Running out of Math Classes

[mathshopeful]

Hi I am a sophmore in high school doing multivariable calculus in a local community college and next semester I will be going into linear algebra with differential equations. The problem is that after differential equations and linear algebra the community college does not have any other math courses. I am doing the math classes a an outreach program by this community college and are taking the classes for free. Any advice on what to do next school year?

BTW I am interested in a math and physics double major

 

[SteamKing]

Well, most sophomores in HS are struggling to learn Euclidean geometry, so you are well ahead of the game. CCs are only going to offer so many math courses, and I'm surprised yours offers MV calculus and DEs. If you want more advanced math, you'll either have to take a breather before enrolling in college or try to find some university courses you can take online or thru distance learning from a local 4-year college or university.

BTW, after doing all this math course work at the CC, you should also make sure your credits will transfer when you start college, especially since you have two more years of HS to complete. It would be a major drag if your credits were not accepted and you would have to retake your math courses.

 

[megatyler30]

Stanford Online High School might be am option. Not sure about price though. Self study is another option, I'll suggest some self study topics if you'd like. What's your physics background currently?

 

[mathshopeful]

Thanks for the quick reply. I have checked on the CC website and I am fairly sure that the credit will be transferred to the university that I am interested in. I am wondering if some four year universities offer a outreach program similar to the CC because I don't want my brain to be out of shape when I get into university. My background in physics is Physics III at the CC and I will start quantum mechanics next semester

Also running out of option in that category too lol

 

[homeomorphic]

Have you done probability and statistics? Someone ought to offer that one. What about physics classes? If you take physics classes, it should keep your math in shape.

Why not teach yourself something else? Maybe naive set theory/intro to proofs, real or complex analysis, PDE, differential geometry of curves and surfaces, or Fourier series.

 

[TheKracken]

Hey, are you in California by chance? If so you can PM me and I can help you find resources near you to take courses for credit. If not, contact your nearest university and ask them about Open enrollment. You should be able to start taking upper division courses next year if you want. I don't think it will be free though.

Also, have you completed the entire physics sequence at your CC as well? That is sure an option.

 

[mathshopeful]

Yes I am taking statistics this semester and to be honest it is a complete joke

 

[megatyler30]

You should check out Goldstein's classical mechanics to see if you're ready. If not then go through Taylor first. Also, I second differential geometry but a applied one may be more useful. My class I took concurrently with Linear Algebra is number theory. Also, thermodynamics and/or statistical mechanics would be a good idea. I took classical thermodynamics as a Junior in high school and currently taking graduate level Statistical Mechanics as a Senior.

 

[mathshopeful]

where are you taking these classes? online?

 

[SteamKing]

If you want to take all of these college courses while you are still in HS, why not pull the plug on HS and take the GED already? You've got all these math courses under your belt, but if you keep them on the shelf for another 2+ years, you are definitely going to lose something when you enroll at college. To keep this loss from happening, you're going to have to keep practicing all this math.

 

[mathshopeful]

I am not sure about dropping high school because then i would have to wait till I am sixteen if I am not mistaken and by then i would already be entering senior year anyways

 

[SteamKing]

I am not sure about dropping high school because then i would have to wait till I am sixteen if I am not mistaken and by then i would already be entering senior year anyways

Wait until you are 16 for what? It's not like you are going to be escaping from school. Just how old are you now?

 

[mathshopeful]

The minimum requirement for a GED is sixteen an I am 14 turning 15 next year

 

[PeroK]

The minimum requirement for a GED is sixteen an I am 14 turning 15 next year

There are many free resources online these days. For example:

http://tutorial.math.lamar.edu/

Also, if you pick any maths or physics topic, you will find many free pdf's, ranging from short pieces covering one topic or one problem, to whole textbooks. E.g. if you google "number theory pdf", so would find:

http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf

A whole university course on number theory. And, if you don't like the author's style or you don't understand a particular section, you can look for another text.

 

[Imurhuckleberry]

so you've learned calc 1-3 but how well do you actually know it? I know many people that have finished calc 1-3 and can barely compute derivatives and integrals, and if you were to ask them optimization or finding area/volume they'd be lost

 

[Rocket50]

I think that the online programs offered are too expensive, so the best option probably would be self-studying (unless you can find a nearby university allowing you to enroll there). The next subject in mathematics that you should learn is probably abstract algebra (or some sort of discrete math if you`re interested in it) or analysis.

