To imply something means to suggest it in an indirect way, without saying it directly.
Larry's remarks implied that he'd be leaving the company soon.
The evidence seems to imply that the suspect is innocent of the crime.
To infer something is to form a conclusion from the information available (especially if the information available does not state things directly):
From Larry's remarks, I inferred that he'd probably be leaving the company soon.
Based on the evidence, the judge inferred that the suspect was innocent.
These two words describe the same event but from the two different sides (similar to lend and borrow). The speaker or writer implies a point (suggests it indirectly). The reader or listener infers a point (comes to their own conclusion after considering the indirect information).
What topics does your professor appear most excited about
All professors have a preferred topic. Not surprisingly, this topic usually makes up a significant portion of any test that your instructor administers. I would suggest keeping a list of the topics that your professor spends an excessive amount of time exploring. This will help you remember the most main highlights of the class when the time comes to prepare for an examination.