[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.
Hey ryjm, thanks for taking the time to give me advice. I found it helpful. I appreciate when older students take the time to send some words of advice down the ladder. These are my thoughts, in no particular order.
There are some subjects that I find it easy to excel in. But math certainly isn't one of them. For me, math takes some serious work to understand and master. And it's only been recently that I've gained an interest in really understanding it. In high school, I was definitely not in the top of my class when it came to math, never mind anything like Gauss.
While I think my OP gives off a different vibe, I fear precisely what you described: that I'll get in over my head, that I'm just not cut out for a math major, or that I'll have no fucking clue what's going on. A part of my brain says to just do a philosophy degree. Because philosophy is something I've been studying almost non-stop since I was 11. It's something I won't struggle at. At least for me, a philosophy major would be orders of magnitude less difficult than a math major. Heck, I don't think I really comprehend at a gut level how hard a math major will be. All of that scares me.
But while I think I'd enjoy taking a philosophy of science class than Linear Algebra, I think I have very good instrumental reasons for taking the math route. Rather than seeing math as something I value in and of itself, I see math as a gateway to other things I want to do in life. Don't get me wrong, I do find a lot of math fascinating. But I'm more attracted to it because it allows me more financial opportunities than, say, philosophy. I'm making an investment with my college education. I want an optimal rate of return.
So while I really do want to understand the mathematics of linear algebra, I am more so concerned about keeping a high GPA. I need the scholarships, the internships, and the job opportunities for when I get out of school. But I don't quite see where the two goals diverge. My line of think is this: if I really work hard to understand and internalize the knowledge, wouldn't that lead me to have higher grades than if I didn't?
At least in far-mode, I am determined to work hard. But I also want to work smart. I know that if I approached a math class with a brute force approach, then I won't succeed. I could do that in high school history classes, but not now. So I'm trying to compile a strategy beforehand so I can work smarter. Here are some of the ideas that come to mind.
First, what you said about limiting the rate at which I want to speed ahead. One of my biggest concerns is that I'll be unprepared for some of my math classes. I took that placement test the other day and placed into calculus, but there was some material which I really didn't know. Particularly some higher level trigonometry and logarithms. I need to make sure I have that down before this fall.
But I'm also over qualified for the precalculus course. Beyond that material, I have a really pretty great grasp of precalculus. As of now, this is my tentative plan for my math course-load during my freshman and sophmore years. This fall I'll take Calculus I. That will let me take Calculus II in the spring. During that spring, I'll also take Statistics Honors, which is a combination of stats I & II. Fall of next year I'll take Differential Equations and Linear Algebra. The spring after I'll take Calculus III and Discrete Math. (Differential Eq. and Calc III can be swapped if chosen.) Would you say this is an okay rate, or is it still too fast? I'm trying to pretty evenly distribute my course work so that I don't have to take three math's in one semester.
Another strategy is to use SRS. I'm pretty awful at programming with LaTeX, which is necessary for using math with Anki. But if I could master it, I think it could reap some benefits.
And I plan to use my summers to study for upcoming math classes. This summer I'm preparing for Calc I and Calc II.
Lastly, I'm told I should take notes of the material before I come to class. That way I can just absorb the lecture and make adjustments as needed. Then do all the homework.
If you have any comments or other advice, I'd love to hear them. That goes for any other math majors, too. Heck, might as well let the scientists join in on the fun, as well.
If you understand that you have to work very hard and you are able to judge how much you can handle, you'll probably be okay. I've just seen a lot of people doing a math degree because they were always good at math and they thought they could breeze through it. That won't happen.
I use SRS daily for math stuff, and the best thing you can do is get one of those cheap graphics tablets. I think mine was about $60. Then you can just write out all your question answer pairs. I did the LaTeX route for a while, but the amount of time you have to spend inputting everything is not worth it. If you really want to get into this kind of studying, you can try this incremental learning technique. And definitely read ahead before each lecture.
Your course selection looks pretty good, but I would swap Differential Eq. and Calc III. I took Differential Eq. freshman year (stupid) while taking Calc III, and it was heavy on both linear algebra and calc III material. Your class may be different, but I would recommend a full semester of linear algebra before. Try to find some fellow students to ask though; professors can be either too strict or too lenient when it comes to what they require before taking a course.
You might want to consider throwing in some computer science courses too. Even a minor will increase your opportunities immensely after college.