Learn Hardcore Chinese: wǒ zài xuéxiào xǐhuan xué shùxué.

The main verb here is 喜欢 (“to like”). Chinese doesn’t need an extra “be” verb in front of it.
You only normally use 是 to link two nouns/pronouns or a noun and a noun-like phrase, e.g.:

我是老师。 – “I am a teacher.”
他是美国人。 – “He is American.”

So you don’t say ✗ 我是喜欢学数学 in this kind of sentence.

What exactly does 在 mean here?

Here 在 means “at / in” and introduces a location:

在学校 = “at school”

So the structure is:

我在学校喜欢学数学。
Subject – at + place – main verb phrase

In this sentence, 在 is functioning like a preposition (“at”). It is not marking a progressive action (like “am doing”) here; it just tells you where the “liking to study math” happens: at school.

Is 在 here the same “progressive” 在 as in 我在学数学?

No, they are related but used differently.

Location 在 + place
- Pattern: 在 + noun (place)
- Example: 我在学校喜欢学数学。
  “At school, I like to study math.”
Progressive 在 + verb
- Pattern: 在 + verb
- Example: 我在学数学。
  “I am studying math (right now).”

In your sentence, 在 is followed by 学校 (a noun), so it clearly marks location: “at school.”
If it were progressive, it would be 在 directly before the verb (学), like 我在学数学.

Where does 在学校 usually go in the sentence? Can I put it at the end?

The most natural place for a location phrase like 在学校 is before the main verb:

我在学校喜欢学数学。 ✓
在学校，我喜欢学数学。 ✓ (location placed at the very start for emphasis)

Putting 在学校 at the very end as:

✗ 我喜欢学数学在学校。

sounds unnatural in standard Mandarin for this meaning.

A useful word order template is:

Subject + (Time) + (Place) + (Manner) + Verb + Object

So 在学校 (place) should go before 喜欢学数学 (verb phrase), not after it.

What is the difference between 我在学校喜欢学数学 and 我喜欢在学校学数学?

Both are grammatically correct and very close in meaning, but the focus is slightly different.

我在学校喜欢学数学。
- Rough idea: “When I’m at school, I like to study math.”
- 在学校 sets the overall situation: in the school context, this is something I like to do (maybe compared to other things at school).
我喜欢在学校学数学。
- Rough idea: “I like to study math at school.”
- 在学校学数学 is one whole activity: “studying math at school,” and that whole activity is what I like (maybe as opposed to studying math at home, online, etc.).

In everyday conversation, most people would treat them as almost the same, but:

前面放“在学校”: “At school, I (among other things) like to study math.”
放在“学数学”前面: “The place where I like to study math is at school.”

Why are there two 学 characters (in 学校 and in 学) in one sentence? Are they related?

Yes, they are related; they share the same basic meaning of “study / learn.”

学 (as a standalone verb): “to study / to learn”
校: “school” (originally “school; to proofread” in older usage)
学校: literally “study + school” → “school”
学 before 数学: the verb “to study”

So in:

我在学校喜欢学数学。

you have:

学校 – the place where studying happens (school)
学 – what you do (study)
数学 – what you study (math)

Chinese often uses the same character in both compounds and as an independent verb, so you’ll see this kind of repetition a lot.

Why do we need 学 before 数学? Could I just say 喜欢数学?

You can say both, but they mean slightly different things.

喜欢学数学
- Structure: 喜欢 + 学 + 数学
- Meaning: “like studying math”
- Focuses on the activity of studying/learning math.
喜欢数学
- Structure: 喜欢 + 数学
- Meaning: “like math (as a subject)”
- Focuses more on liking the subject itself, not explicitly on the act of studying it.

So:

我在学校喜欢学数学。 – “At school, I like to study math.”
我在学校喜欢数学。 – “At school, I like math.” (not necessarily emphasizing studying vs just liking it)

Both are natural; choose 学数学 when you want to highlight the learning activity.

What is the difference between 学 and 学习 here? Could I say 我在学校喜欢学习数学?

Yes, 我在学校喜欢学习数学 is correct.

General guideline:

学 – shorter, a bit more casual, very common in speech.
学习 – a bit more formal or “bookish,” often used in written or serious contexts.

In many cases they are interchangeable:

学数学 / 学习数学 – both okay
学中文 / 学习中文 – both okay

Nuance:

学习 can sound a bit more serious or process-oriented (“to engage in learning”).
学 is just the everyday “study / learn.”

In this exact sentence, both:

我在学校喜欢学数学。
我在学校喜欢学习数学。

are natural; 学 just sounds a bit more colloquial.

How does 喜欢 work when it’s followed by another verb like 学?

The common structure is:

Subject + 喜欢 + Verb (+ Object)

This is how you say “like doing something” or “like to do something”:

我喜欢吃饭。 – I like eating / I like to eat.
他喜欢看电影。 – He likes watching movies.
他们喜欢打篮球。 – They like playing basketball.
我喜欢学数学。 – I like studying math.

Chinese doesn’t change the verb form (no “-ing” or “to” forms). You just put the plain verb after 喜欢:

English: “like to study / like studying math”
Chinese: 喜欢学数学 (one simple pattern)

How is tense expressed here? Can this mean past, present, or future?

Chinese verbs do not change form for tense. 我在学校喜欢学数学 by itself usually implies a present or general/habitual meaning:

“At school, I (generally) like to study math.”

To make it clearly past, add a time word like 以前 (“before, previously”):

以前，我在学校喜欢学数学。
“Before / In the past, I liked to study math at school.”

To make it clearly future, add a time word like 将来 / 以后 / 明年 etc.:

将来，我在学校也会喜欢学数学。
“In the future, I will also like studying math at school.”

So the sentence itself is neutral; context or extra time expressions show whether you’re talking about past, present, or future.

Do I need any particle like 的 in 学数学, for example 学的数学?

No 的 is needed in 学数学.

学数学 is a straightforward verb–object phrase: “study math.”
You normally don’t put 的 between a verb and its direct object.

的 is used more for making descriptive phrases that modify a noun:

我喜欢的数学老师 – “the math teacher (whom) I like”
在学校学的数学 – “the math (that was) studied at school”

But in your sentence, you’re just describing an action you like doing, so you keep it simple:

我在学校喜欢学数学。 – no 的 needed.