<p>Hi, I am a freshman student in a high school, the school enrolled me into Precalculus. However there is no challenging and i am getting 97%(3% is careless mistakes). I finished all calculus 1 and most of calculus 2 by myself. I am doing some multivariable calculus and some real analysis and some linear algebra by myself. If I keep this speed I will finish all undergrad and grad level math by the time I finish high school. I really enjoyed math, if I have this situation what can I do when I go to colleges?</p>
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<p>Mathematicians specialize in grad school, and the point of grad school isn’t really to take classes anyway…it’s to do original research. I don’t think anyone alive today knows all the math known to humanity. If you go to a top math school, they’ll find a way to challenge you. </p>
<p>Are you just reading textbooks? Do you have a mentor or anything similar? Are you doing math contests or summer programs, or are you planning to? Could you take classes at a local university?</p>
<p>you make me feel bad about myself</p>
<p>liek i couldnt even understand ap stats LOL</p>
<p>Hold on, I only know a handful of students who have studied graduate-level math while in high school (most of them are IMO medalists). You don’t “finish” grad-level math. There are so many topics out there such as algebraic geometry, topology, Lie theory, etc. that very few high school students can understand all of them. It’s fine to study these topics in high school, but make sure you actually understand them before going on to more advanced topics.</p>
<p>You may want to read the following article:
[The</a> Calculus Trap](<a href=“http://www.artofproblemsolving.com/Resources/articles.php?page=calculustrap]The”>Don’t Fall into the Calculus Trap)</p>
<p>Adding on to what others have said, there are a lot more math classes at universities than the basic calculus sequence, and MV Calc, and Linear Algebra/Differential Equations. There’s definitely other topics, that prepare you for research and the like, such as analysis, computational mathematics, logic (past the one unit geometry classes usually have), just to name a few. Of course, you may be able to graduate a year early or something from college, but I don’t think grad-level will be covered.</p>
<p>I followed the Chinese undergrad curriculum, since I am a Chinese. Their topics seems a lot harder than American/Canadian math materials. For MVC, all chinese universities make it first year. For real analysis, they offer it in the second year. Their textbooks are easy to understand, and I search the internet for variety of tests and quizzes for the material. Most the times I get about 75%-85%.</p>
<p>I obviously know that. MVC are first year in all chinese math books, I learn from them and some online lessons. Most of third year math in China are grad level in north america, I like analysis the best.</p>
<p>Thanks. I never move on to next topic until I fully understand the topic before it.</p>
<p>Ignorance Is Bliss.</p>
<p>You do this self-study, but do you have any verification or external testing of your completion. For practical purposes, what does this self-study gain you without having some verification. Also, how is your long-term retention? If you rush through all this and get good scores when you test a week later, how well will you remember it 6 months from now?
I would talk to someone at your school and see if there is a way you can actually take some advanced math classes.</p>
<p>See if you can get your school to move you into a more advanced math class. Why would you be taking precalculus if you’ve already learned calculus? Really, you should have had this discussion with them at the beginning of the year–at this point, they may say it’s too late to switch classes. Can you get some independent verification of your calculus skills? (A placement test, or you might have arranged to take an AP test last spring…) If you feel they are very solid, then maybe you can arrange to drop out of precalculus and do an independent study of multivariable. No point in wasting time in precalculus. For the rest of your years, if you can enroll in classes at a local college, that may be best. Otherwise, independent study, and when you get to college, make sure you go to a University where you can enroll in graduate-level classes if you are ready.</p>
<p>I think the Calculus Trap article was the perfect thing to post: it’s a mistake to just whiz through a ton of math courses without really challenging your problem-solving skills. I don’t really see the point of taking as much advanced math as possible, because if you want to major in math I’m pretty sure you’d just have to take it again anyway. Also, if you go to a school with a good math program, I imagine most of the courses would be much harder than what you would get by just self-studying a textbook. I have some friends taking Commutative Algebra and Measure Theory, and these two courses by themselves probably take 30+ hours a week. To really learn math, it’s not enough to just learn all the definitions and theorems and stuff: you have to struggle with lots and lots of really hard problems to build your intuition.</p>
<p>I think your time would be much better spent working on problem-solving by studying for math competitions. The best site for this is artofproblemsolving.com. The math for these problems is supposedly all high-school level, but there’s a ton of material that’s never taught in normal high-school classes, like basic combinatorics, number theory, advanced synthetic geometry, inequalities, etc. In my experience people who excelled in high-school math competitions are better prepared for college than people who just took a ton of college courses but didn’t get as much problem-solving practice.</p>
<p>Certainly the OP should do whatever competitions he is able to participate in. Practice solving really hard problems that are beyond the scope of typical math classes. There are plenty of online resources for this. </p>
<p>But I disagree that it is a bad idea to self-study college-level math, (provided you are able to understand it without help). I disagree that you will just have to take it all over again. That will depend on the policy at your University, and also how well you really do know the material. </p>
<p>Also, OP, don’t worry, you are not going to finish all undergrad and grad level math studying in your spare time in high school.</p>
<p>i did verify myself with real university tests and exams. my dad is M.Sc. in mathematics</p>
<p>By the way I got 16/18 in a real university calc 2 exam</p>
<p>well my school is REALLY REALLY tricky and they doesnt allow me to take a placement exam</p>
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This. 10char</p>
<p>Make USAMO then come back and tell us</p>
<p>do the Amc/aime/Usamo series.</p>