In the morning, for various reasons, there is often a considerable amount of time from when I wake up until I go to shul to daven.
Can I study for college before I go to daven? Are there any parts of davening I can say at home which would permit me to study after saying them but before going to shul?
It is hard to say something definitive without knowing your situation, however if your situation is such that you can not daven earlier, then there is room to be lenient, that it isn’t yet the time to daven for you and you would be able to study. If you can however daven earlier then you should not be studying until after you have davened. Before studying, you should say all the morning brachos and korbanos.
Poskim, Tefilah Khilchoso 6 ftnt. 26.