 

[mathshopeful]

I know many people that have finished calc 1-3 and can barely compute derivatives and integrals, and if you were to ask them optimization or finding area/volume they'd be lost

I feel like I do understand the concepts of applied maths that I have done so far.

PeroK thank you for those resources
Rocket50 Ya I am thinking about abstract alg and analysis

 

[Vanadium 50]

so you've learned calc 1-3 but how well do you actually know it? I know many people that have finished calc 1-3 and can barely compute derivatives and integrals, and if you were to ask them optimization or finding area/volume they'd be lost

This is a very good point. It's not a race, and if one can get more comprehension by slowing down, one should.

As Woody Allen once said, "I took a speed-reading course and read War and Peace in twenty minutes. It involves Russia."

 

[Imurhuckleberry]

*(Do you what you think is best but really think about this)

I feel like I do understand the concepts of applied maths that I have done so far.

Okay, but realize that calculus is probably the most useful area of mathematics in all of science, real and complex analysis is literally nothing but calculus and calculus is so damn useful that other fields have emerged from it like ODE and PDE ,and they apply it to other fields of mathematics like Topology and Geometry (this is just off the top of my head), you are very young and you have a lot of time before you get into college, a strong foundation in calculus will make everything else so much easier. I'm just saying that because you are so young that perhaps mastering calculus would be wiser than becoming a jack of all trades right now because honestly, no one becomes extremely proficient in a subject after reading one book on that topic or taking one course on that topic, unless you are some Gauss.

Since you are already taking what I am assuming to be calculus based physics(and I am assuming that you are doing well in this also), start reading harder texts in calculus and physics, like for example Calculus by Apostle or The Feynman Lectures on Physics. I really suggest that after you finish your linear algebra and ODE next semester that you buy Calculus by Apostol, it is very very rigorous and if you buy both volumes (they're pricey) you will be going over Differential Calculus, Integral Calculus, Linear Algebra, Ordinary Differential Equations, Analytic Geometry, and many people consider it an introductory to real analysis because it is so rigorous

Regardless of the path you take, good luck, I wish I was this interested in academia at your age

 

[SteamKing]

The minimum requirement for a GED is sixteen an I am 14 turning 15 next year

This requirement is not written in stone. Check with the education authorities in your state. GED applicants can be tested if they can furnish a letter of permission from their parents and/or the state education authorities. Students have matriculated to college before turning 16. There's no use killing time in HS if you are ready for college work.

http://en.wikipedia.org/wiki/General_Educational_Development

Check the section 'Eligibility' under 'Test Administration'.

 

[Imurhuckleberry]

Also, once you do run out of classes, another reason why I think you should start reading harder texts is because you are young and you don't want to waste your youth. I'm not trying to tell you what your idea of fun should be, if you get a lot of joy out of doing math and science that's great, but you should put ample time aside for going out and socializing(its extremely important, no one likes working with a social idiot, yes this really can hurt you), don't try to rush your youth because I guarantee you will regret it, now is the time in your life that you can go out and be stupid and get your penis wet with minor repercussions. Stay diligent with your studies but also HAVE FUN, knowing how to communicate effectively and having confidence is very important for jobs and life in general.

Edit: the reasoning I am suggesting reading the texts vs. more classes is because you can read the texts at your own pace, so if you want to be spontaneous (or your friends do) you can still do it, you don't worry about getting "whatever" done for some class

 

[mathshopeful]

Imurhuckleberry thank you for the advice. I am at the moment trying to wrap my head around of what the Riemann Hypothesis and reading a bunch of book about that but if I have time to get to those books I'll take a look. I am also trying to make friends with people my age and I feel as if I can connect with people my age, and occasionally get some ;) . Social life is not too important to me because I really just want to learn and discover as much as I can. I'm still unsure of what to do as of now but I have time till the end of the semester

 

[homeomorphic]

If you want to learn about the Riemann hypothesis, you should learn complex analysis. I recommend Visual Complex Analysis by Tristan Needham. Kind of an expensive book, but worth it. It's quite a thrill to read. Reading about the history of math might also be a good idea. Just don't overwhelm yourself with too much stuff.

