozentin unsere Hausarbeit vorstellt.
  In subordinate clauses, the whole verb complex goes to the end, and the prefix is attached again: vorstellt.
Infinitive with zu
- Sie hat vergessen, unsere Hausarbeit vorzustellen.

Basic rule:

Main clause, one finite verb: verb in position 2, prefix goes to the end.
Subordinate clause or non-finite forms: verb parts stick together at the end.

Which meaning of vorstellen is used here — “to imagine”, “to introduce”, or “to present”?

vorstellen has several meanings, depending on structure and context:

jemanden (jemandem) vorstellen = introduce someone (to someone)
- Ich stelle dich meinen Eltern vor. – I introduce you to my parents.
sich etwas vorstellen = imagine something
- Ich kann mir das nicht vorstellen. – I can’t imagine that.
etwas vorstellen = present something
- Der Chef stellt den Plan vor. – The boss presents the plan.

In Am Schluss der Vorlesung stellt die Dozentin unsere Hausarbeit vor, we have:

subject: die Dozentin
direct object: unsere Hausarbeit

So this is meaning 3: to present something.
It means: she presents / explains / introduces our term paper/assignment (to the audience).

Why is it unsere Hausarbeit and not unser Hausarbeit?

Because possessive determiners (mein, dein, sein, ihr, unser, euer, Ihr) agree with the gender, number, and case of the noun they modify.

Hausarbeit is feminine, singular.
Here it’s a direct object → accusative singular feminine.

The accusative singular feminine ending for possessives is -e:

unsere Hausarbeit (our term paper / assignment)

Compare:

Nominative feminine: unsere Hausarbeit ist schwierig.
Accusative feminine: Wir schreiben unsere Hausarbeit.

For a masculine noun, you wouldn’t add -e in the nominative:

unser Kurs (nom. masc.)
unseren Kurs (acc. masc.)

What case is unsere Hausarbeit in, and how do we know?

unsere Hausarbeit is in the accusative case because it’s the direct object of the verb vorstellen.

Ask: What is the Dozentin presenting? → unsere Hausarbeit.
That’s the thing the action is being done to → accusative.

Structure:

Subj. (nom.): die Dozentin
Verb: stellt … vor
Direct object (acc.): unsere Hausarbeit

Why does the sentence start with Am Schluss der Vorlesung instead of the subject die Dozentin?

German main clauses follow a verb-second (V2) rule, not a strict subject-first rule.
Exactly one element usually comes before the finite verb, and that element can be:

the subject
a time expression
a place expression
an object, etc.

Here, the time expression Am Schluss der Vorlesung has been fronted to emphasize when something happens.

Word order:

Am Schluss der Vorlesung – first field (Vorfeld)
stellt – finite verb in second position
die Dozentin – subject
unsere Hausarbeit – object
vor – separable prefix at the end

You could also say:

Die Dozentin stellt am Schluss der Vorlesung unsere Hausarbeit vor.
(Here the subject is first, but stellt is still 2nd.)

Are there other correct word orders for this sentence?

Yes. As long as you respect verb-second and keep stellt … vor around the object(s), you can move the adverbial around:

Original:
- Am Schluss der Vorlesung stellt die Dozentin unsere Hausarbeit vor.
Subject first:
- Die Dozentin stellt am Schluss der Vorlesung unsere Hausarbeit vor.
Time after object (still correct, but slightly less typical):
- Die Dozentin stellt unsere Hausarbeit am Schluss der Vorlesung vor.

All are grammatically fine.
Differences are in emphasis and flow, not in basic correctness.

What exactly is a Dozentin, and how is it different from Lehrerin or Professorin?

Dozentin (female; male: Dozent) is typically used in higher education:

a university or college instructor/lecturer
can be a professor, but often someone who teaches courses without being a full professor (e.g. lecturer, adjunct).

Comparisons:

Lehrerin – general “female teacher”, especially in schools (primary, secondary).
Professorin – female professor; a specific academic title.
Dozentin – female lecturer/instructor at a university, not necessarily a full professor.

So in English, Die Dozentin is usually best translated as the lecturer or the instructor.

Could we say Am Ende der Vorlesung instead of Am Schluss der Vorlesung? Is there a difference?

Yes, you can say:

Am Ende der Vorlesung stellt die Dozentin unsere Hausarbeit vor.

This is fully correct and very natural.

Nuance:

am Ende – neutral “at the end”
am Schluss – often slightly more like “finally / in the final part / as a last point”

In most everyday contexts, they’re interchangeable; any difference is subtle and stylistic.

Why is the present tense (stellt) used, even though this could be about a future event?

German often uses the present tense for future events, especially:

when the time is clearly indicated (here: Am Schluss der Vorlesung)
for scheduled or planned events

So:

Am Schluss der Vorlesung stellt die Dozentin unsere Hausarbeit vor.

can mean:

She normally presents our assignment at the end of the lecture (habit), or
She will present our assignment at the end of this lecture (planned future).

You could also say wird … vorstellen (future tense):

Am Schluss der Vorlesung wird die Dozentin unsere Hausarbeit vorstellen.

But it’s not necessary; the present tense + time expression is often more natural.