<p>so i'm going to finish calc bc at my school as a sophomore in high school and i was wondering what math classes i could take at a local college and how they would transfer to college when i eventually get there
i know of multivariable calc, linear algebra, ordinary differential equations and partial differential equations but I'm not sure of the prereqs or the difficulty of them
if you guys could help me out that'd be great. Thanks!
ps, I've been really good at math so far and i like it and I'm taking these classes because i want to not to have a "good looking" college application, and i want to be a physicist when I'm older (obviously)</p>
<p>Calculus BC is usually counted as 2 semesters or 2-3 quarters of freshman calculus.</p>
<p>In most not-super-elite schools, you would continue with multivariable calculus, linear algebra, and differential equations as typical college sophomore level math. These courses are the typical requirement for those majoring in physics. These courses are usually not heavily theory and proof oriented, unless you take honors versions if offered.</p>
<p>There may also be other courses like discrete math, which does not really depend on calculus and is mainly used in theoretical computer science, but is generally taught at the level appropriate for college sophomores, and may introduce proof techniques needed for college junior level math. Calculus-based introductory statistics may be offered as well.</p>
<p>If your can take courses at a four year school, the college junior level courses include proof and theory heavy courses in intermediate/advanced linear algebra, abstract algebra (groups rings, and fields), real analysis (theory behind calculus), and complex analysis. The latter three are often recommended for physics majors. (You might not be that far from completing a math major to go along with your intended physics major – this might help you both for graduate study and jobs and careers otherwise.)</p>
<p>You can, of course, also take a calculus-based introductory physics for scientists and engineers course sequence at the local college to get a head start on the physics courses as well. Such courses may have better transferability than AP Physics C.</p>
<p>It’s actually more important that you have a good math background than a good physics background when you start taking physics in college because the way it is taught is much different than in most AP courses. I took the honors sequence for freshmen physics and we rarely used numbers, instead of being about calculations, it was about understanding and applying central concepts. That being said multivariable calculus, differential equations, and linear algebra will probably be the most helpful courses for starting physics. Then later on you will need complex analysis, partial differential equations and Fourier analysis. </p>
<p>As for proof based courses Abstract Algebra and Real Analysis are really great, very interesting too. Another course you might want to look into is Topology which also has many applications to physics.</p>
<p>I would look into taking a multivariable calculus and a differential equations course. ODE’s are pretty much my whole life in sophomore physics at the moment.</p>
<p>thanks for the reply guys
@ucbalumnus: yeah, i intend to do math as well as physics in college. my dad did and said it was pretty manageable seeing as there is an overlap in classes. and my school doesn’t even offer either AP Physics C classes so I will be looking into some college physics classes as well. also, how much harder are the honors version of the classes as opposed to the regular? i know one kid at my school is taking mutlivariable at a college and has said its not that hard but I’m not sure if it is honors or not. the real analysis class you mentioned seamed pretty interesting by the way</p>
<p>Additional difficulty of honors college courses depends on the college. Honors math and physics courses are likely to emphasize more theory, proofs, and difficult problems (however, even regular courses in real analysis, complex analysis, and abstract algebra tend to be theory and proof heavy).</p>
<p>I took both AP Calculus AB and BC in high school and received credit for both. The next step for you in college would indeed be to complete the Multivariable/Diff EQ/Linear Algebra sequence. I’m taking Multivariable right now and will take the other two in the upcoming semesters. After that, I will have completed the highest level of math possible at my community college and will then transfer to a four year school to take the rest of the upper level math requirements.</p>
<p>As far as difficulty, it depends on your current grasp of calculus. I got a 5 on both of my AP exams and felt pretty confident that I had grasped calculus concepts. Multivariable for me right now has been a bit difficult. I’d say I struggle with about 50% of the material. However, that may be due to the fact that I am taking this class completely online.</p>
<p>If you took Calculus AB and BC over two years, multivariable calculus in college will seem more difficult because you took freshman calculus (AB and BC) at half the speed that it is normally taught in college.</p>