あした、すうがくをべんきょして、すうがくをおしえるつもりです。
I am trying to connect two grammatical structures and I do not know if that is how it works. Also, is there any difference between: だが and だけど
The first one is just the informal desu + ga meaning I am about to say something that contrasts something I have just said. However, I encountered the second phrase more often than the first. Is there a reason for it?
Your sentence can be rewrote as the following.
明日、数学を勉強して、数学を教えるつもりです。
(Tomorrow, after studying math, I will teach math.)
It seems that the main purpose of your question is to ask the meaning and usage of だが and だけど, but the sentence you've shown is irrelevant to those grammar terms.
Anyway, I can explain about だが and だけど.
だが and だけど are both conjunctions. There are no big differences between the usage of them.
明日、数学を勉強するつもりだが、数学を教える時間はなさそう。
(Tomorrow, I will study math, but I don't have time to teach math.)
明日、数学を勉強するつもりだけど、数学を教える時間はなさそう。
(Tomorrow, I will study math, but I don't have time to teach math.)
Both sentences can be regarded as expressing the same meaning. However, 「だが」sounds much heavier then [だけど]. I would expect to hear だが in daily lives only when I hear some speech from politicians' press briefings, and when some old boss give some speeches to their young employees.
Also please note that だが and だけど are both non-honorific languages, which are an important part in Japanese.
The honorific version of them would be だが → ですが and だけど → ですけど. When you speak Japanese in your daily lives you will need to be speak with honorific languages for the most of time.
In the same manner, ですが and ですけど can also be regarded as the same meaning. However, if I search for other people's opinions with this link, they say that だけど＆ですけど are informal than だが＆ですが and I can agree with them.
So if you are working in a company and having some speech and conference that needs to be formal and polite, you are recommended to choose だが＆ですが over だけど＆ですけど.
