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Usually the options become quite broad after those courses. Usually, the course taken after is advance calculus, complex analysis or partial differential equations (NOTE: ordinary differentials comes before partial differential equations at introductory level). With the foundations you learned, beginning with algebra, calculus, ODE's and Linear Algebra, you can now tackle on more advance courses such as: abstract algebra, number theory, upper division ODE's (this means you'll be going into more complex topics than you covered in your first ODE course: casic existence and stability theory, more difference equations, and boundary value problems), real analysis, differential geometry (which is basically a hardcore more advance calc-3/ vector calc). If you're pursuing engineering, you'll probably be required to take a course called "discrete mathematics" some type of probability/ statistics course (for engineers and physicist) and topology.
However, you should note that all schools are different in their requirements and some schools don't require many of those applied courses such as PDE's and differential geometry. Since most mathematicians don't really care about the application of it, that's what they have engineers for. Instead, they care more about proofs, theories, and such. So you'll probably be required to focus on more theory based courses dealing with proofs and all this bull crud.
So is it better to take Advanced Calculus after Linear Algebra?
I would take complex analysis or mathematical reasoning if offered :)
Okay, thanks, but do you know if community colleges like LACC let you take the Calculus 3 (multivariable calculus) test and write you a proof that says you know the material without taking the class? I know that if you don't take the class, you don't get college credits, but I'm fine with that. And do you need to pay for taking the test?
Lol. You're from LA. Awesome. And no. I don't think that colleges offer tests like that to sort of "skip" the course and get credit for it. You can always talk to the professor to see if you could maybe take one of his finals to get exempt from taking the course, but the final decision is usually given by the department chair of mathematics and is very rare. It wouldn't hurt to try though. Usually schools only accept AP scores of 3 or above to get credit and it's usually for Calculus 1 and 2. Oftentimes, people are required to start with Calculus 3. and also, by the way, LACC is a community college and does not offer courses such as complex analysis, PDE's or any of the others mentioned above, you must take those courses at a 4-year university when you are enrolled OR you can take them through open-university. If you do that, I suggest CSULA as it's relatively close to LACC and also cheaper than UCLA and or Loyola Marymount.
So as a high school student, do I need to pay for taking the math class at CSULA? It's okay if I don't get college credits, all I want is to take the test and let them write me a paper that has the score on it and that I know the material. Do I need to pay for that at CSULA? Also, is CSULA a 4-year college or what?
Can you give me your email address?
aBBOT math chat now
If you are not enrolled at CSULA then you must pay out of pocket (that means no financial aid). In college, you are responsible for paying for your classes. I believe that it's $298/ unit. I'm not sure how many units complex analysis is at CSULA, but I'm guessing it's maybe 3, which means it's around $1000 dollars (IF you're not enrolled at CSULA). Also since you're in high school, the math is much tougher in college. Often requiring more independent and critical thinking from the student, which is the main reason they DON'T give credit and or exams to students to place in a Calc II or Calc III or above, math course. I suggest you not skip so that you can adjust to college level mathematics. It can sometimes be overwhelming for freshman since the pace goes much faster than it does at high-school level. Often covering 2-5 chapters in a 50-90 minute lecture. Which means that they will not go into great detail and expect you to have mastered the material by the time next lecture comes around as well as know how to apply it in a variety of ways to more complex problems.
So will they charge fee for taking the test only? I just need the score and it's okay if I don't get college credits. Can you please give me your email address?
Most schools have an "entrance" exam to see what level of math you're at. Usually if you do well, they place you in Calculus 1 or 2. And it is free. However, if you're not taking any Calculus AP courses, such as AB or BC, then you will not get exempt from this placement exam and will be placed in the math course they feel you are at.
based on your score on this placement exam.
If you don't mind, can I give you some math questions? So I know where you are at in math. I am curious as to why you want to skip Calc III it's a really fun class in my opinion.
It's pretty late. Can I have your email address so I can contact you later? I have more questions.