 

[mathshopeful]

Wouldn't I have to take analysis 1,2,3, and real analysis first though? I will look into that book thank you.

 

[homeomorphic]

Depends on which version of complex analysis. For Visual Complex Analysis, you just need calculus. And for the most rigorous version, you would probably just do two real analysis classes, not 4.

 

[modnarandom]

It's great that you have a lot of these things out of the way already! But I'd like to repeat other people's comments about how well do you actually know the material in classes you've taken. I've found that a lot of lower-level classes are computationally focused and don't actually require a deep understanding of the concepts described in class. Have you tried explaining what you did in class to someone else? But I definitely do think it's easier to understand a more rigorous treatment of a subject once you have a first exposure that let's you get a bit of basic intuition.

Have you taken any combinatorics or elementary number theory classes? They're a great way to teach you how to think mathematically without getting bogged down by abstract definitions (although one could say that this is later an important part of "mathematical maturity"). The reason I mentioned this is that I really hope you don't get turned off by all the abstraction that happens in a lot of topics in theoretical math before have some idea of what thinking mathematically is like. You could also try reading about complexity theory, algorithms or related fields in theoretical computer science. Also, have you heard of http://www.artofproblemsolving.com/ or math contests (e.g. math olympiads)? I think they're quite good for the same reason as I mentioned about learning some combinatorics (i.e. easy to understand problems, but interesting solutions). Another thing is that you have something you can use to check your understanding, which is really useful if you don't have a friend/mentor to discuss this stuff with. You mentioned that you're interested in double majoring with physics. What kind of physics are you interested in? That could provide some direction on areas of math to learn more about (unfortunately I don't know much physics at all).

From classes you've already taken: It looks like analysis, complex analysis or abstract algebra could be courses you would be able to take next. However, I highly recommend taking some time to learn how to think rigorously before you take them (take a look at some books in these subjects, e.g. Apostol, Stewart, Rudin, Stein & Shakarchi). Since you still have so much time left, it would be a nice idea to try to read these texts at your own pace and maybe write a blog or something trying to explain what you've read to yourself. I don't know if it's the best idea to rush through high school, but I guess it depends on how interested you are in other subjects or working on your social skills like others have mentioned. That having been said, I think you should probably /not/ stay in high school if you find it boring/like an endless time loop. Most importantly, have fun!

 

[mathshopeful]

I actually happen to be doing tutoring for all levels of math to sharpen my understanding in these courses. I tutor some of the upperclassmen that need tutoring and was able to strengthen understanding of calculus bc. I have heard that if one can prove/explain the concepts then one actually understands how to do the subject. Plus I get paid lots :) I'm tutoring for 30 an hour :p

I want to do either quantum or applied.

I like the social aspect of high school and I am unsure if an early enrollment to college would help with social life:p

 

[IGU]

Hi I am a sophmore in high school doing multivariable calculus in a local community college and next semester I will be going into linear algebra with differential equations.

Sounds like you're doing the right thing if this is helping you learn the subjects. One of the problems with CC classes like this is that they often are pretty bad. It's hard to tell if you are really learning anything much if the bar they set is too low.

The problem is that after differential equations and linear algebra the community college does not have any other math courses. I am doing the math classes a an outreach program by this community college and are taking the classes for free. Any advice on what to do next school year?

Well, it really depends on what you're after. Are you looking to save money on college by getting credit for various classes? Are you looking to learn interesting things regardless of whether it saves you money (i.e. it may gain you eventual placement but not credit)?

BTW I am interested in a math and physics double major

Does this mean that you're pretty much interested in applied math, e.g. things like number theory don't hold much interest for you?

There are many different paths you can take. Much depends on your specific goals and how willing you are to step off the beaten path. Are there any real universities near you?

My approach with home schooling my math kid, who is just now starting at Cambridge in mathematics, was for him to self study and audit lots of university classes. Other home schoolers just go to university early (mostly 14 and up). The basic story is that you can pretty much do whatever works for you if you're willing to take responsibility for your own path. There's no need to march to anybody else's drummer.

Check out this site for one ambitious approach to theoretical physics.

I'm happy to discuss specifics off the forums.