I would certainly change your sentence to "at that time".
What I believe you are missing is that "in" implies a duration and the phrase is actually a shortened version of "within" and skipping "amount of":
[with]in that [amount of] time I managed to undo the knot.
This means:
- I was given some amount of time
- I was able to complete the task
A longer version of the sentence, to put it in context, would be something like:
I was tied up in a closet and knew the bomb would go off in two minutes. In that time I managed to undo the knot, get out of the closet and escape the building just before it exploded.
And, if you were telling the story to someone, you might include "at that time":
A: Where were you yesterday evening?
B: I was tied up in a closet at that time and a bomb was going to go off in two minutes.
"Faculty" is a venerable term for a university division1, still used by some schools either in place of or alongside more modern designations like "department" and "school"2.
In all cases (Faculty of X, X Department, etc.) you could say either
I'm a student in [Your Division] at [Your School].
or, if your division has its own "name", such as a named College or professional school within a larger university,
I'm a student at [Your Named Division] at [Your School].
You could also say
I'm a(n) [your subject] student at [Your School].
Your specific example doesn't work, because as far as I can tell, the University of Oxford (the famous old one in England) doesn't currently have a Faculty of Arts.3 However, one could say:
I'm a student in the Faculty of Music at the University of Oxford.
I'm a student in the History of Art Department at the University of Oxford.
I'm a student at the Ruskin School of Art at the University of Oxford.
or, respectively,
I'm an art history/art/music student at Oxford.
The first set are quite formal, suitable for writing in a cover letter to a resume; the last is probably more natural when speaking, and I think would be most universally understood.
Note that you should avoid saying "I'm an Arts Faculty student", at least in the US, because "faculty" can mean "professor" so it sounds contradictory.
1 According to Wikipedia,
A Faculty of Arts is a university division specializing in teaching in
areas traditionally classified as "arts" for academic purposes,
generally including creative arts, writing, philosophy, and
humanities. It was one of the four traditional divisions of the
teaching bodies of medieval universities, the others being Law,
Medicine and Theology.
2 (Source)
(Source)
3 (Source)
Best Answer
The more idiomatic preposition that goes with the job market is usually "in".
But I definitely see where you are coming from. I gather you are drawing a parallel between merchandise "on the market" and a person or a form of labor "on the job market".
It is true that we often talk about a product/commodity being "on the market", while the trader of the commodity is "in the market".
But as with any other language, English has exceptions to almost every rule and idiomatic usage. Prepositions are tricky. You can also talk about commodities being in the market. This usage is less common but not uncommon:
It'd make sense your intuition tells you "on the job market" might work. And it does, though not so popular as "in the job market", as this Google Ngram chart shows:
Examples:
To sum, your sentence could go either way, although "in the job market" is certainly more common than "on the job market".