Hi everyone. I’m currently a high school junior signing up for courses next year. However, my predicament is a bit unique, as I’m planning to take 12 credit-hours worth of university courses first semester and 11 credit-hours worth of university courses second semester. I was hoping if any math majors can tell me if my course load next year is doable:
First Semester
AP English Literature
AP Psychology
Numerical Analysis*
Intro to Ordinary Differential Equations*
Statistics I*
Financial Mathematics*
Second Semester
AP English Literature
AP Psychology
Statistics II*
Abstract Algebra*
Fundamental Properties of Spaces and Functions*
Courses marked with an * are dual-enrollment courses at the local University.
It depends on your ability, but I would recommend taking more AP courses in other subjects. For example, you are taking no science, which normally should go along with math. I don’t see the point in getting in so many college classes.I would also recommend not taking theoretical math like Abstract Algebra in high school.
Abstract algebra is typically a heavily proof-focused course. If you have not had heavily proof-focused courses before, you may want to check with the college’s math department to see what course it advises for your first heavily proof-focused course.
At some universities, ODEs is a prerequisite for Numerical Analysis. Having it first definitely helped me.
Honestly the doability depends on your math ability. If you thrive on math, it may be doable, but if you don’t want to spend the majority of your school time doing math, cut out a few courses. (FYI I am also a dual credit junior in math/stats and have spent a lot of my academic time with math.)
Have you had stats before? Some people click with it, but many don’t.
I will have taken 5 years of science by the end of junior year, including the 3 “main” AP science courses at our school, AP Physics, AP Biology, and AP Chemistry. The only graduation requirement I have left is one more year of English.
I took STAT 3100 (Intro to Mathematical Statistics I) at the university first semester this school year and I’m taking STAT 3101 (Intro to Mathematical Statistics II) this semester.
I think this is going to depend upon how strong you are in various subjects. This is a very tough course load that you are proposing.
As one example, I was a math major in university and did very well in math. There is no way that I ever would have considered taking AP English Literature in high school. I was strong in math and physics and computer science (and a couple of engineering courses that I took in university) but I was a slow reader and not good at all in English.
Therefore personally I would have been more worried about the heavy reading load of AP English Literature rather than the heavy math load of four math courses. However, you might be good in different subjects compared to me or compared to any other student.
Also, I was a lot older than you are now with a lot more math courses already taken before I took numerical analysis. This was a tough course when I took it. That might or might not have been a function of the particular professor that I had.
I’ve heard that abstract algebra is hard. I don’t think I’ve taken a proof-heavy course, as the math courses I’ve taken in high school are AP Calc BC, Linear Algebra, Calc III, and Intro to Stats I & II. I am also taking discrete structures right now, which is slightly more proof-based.
Is “Fundamental Properties of Spaces and Functions” an introduction to proof techniques and practice? If so, you may want to take that before abstract algebra.
I would take some more AP classes. You could also take college classes in related areas such as physics and computer science. I do not recommend theoretical classes such as Abstract Algebra and Spaces in high school. You don’t have to complete a math major in high school. From a career point of view, it is probably better not to be so focused on mathematics anyway. There is more market for math with science, programming, or finance.Even in academia, a career as a theoretical mathematician is difficult.
OP is planning on taking more like a junior math major schedule. I assume he already has taken Calculus III, Linear Algebra, and Statistics.
It’s fine to keep taking more advanced classes, but I would limit it to two a semester.This is better in terms of college applications,not getting overwhelmed, and career long term.
I think 3 math courses per semester is reasonable since the OP is obviously very advanced in math. I’ve taken 3 math/stats courses while being a high school student and was fine. But I also would encourage taking only 2 to allow more free time to really grow and enjoy the rest of high school years.
I would NOT recommend taking abstract algebra without any knowledge from an intro to proofs class. Question: why do you want to take abstract algebra? Numerical analysis usually has a prerequisite of either differential equations or linear algebra. What previous math courses have you taken?
I’d skip financial mathematics unless and until you have a decent real world grasp of finance. The relationship between Brownian motion and Black Scholes can get pretty boring if you’ve never had any money on the line trading options
ODE makes a lot of sense given your background, and should be doable imo.
As a transition towards more proof-intensive courses, how about taking a step back in the sequence (sort of) and taking a number theory course? These are typically very accessible to anyone who has done some linear algebra, and are a great way to start thinking more deeply about fundamental concepts. It could be a nice bridge, methodologically, to something like group theory, etc. Ditto for a rigorous course on probability, at least with respect to thinking about proofs. I can’t see numerical analysis helping you make the leap from high school, algorithmic math to more rigorous math, but ymmv of course.
Rigorous courses in stats are always a plus imo - wish I had taken more of them! Anyway, best of luck with your learning!
AP Calc BC (5), Calc III, Linear Algebra, and Intro to Stats I & II. One of my friends who hasn’t really taken any proof-based courses is taking abstract algebra right now and he finds it challenging but doable. I guess I want to take abstract algebra simply to challenge myself and pursue my interest in math.
I want to take financial mathematics because I’m interested in a career in quantitative finance (trading, hedge funding, etc), but I definitely understand what you mean.
I didn’t think about taking a number theory course before. Now that you mention it, I’ll look into it. Thanks!
You sound like @SuperGeo5999 who likes to take courses because their friends are taking it. Challenging yourself is good, but I wouldn’t take abstract algebra to be that kind of course. You already challenged yourself with calculus 3 and linear algebra. What if proofs isn’t your thing and you drop out of the class? I would recommend reading a abstract algebra book at the library amen check it out. See if it’s something you are interested in taking.
I am not fond of your choice of math classes. Financial Math, Numerical Analysis, and the advanced statistics class seem OK. Ordinary Differential Equations covers an engineering / physics related topic from a theoretical math point of view. It doesn’t seem like the best choice for financial mathematics. As mentioned, the Algebra and Spaces courses seem too theoretical and advanced. I would recommend more general and less advanced classes, such as Advanced Calculus, Discrete Mathematics (which is oriented towards computer science majors and covers a number of topics briefly) and the basic Differential Equations class taken by engineers. You could also take an operations research class, which seems relevant to your career goals.
