You had better already know why you'd want to study probability coming into this course, because you're going to have a hard time connecting what you learn in this class to applications in science or economics. Professor Heyde used only a handful of examples, even of the toy sort that inhabit most probability books. When he did work these (straight from the text), he would often pause for long, uncomfortable stretches, as though not sure where to go. You will spend most of your class time following him through proofs. If you don't know the meanings of the fundamental concepts (which are often simple to state), you will not learn them in class.
There are two texts for this class, the brilliant (though spare) Durrett and the hopeless and foggy Bean. Homework was assigned almost exclusively from Durrett. Buy Durrett and ignore the Bean, which does a poor job of explaining most concepts and often leaves important parts of a topic as an excercise for the reader. Also, if you're not going to be an actuary, the pervasive actuarial topics in Bean are depressing.
The practice exams are much more difficult than the real exams; don't let that frighten you. Seeing the math done in lectures was sometimes illuminating if your math is as rusty as mine.
In Heyde's favor, he is looking for evidence you understood the probability concepts rather than mastery of the calculus. This is fortunate, since it seems most of us this term were quite deficient in the "tedious technical manipulation". Setting up the integrals correctly and making an effort to solve them is really all you need to do. If you make an effort and write neatly, you'll get an A-.
If you're motivated enough to study the textbook until you grasp things but you're not a first-class math stud then this class is a decent warmup for more strenuous statistics courses. If you can hack it, take a more advanced course instead.