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Running out of Math Classes

  1. Oct 21, 2014 #1
    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
  2. jcsd
  3. Oct 21, 2014 #2


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    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.
  4. Oct 21, 2014 #3
    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?
  5. Oct 21, 2014 #4
    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
  6. Oct 21, 2014 #5
    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.
  7. Oct 21, 2014 #6
    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.
  8. Oct 21, 2014 #7
    Yes I am taking statistics this semester and to be honest it is a complete joke
  9. Oct 21, 2014 #8
    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.
  10. Oct 21, 2014 #9
    where are you taking these classes? online?
  11. Oct 21, 2014 #10


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    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.
  12. Oct 22, 2014 #11
    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
  13. Oct 22, 2014 #12


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    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?
  14. Oct 22, 2014 #13
    The minimum requirement for a GED is sixteen an I am 14 turning 15 next year
  15. Oct 22, 2014 #14


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


    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 text books. E.g. if you google "number theory pdf", so would find:


    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.
  16. Oct 22, 2014 #15
    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
  17. Oct 22, 2014 #16


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    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.
  18. Oct 22, 2014 #17
    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
  19. Oct 22, 2014 #18

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    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."
  20. Oct 22, 2014 #19
    *(Do you what you think is best but really think about this)

    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
    Last edited: Oct 22, 2014
  21. Oct 22, 2014 #20


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    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.


    Check the section 'Eligibility' under 'Test Administration'.
  22. Oct 22, 2014 #21
    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
  23. Oct 22, 2014 #22
    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
  24. Oct 22, 2014 #23
    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.
  25. Oct 22, 2014 #24
    Wouldn't I have to take analysis 1,2,3, and real analysis first though? I will look into that book thank you.
  26. Oct 22, 2014 #25
    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.
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