A few troubling words...

[quickly]

Hi, I am looking for possible ways to translate the following words or phrases:

(1) quarter, as in "Spring quarter," "Fall quarter," or "two quarters."
(2) course, as in "...took a Latin course at...".
(3) sponsor and contract, as in "my sponsor for these contracts," or "would you sponsor these contracts."
(4) to take, as in "I have been taking Latin with..." or "...to continue to take...".

I have a number of words in mind, but using quartus, -a, -um for "quarter" in this sense sounds odd; using cursus, -us seems awkward; and using foedus, -i for "contract" sounds, well, slightly more marital than I would like, which leads me to suspect that condicio, -ionis would be the better choice. For "take," my best guess would be to construe it as "study," writing studere, or "learn," writing discere.

Secondly, some syntax:

(1) would, as in "I would appreciate the opportunity," or "I would like for you to sponsor."

While I would usually use velle to express wishes, It doesn't seem appropriate.

[Bretonus]

I have to ask, who are you looking for as a sponsor? And what is the context of this?

I like condicio, since it gives the sense that you are subordinate to your sponsor. But I also like cursus quite a bit, since it can also mean career, it carries an idea of continuity to it. If you use cursus you could also maybe use the more stylistic ineo for your verb to take.

For sponsor, perhaps fautor? It gives the sponsor the superiority of a patron without sounding so patriarchal.

I'm terrible with all things numerical so I won't even make a suggestion for quarter.

[quickly]

Bretonus,

There are no regularly offered Latin courses at my college. However, the school uses "Independent Learning Contracts" in order to allow students to pursue interests apart from regularly offered courses. The professor I usually contract for Latin is leaving for Greece and Italy with a group of students, so I have to find a new sponsor for my Latin contract. I'm not sure that fautrix is the word I want, therefore, as my dictionary glosses it "a favourer, protector, promoter," with additional entries for fautor: "applauder, patron." The context for such a sponsor would be a professor with whom I would meet on a regular basis, would write papers for, read texts with, and so forth, either alone or with other interested students.

With cursus, I would rather be clear than clever, and show a command of relevant grammar. Presumably, I have "mastered" Wheelocks, and for the last several weeks we have been reading Catullus, Ovid, and Virgil. My letter should ideally reflect this.

[adrianus]

Salvete quickly/celeriter Bretoneque

(1) quarter, as in "Spring quarter," "Fall quarter," or "two quarters."
(anni) quarta pars, vel (spatium) trimestre
two quarters = (spatium) semestre

(2) course, as in "...took a Latin course at...".
cursus -ûs (seu curriculum) studiorum
curriculum latinum

(3) sponsor and contract, as in "my sponsor for these contracts," or "would you sponsor these contracts."
tutor (vel custos)
contractus -ûs, vel pactum, vel pactio

(4) to take, as in "I have been taking Latin with..." or "...to continue to take...".
[Latinum] studere

ADDENDUM
"would" = use the subjunctive // modo subjunctivo utere
"would you sponsor me...if it's not too much trouble"
"Te tutorem mihi futurum [-am] quaeso...si tibi non nimìs molestum sit"

[Damoetas]

A word of practical consideration: Are you sure that your professors are actually going to like receiving a letter in Latin? I know that expectations vary by institution and by individual. But in all the academic contexts where I have experience, writing a letter in Latin would be perceived as overly earnest at best, and perhaps even annoying, pretentious, and unprofessional. And besides that, it doesn't really demonstrate the skill set that they're interested in; they want to see that you can read Catullus, Ovid, and Vergil, so they might be more interested in seeing your grades for those classes or letters of recommendation from other professors.

Again, that's just a thought based in my own experience; your situation might be entirely different.

[quickly]

Adrianus, thank you for your help. I am convinced by Damoetas, however, that my interests are better served by sending a letter in English. As he (or she) said, it could come off as "over earnest," and although I would like to think that previous letters sent to previous instructors in Latin had something to do with their sponsoring me, I don't know the target faculty well enough to guess. However, I have diligently copied your post into my notebook, and hopefully it will come in handy later. Your explanation of "would" was very helpful.

[adrianus]

Language in itself isn't dangerous, of course, just how you might use it. That's why I always have a disclaimer on all my Latin.

Lingua in ipsâ verô non perniciosa est; quâ eâ utereris aliter potest. Semper ergo monitionem ego infra epistolas meas ostendo.