[Requesting Advice] Applying Instrumental Rationality to College Course Selection Dilemma
I'm faced with a dilemma and need a big dose of instrumental rationality. I'll describe the situation:
This fall, I'm entering my first semester of college. I'm aiming to graduate in 3-4 years with a Mathematics B.S. In order for my course progression to go smoothly, I need to take Calculus I Honors this fall and Calculus II in the spring. These two courses serve as a prerequisite bottleneck. They prevent me from taking higher level math courses.
My SAT scores have exempted me from all placement tests, including the math. But without taking a placement test, the highest any math SAT score can place me into is Pre-Calculus Honors, which is one level below what I want to take in the fall. The course progression goes Pre-Calculus Honors to Calc I Honors to Calc II Honors.
So in order to take Calc I Honors in the fall, I either need to:
(1) Score high enough on a College-Level Math placement test or
(2) Forgo the test and take Pre-Calc Honors for 9 weeks this summer
I've taken both pre-calculus and calculus in high school. I've also been studying precalculus material over the past few days, relearning a lot of what I've either forgotten or wasn't taught in class. If I decide to take the test, I'm pretty confident I'll place into Calculus I. I'd estimate that chance being within 0.8, plus or minus 0.1. If I pass the test, I'll save 9 weeks of studying in the summer and use them to prepare for classes I'll be taking in the fall. I'd also free me up to take another summer class worth 4 credits and fulfill a prerequisite.
But if I decide to forgo the test and take Precalc this summer, I'm also pretty confident I'll do very well in the class. I'd confidently wager above a 90%. The class would ensure I've got the material down better than the placement test and would also give me my first six credits.
The questions going through my mind right now include: How can I best decide between these two options? How can I compare the heterogeneous benefits/costs? Are there any other relevant factors that I'm leaving out?
Advice would be greatly appreciated.
Edit: Writing this post, as well as reading and responding to the comments, has clarified the situation for me. Unless there is something else important I've missed, I'll take the test, place into Calc I, spend the summer taking a different summer class and preparing for fall classes. Thanks to everyone who helped me out.
Wow, I hadn't thought of using a graphics tablet before. I'll definitely look into that, as well as the incremental learning technique you linked to.
I had tentatively placed Differential Eq. before Calc III on a whim. I had no idea it drew on LA and Calc III. According to a prereq. flow chart I have, the only requirement for Calc III, Differential Eq., Discrete Math, and LA is Calc II. This very well may be a case of prerequisites being too lenient. I've penciled in the appropriate swap.
I'm looking to take some computer science courses. If nothing else, at least Foundations of Computer Science. Hopefully this summer. I'll have to look into precisely what the major/minor requirements are for CS. In the mean time, I'm trying to navigate the minefields of general education requirements.
The gen eds are tricky to deal with. You can't usually get out of them, but some schools are pretty good with what classes satisfy them. I would suggest ignoring the recommended gen ed courses (though try to get specific advice from fellow students and listen to them if it contradicts this) and going straight to the department which is related to the requirement. Look around and see what courses they offer, and then ask if it will satisfy a gen ed. I've found that taking department specific introductory courses is WAY more interesting than trying to slog through the default ones, which are usually filled with the same people you had to deal with in high school. It's also been my experience that most of the default courses are actually harder (I think this might be because they want to push freshmen into college mode). Again, this varies with the school, so take it with a grain of salt.
One more thing that I wish people had told me: find all the problem solving strategies you can, and use the hell out of them. You might think you are good at this and you don't need anyone's advice on how to think (actually you probably don't, since you are on this site...), but the falseness of this statement will become increasingly clear when you attempt problem sets. I thought I knew this, but looking back I would spend hours on one problem just trying the same method over and over, thinking I was doing something new.
If you don't see a solution or the path to the solution within 5 or 10 minutes, try something completely new no matter how close you think you are. Keep prodding your brain like this, and eventually one of those stubborn folds of tissue will spill its guts for you. But if you keep hitting the same part over and over again, you're just gonna have a pissed off commander in chief. Yeah, it does sound obvious... but if you don't check to make sure you're doing it, most of the time you're just going to keep hacking your way to nowhere.
Also, find or make a study group. I was too damn stubborn to do this - biggest mistake of my college career. It might be annoying when you know all the answers and everyone else doesn't, but that won't happen often.