I received my bachelor's degree this year with good grades; all praise is due to Allaah The Exalted. Before my final exams, I swore an oath not to memorize the law subject, because it was difficult and long. However, while I was surfing the internet, I found good summaries for this subject; so, I studied these summaries and I managed to memorize the subject. Should I offer an expiation? Did I break my oath?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

If your intention while swearing that oath was not to memorize the law subject at all, then you broke your oath and expiation becomes due on you. The expiation is to feed ten poor people, clothe them, or free a slave. If you cannot afford any of these options, you should fast three days.

However, if your intention was not to memorize the subject because it was long and difficult and then you found an easy short summary and memorized it, it is not incumbent on you to offer expiation since the oath is interpreted according to the intention of the oath-taker according to the statement of the scholars. The Maaliki scholar Khaleel said, "The intention of the oath-taker specifies the oath and sets limits for the general indication of its wording." [Al-Mukhtasar]

Based on the information provided in your question, the reason that caused the oath to be taken was that the subject was long and difficult. Some scholars refer to this as "Bisaat Al-Yameen (i.e. the context of the oath)". Therefore, if this was the reason that drove you to swear that oath and then you found an easy short summary and memorized it, it is not incumbent on you to offer expiation as long as this was the case.

 Allaah Knows best.