Math Study Order: Advice for Self-Study

[noobilly]

Hi everyone, would appreciate a bit of advice here.

I did Finance in college, however I feel that the classes weren't quantitative enough, only having Business calculus and very basic statistics. So now I am self studying maths again. What I did was take an online course in calculus which roughly covered Calculus 1 and part of Calculus 2, then continue with self study off Paul's Maths notes, Khan Academy and grading myself by downloading calculus final papers off American university websites and doing them. If I pass I move to the next. Now I'm halfway through Calculus 3.

After I finish with Calculus 3, I plan to continue with a differential equations course (possibly off MIT OCW), then linear algebra and a proper statistics course.

My questions are:

1. Are differential equations - linear algebra - statistics the right order to go?
2. After I finish all that, would I have quantitative skills roughly on par with a guy with a technical degree such as physics or engineering?
3. Is there anything wrong with the way I'm going about it, or any way I could improve?

Thanks!

 

[bpatrick]

1. Are differential equations - linear algebra - statistics the right order to go?

Well, depends how far you want to go into differential equations. You'll need some linear algebra to solve systems of ODEs. You could merely bypass those chapters until you've studied enough linear algebra (there is plenty of material to cover with differential equations) ... or simply make sure you learn how to do the eigenvalue/eigenvector algorithms (even if you haven't covered the theory) when you start getting into systems.

Most intro stats books/lectures/courses you could get into right after calc 2, but calc 3 and linear algebra will help too, especially if you want to get into more in depth stuff. Markov chains is an example of where you'll need some linear algebra while learning prob/stats. Being able to solve multiple integrals (pretty easy even without calc 3) is also needed depending on what all you're doing with probability models.

I'm a huge proponent of learning linear algebra as soon as you are able. Even the stuff you'd learn in an intro LA course has so many applications that you'll start to see in differential equations, vector calculus, probability, abstract algebra, etc...

2. After I finish all that, would I have quantitative skills roughly on par with a guy with a technical degree such as physics or engineering?

Probably getting close ... being good with complex numbers / e^ix notation of trig stuff, and complex matrix + Fourier analysis would get you a bit closer to the math abilities of most engineers upon finishing college. Physicists are pretty well versed in solving PDEs through classes in thermo, E&M, and QM.

Most of those technical / scientific degree programs have calc 1, 2, 3, ODEs, and LA as required courses, then the specific upper level courses within the major build on all that via working problems and learning additional tools to solve more advanced problems. So yeah, when you're done with that progression, you're about on par (as far as quantitative skills go) with somebody who is about to start upper level study in one of those fields.

3. Is there anything wrong with the way I'm going about it, or any way I could improve?

Possibly look into numerical analysis too if you want some additional skills that will certainly be useful.

Seems like you're doing fine otherwise. Like I said earlier, I always recommend linear algebra early and in great magnitude since you can never be too good at it, but that's just a personal thing.

Prof. Strang's linear algebra lectures on MIT's OCW are great. I recommend them to anybody. I've only seen a few of them since I am already very familiar with the subject, but thumbs way up. I used Anton's elementary linear algebra 8th when I was in school, I thought it was great. I'm sure there are many other wonderful books out there too.

Doing physics problems is a great way to practice the math stuff you've learned and keep the "important" / "applicable" math tools from getting rusty.

Good luck! Self-teaching is pretty sweet, I've done loads of it over the years considering, by formal education, I'm a classical musician, haha.

 

[noobilly]

Thanks for the advice, I'd never have guessed you were a classical musician if you didn't say it! If you don't use any of that on your job, how do you avoid getting rusty? Flip open a book and do a couple exercises once in awhile?

 

[20Tauri]

I would say do linear algebra before differential equations. My school suggests but does not require linear algebra as a prerequisite for DE. I am in DE now and we are definitely touching on some linear algebra topics--linear independence, bases of functions, etc.

As for the stats, it really depends on what kind of stats you're thinking about doing. If you're doing intro stats or stats for social scientists, you can probably do it whenever you want--it'll just be high school algebra and some z-score tables. If you're doing mathematical statistics (aka intro probability or prob/stats) you are probably good to do it after multivariable calc. If you're planning to do linear algebra and DE first, even better.

As for the quantitative skills, it's hard to say. My undergrad degree will be creative writing, with a mathematics minor. I've taken essentially what you're describing and then a few math electives. I would say at this point I am reasonably competent as compared to, say, science students, but there really is no substitute for putting in the hard hours. I know physics majors who can kick my butt when it comes to calculus, just because they have to use it all the time and I don't.

 

[Jorriss]

My questions are:

1. Are differential equations - linear algebra - statistics the right order to go?
2. After I finish all that, would I have quantitative skills roughly on par with a guy with a technical degree such as physics or engineering?
3. Is there anything wrong with the way I'm going about it, or any way I could improve?

Thanks!

1) That's one way to go. I would say study linear algebra next for sure but then you have choices on what you want to study.

2) Only a physics major who did around the minimum. Calculus, differential equations and linear algebra are generally courses taken during the first two years of ones UG education but a physics major keeps learning more through out their entire bachelors. You'd need calculus of variations, complex algebra, certain PDEs techniques, etc and even then, a lot of physics majors just go the whole way and take full courses on complex analysis, pde's, algebra, etc. But, what you are learning now IS a good way to start off and build a base.

3) You seem to be doing a good job. If there is a local university or college though you could always just sit in on classes there.

 

[noobilly]

Ok thanks guys, I think I will proceed with linear algebra before differential equations. I'm wondering whether the later courses such as PDE's and so on are as easy to self-learn or not, at the moment they look really tough to me. But then again so did Calculus 3 at the start... I'm hoping they will become easy when the time comes, the same as Calc 3 did.