Math 300 teaches students the thinking and communication skills of a professional mathematician. It is intended to prepare math majors and other students for Math 311 and Math 351, and more generally, to help them make the transition from the computational courses of the first two years to abstract courses based on reading and writing mathematical proofs.
Math 300 is a challenging course. Despite its number, it is not the easiest upper-level math course. Most students find it a tough course. Over the past 5 years, 30% of registered students either withdrew or received a D or F.
The formal prerequisite for this course is 152. However, it is better to have had at least one 200 level course. This is especially true for transfer students: you are much better off taking some 200 level math courses at Rutgers before taking 300.
Students whose grades in 100 and 200 level courses are in the C or C+ range are strongly cautioned against taking this course.
If you are not planning on taking any proof-based mathematics course you probably don't want to take Math 300. If this is the last math course that you plan to take, you should not take Math 300. If you are just looking to fill a slot in your schedule you should not be taking Math 300.