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In reply to:

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.

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.

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[Requesting Advice] Applying Instrumental Rationality to College Course Selection Dilemma

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May 11, 2012

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.

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Upvoted. Discussion posts like this, that ask for help with an actual problem, are great stuff. They're just the working material we need.

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Thanks for the positive feedback. I wasn't sure how the post would be taken. I would like to see more material like this, too. Helping others with applications of instrumental rationality is what I find most valuable about the LW community.

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I'm surprised nobody has suggested talking to the professor of the course you want to take. They usually have the power to waive prereqs, and are willing to do so for students who show motivation. That would be my first stop when considering this sort of problem.

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Will the Precalc class really be helpful, or will it be a waste of your time?

Consider the opportunity cost; what else could you be doing this summer?

Do you know who is teaching it and how good of a class it is? If the material seems like a waste of your time once you're in the class, how easy would it be to drop it and do something else? Try to obtain a copy of the syllabus and, ideally, past homeworks and tests to judge better whether this would actually be useful to you.

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As far as the learning is concerned, most of it is a waste of time. I do need to continue brushing up on trigonometry and logarithms, but most of the material in the class I know.

I'd likely spend the time studying for Calculus I and/or take Intro to Computer Concepts & Program to fulfill a requirement. I'd save a few hundred dollars but only gain four credits by doing that option.

I don't know the teacher, but the Rate my Professor score is okay. (Rated a 4 overall.)

Good idea about obtaining the syllabus. I checked it over and I am familiar with almost all of the material. I think I could pretty easily teach myself the rest.

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As someone who just finished my sophomore year as a math major, I think I can give some useful advice in the vale of tears that is a mathematics degree.

All in all, it comes down to how much your GPA matters to you versus how much math matters to you when choosing courses. Even if you are ridiculously smart, most of the stuff you see after calculus and linear algebra is going to be pretty damn hard, and in order to get something substantial out of those courses you'll have to spend a large amount of time staring at symbols.

So if you want to maintain a good GPA, limit your desire to speed ahead and focus on the recommended courses. You'll then have the time to be able to really understand the material and have good grades. Even if you were at the top of your class in high school, your GPA will benefit from understanding this. I would even recommend going slower than the pace set by the administrators. No matter how ready you think you are for a certain course, there will be a point where you have absolutely no clue what the fuck is going on. Trust me.

In my opinion, you will get as much out of doing this as you would if you sped ahead but kept the same work ethic. I use this heuristic: If I want to take another math course and have the same GPA and an increased net mathematical knowledge gain, I need to increase my work ethic by ten. If I'm missing a pre-requisite, I need to increase it by twenty. Grad courses are a hit or miss; sometimes they can be an easy, relaxed way to get into higher math, and sometimes they can be insanely hard.

Now, if you don't care about your GPA, then take as many math courses as you can. That's what I did. Worked my ass off for B's and C's. The only reason why it works for me (in terms of my level of satisfaction with my choices) is that I don't (and didn't) do much of anything other than math. So I was able to really delve into all of these topics and come out with internalized knowledge - but I had to sacrifice my ability to complete assignments on time and prepare adequately for exams. Had I focused on getting A's... I might've been able to do it, but it would be at the expense of optimal learning (not that I didn't try to get A's with my "internalized knowledge", I'm just really driving home the point that this shit is hard, especially in timed situations).

I guess what I'm getting at here is: don't overestimate yourself if you want to keep doing and loving math. Know your breaking point, or at least remember that you have one - you will hit it, and it will hurt. Even if you are not super into math and just want to use it another things, the core courses are still very hard and this advice is still valid. And if you do want to skip ahead and do as much as possible, think about how much harder you think you will have to work, and multiply that by ten. This is if you actually want to get anything out of these courses - I'm sure you can skip ahead and get A's, but you won't have gained much. Unless you're Gauss. (On that note, you will encounter a lot of this, even as an undergrad).

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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.

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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.

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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.

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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.

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Is the summer class factored into your GPA and does it cost money?

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Yes, it is factored into my GPA. It costs $824.

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Forgot to ask. If you take the test and don't pass can you still sign up for the summer course?

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Yes. Once I take the test, I can register for summer and fall courses.

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I do like this type of post. Upvoted.

You told beoShaffer that you can sign up for the summer class after you take the placement test. Therefore, unless you can get some sort of major benefit out of the summer class, you should take the test (assuming the costs associated aren't very high).

Possible benefits to taking the class: You already know the material, and would presumably score well (be cautious about this one, though, since college coursework is often a shock to people coming out of high school, especially intelligent students). Since that factors into your GPA, if achieving a high GPA is important to you, you should at least consider it. More directly having to do with transitioning from high school to college, it might be a smart idea to ease into college work with a course whose material you basically already know. My first semester freshman year I tried to jump straight into organic chemistry, since I had scored a 5 on the AP Chemistry exam, and was ... unpleasantly surprised.

I don't know if you yourself, or your parents, or a scholarship would be paying the tuition for the class (don't forget things like housing and food when you're calculating that number), but it seems like most of the costs associated with the class would be opportunity costs. Taking this class means you wouldn't be preparing for other courses (at least not as much), or getting a job to earn some money, or doing anything else that you're interested in.

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More directly having to do with transitioning from high school to college, it might be a smart idea to ease into college work with a course whose material you basically already know. My first semester freshman year I tried to jump straight into organic chemistry, since I had scored a 5 on the AP Chemistry exam, and was ... unpleasantly surprised.

I will second this. I was in a similar position with physics, except that I decided not to opt-out of the intro course. This did result in it feeling a bit repetitive but I think it was worth it.

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You could take the placement test, and then start studying calculus in the summer (perhaps this is what you meant by "prepare for classes I'll be taking in the fall"), reviewing specific precalc topics as needed when and if your calculus book seems to assume prior knowledge that you don't have.

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Yes, that's what I meant by preparing for fall classes. What you've described has been my plan. I suppose if I boil it down, the real question is:

"Is 6 credits and a good grade worth 54 hours of class, plus study time, plus $824?"

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Is 6 credits and a good grade worth 54 hours of class, plus study time, plus $824?

Almost certainly not.

You need those credits anyway, and if I'm correct about the pricing scheme you're under you'll be able to get them later without spending extra money. And you can take a class that will actually be worthwhile/interesting for 6 credits instead.

It sounds like getting a GPA shouldn't be a difficult problem for you. Concentrate on finding ways of doing that for worthwhile/interesting classes, and you'll be fine.

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I think that puts it into perspective for me. Thanks for the help!

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