Learn Hardcore Czech: V kurzu píšeme krátké věty, abychom nové gramatice dobře rozuměli. - In the course we write short sentences so that we understand the new grammar well.

v kurzu = literally in the course / inside the course. It slightly emphasizes the course as an environment or context.
na kurzu = literally on the course. Very common in everyday speech for “on a course, in a course”.

In this sentence, v kurzu is completely natural and idiomatic. If you replaced it with na kurzu, the meaning would stay practically the same: In the course / On the course, we write short sentences...

What case is kurzu, and why does the noun change its ending here?

kurzu is the locative case singular of kurz (a masculine inanimate noun).

Nominative: kurz (the base form)
Locative: v kurzu (in the course)

The preposition v (in) normally requires the locative case when it expresses location. That’s why kurz changes to kurzu after v in this meaning: in the course → v kurzu.

Why is the verb píšeme (simple present) used rather than a form meaning “are writing”?

Czech doesn’t have a separate “-ing” / continuous tense like English. The simple present usually covers:

We write short sentences (regularly, as a habit).
We are writing short sentences (right now).

Context tells you which one is meant. Here, píšeme describes a regular activity done in the course, so English naturally translates it as we write or we are writing, but in Czech it’s just píšeme in both cases.

What case and gender are krátké věty, and why do they have those endings?

věty is the accusative plural of věta (feminine noun: sentence).
krátké is the matching accusative plural feminine of the adjective krátký (short).

Nominative singular: krátká věta (a short sentence)
Accusative plural: krátké věty (short sentences as direct object)

We use the accusative because věty are the direct object of píšeme (we write what? → short sentences). The adjective must agree with the noun in gender, number, and case, so both appear as krátké věty.

What exactly does abychom mean, and why is it written as one word?

abychom introduces a purpose or result clause: so that we (would)... / in order that we (would)...

It is historically a combination of:

aby – a conjunction meaning so that / in order that
bychom – the 1st person plural form of the conditional auxiliary (we would)

These two are usually fused into one word in standard Czech: abychom. It marks:

a subordinate clause (introduced by aby)
in a sort of “subjunctive/conditional” mood (that we would understand)

So abychom rozuměli ≈ so that we would understand.

Why is there a comma before abychom in Czech?

In Czech, a comma is generally placed before most subordinate conjunctions, including aby / abychom, to separate the main clause from the subordinate clause.

Main clause: V kurzu píšeme krátké věty
Subordinate purpose clause: abychom nové gramatice dobře rozuměli

So the comma marks the boundary: In the course we write short sentences, so that we understand the new grammar well.

Why is rozumět followed by nové gramatice in the dative, not accusative?

The verb rozumět (to understand) always takes the dative case in Czech, not the accusative.

rozumět komu/čemu – to understand someone/something (dative)
- rozumět nové gramatice – to understand the new grammar

So gramatika must become gramatice (feminine singular dative), and the adjective nová must also switch to dative: nové gramatice.

This is just how the verb’s government works in Czech; it’s something you have to memorize with rozumět.

Why does nové end in -é, while gramatice ends in -e?

They’re both feminine singular dative, but adjectives and nouns have different declension patterns.

Noun gramatika (feminine): dative singular → gramatice
Adjective nový (feminine): dative singular → nové

So in dative singular feminine, you typically get:

noun: -e (e.g. škola → ve škole, gramatika → v gramatice)
adjective: -é (e.g. nová → nové, česká → české)

Together they must agree in case, number, and gender: nové gramatice (to the new grammar).

Why is the verb rozuměli in that “past-looking” form, if we are talking about understanding now or in general?

rozuměli here is the past participle, but combined with abychom it functions like a subjunctive / conditional (“so that we would understand”).

Compare:

Past: Rozuměli jsme nové gramatice. – We understood the new grammar.
Conditional: Rozuměli bychom nové gramatice. – We would understand the new grammar.

In abychom nové gramatice dobře rozuměli, the bychom part is fused into abychom, so you get a meaning like:

…so that we would understand the new grammar well.

So although rozuměli looks like a past form, with abychom it expresses a desired or intended result in the future or generally, not a finished past action.

Could the word order inside the second clause be different, for example abychom nové gramatice dobře rozuměli vs abychom dobře rozuměli nové gramatice?

Yes, Czech word order is relatively flexible, especially within a clause. Both of these are grammatical:

abychom nové gramatice dobře rozuměli
abychom dobře rozuměli nové gramatice

They mean the same thing: so that we understand the new grammar well. The differences are only in emphasis / rhythm:

Putting nové gramatice earlier can slightly highlight the new grammar as the important item.
Putting dobře earlier highlights understanding well.

For a learner, you can consider them stylistic variants of the same sentence.

Why is it rozuměli (masculine plural) – what if the group is all women?

The form rozuměli is the masculine animate plural past participle. In Czech:

If the group is mixed or gender-unknown, you use the masculine plural form by default → rozuměli.
If the group is exclusively female, the form would be rozuměly.

So:

Mixed or unknown group: abychom nové gramatice dobře rozuměli
Group of only women (and you want to show that clearly): abychom nové gramatice dobře rozuměly

In many textbook/example sentences, masculine plural is used as the default generic “we” unless the context specifies otherwise.

Why is it dobře and not dobrý or dobrá?

dobře is an adverb meaning well. You use an adverb to modify a verb:

dobře rozumět – to understand well

By contrast, dobrý and dobrá are adjectives meaning good:

dobrý učitel – a good teacher (masc.)
dobrá gramatika – good grammar (fem.)

You cannot use an adjective to modify a verb in Czech, just as in English you don’t say “to understand good” in standard speech; you say “to understand well”. Hence dobře.

Is there any difference between abychom rozuměli and something like aby rozumíme? Why can’t we say aby rozumíme?

You cannot say aby rozumíme – that is ungrammatical.

Reason:

After aby (or abychom, abys, abych, etc.), Czech expects the “subjunctive-like” construction with a past participle and the conditional auxiliary (fused into abychom, etc.).
So for so that we understand, you need abychom rozuměli, not aby rozumíme.

Patterns:

abych rozuměl – so that I understand
abys rozuměl / rozuměla – so that you understand
aby rozuměl / rozuměla / rozuměli – so that he/she/they understand
abychom rozuměli – so that we understand
abyste rozuměli – so that you (pl.) understand

The present indicative rozumíme (we understand) simply doesn’t fit after aby, which calls for this special mood.

Could we use napíšeme instead of píšeme here? What would change?

You could say:

V kurzu napíšeme krátké věty, abychom nové gramatice dobře rozuměli.

The difference is aspect:

píšeme (from psát, imperfective) – focuses on the ongoing, repeated activity: In the course we (generally) write short sentences... (habit / practice).
napíšeme (from napsat, perfective) – focuses on the completion of a specific action: In the course we will write (and finish writing) short sentences... (one-time, specific task, usually future-ish).

In the original sentence, we’re talking about a regular learning technique in the course, so píšeme (imperfective present) is more natural. napíšeme would sound more like a specific plan for one occasion.