So I have credit from the BC test to skip to Calc 3, but I’ve heard that the math sequences at Uchicago are taught with way more proofs and are otherwise quite different from BC calc in high school. In that case, would it be difficult to jump into the sequence at the end and start with Calc 3? I also might have forgotten some stuff over the summer so I’m uncertain about how prepared I would be. Do a lot of people start with Calc 3 or would you suggest starting over with Calc 1 (so starting with 151 or 153)? I’m not majoring in anything math intensive, but probably still science related.
Well, you could meet in the middle and start at Calc 2
In general, AP classes are not completely equivalent to college courses. In my experience at Illinois Tech, some students can come in with AP credit in Calculus and Physics and do quite well in the more advanced courses. Others are better off repeating the courses in college. My two sons have done both things.
The fact that you are uncomfortable starting with Calculus 3 is telling you something. It is better to roll back and take a course that you feel more confident in during your transition to college. In the long term, it won’t really matter and if you build a solid foundation in your GPA by starting at a lower lever, it will be worth it.
This is a great question to discuss with your academic advisor and with the Math Department when you get to Chicago, and after you take the math placement test. Chicago has, effectively, four different calculus sequences, with different levels of “proofiness.” You could easily have a choice between starting at a 2 or 3 level in one sequence, or starting at the beginning in a more rigorous sequence. Which choice is best for you depends on your personal math goals and your overall academic goals; there isn’t one right answer.
I think it may be a better idea to go back to Cal 1 or maybe 2 if you really want to go on ahead. When you’re first starting off at uni it’s going to be hectic and it’s going to be a process learning how to get used to the course load and managing your social life. So, if you were just repeat a Calc class it would decrease the difficulty of entering university since it’s one less class you have to worry about.
Math 153 is just about as proof-intensive as Math 151. The first two weeks of Math 151, 152, and 153 in the Fall Quarter teach the same material on a special type of introductory proof called the “delta-epsilon proof” (or, the proof that a limit exists). The course material in all three classes is identical in the first two weeks of the Fall Quarter so that everybody, regardless of course placement, has experience with this kind of proof, because nobody in the 150s sequence is expected to have come across this kind of proof before. Knowledge of delta-epsilon proofs is not fundamental to understanding the rest of the material in the 150s sequence; the math department only teaches it because the curriculum designers felt it was important for everyone to have some kind of exposure to math proofs.
In general, you should not be worried about the level of formal proofs in the 150s sequence, for aside from the first couple weeks there practically are none. The vast majority of students taking Math 153 will be jumping in from high school, so it will likely be everyone’s first exposure to proofs, and you would not be at a disadvantage. If you seriously doubt your calculus skills in spite of your stellar AP score, you should take the Math Placement Test on the Tuesday of O-Week. Doing so will help you gauge how much you remember from BC Calculus in high school, and would provide a more concrete assessment of your schools that would be useful to the math placement advisors should you go to them for a placement consultation later in the week.