<p>Hi everyone,</p>
<p>I was wondering if anyone here has ever taken or is taking a course in Abstract Algebra while they were in high school or if you know someone in high school who took this course. I am a senior in high school and I am taking Abstract Algebra. Thus, I would like to get any idea of how elite I am.</p>
<p>You are the best there ever was, and the best there ever will be. That is how elite you are.</p>
<p>Classes like this seem to be pretty common for schools with decent math curricula.</p>
<p>Abstract Algebra doesn’t have many prereqs, so I can’t say how impressive that is. Did you take Diff Eq, Real Analysis, Lin Alg, etc.? If you just skipped all of them then Abstract Algebra is no better than any of them.</p>
<p>My friend is in Abstract Algebra; he took Multivariable Calculus with Linear Algebra in sophomore year, then a Diff EQ independent study junior year, and now he’s doing Abstract Algebra senior year. We have no clue what that really entails - he’s the only one doing it in our high school. So OP, you are really elite.</p>
<p>Typical minority thing to do.
Average grades, average math background, taking a course that’s not at all appropriate for them.
Have you even taken an intro to proofs class? Or any other type of theoretical course?
You’d be better served taking calc bc or a multivariable calc course if you want to challenge yourself.</p>
<p>I’d love to meet the person who advised someone who got a 4 on the calc ab exam to take algebra.</p>
<p>I’m white, which doesn’t make me a minority. If you were looking at other threads were I wrote that I put on my application that I am Hispanic, that is because my parents are from Argentina, but my grandparents are from Europe/Russia. However, I am a minority because I am Jewish, but that does not with the negative associations that you are suggesting.</p>
<p>My Abstract Algebra course is taught by the person who recommended to me. The course includes an introduction to mathematical proofs, and the only other true prerequisite for this sort of course is one’s ability for higher level mathematical think, which I have. Furthermore, I am not attempting to optimize my education with what will be the most useful. I am taking this course because I am not going into mathematics and it will be the only opportunity to learn this stuff. Way more people know calculus than abstract algebra. So I suppose it is the “Typical minority thing to do”, since Jews value knowledge for its intrinsic worth.</p>
<p>Also, Calculus BC is not an appropriate course to proceed Calculus AB because the bulk of the topics are the same. Calc BC does not start where Calc AB leaves off. Some people will take pre-calculus and then BC calculus. I skipped pre-calc and went straight to AB calculus after Algebra II. Yet know, when I finish high school, I will know abstract algebra, and the very slight deficit in calculus will be covered for entirely and much more comprehensively when I go to college. Plus, I am taking statistics this year, which is incredibly applicable to a myriad of areas.</p>
<p>One more thing. The other person in the class only got a 3 on the calculus AB exam, which would make me the top student in the class to begin with.</p>
<p>I was going to but I couldn’t fit it into my schedule. I’m a junior. Next year I’ll be taking multivariable/vector calculus and diffEQ or an analysis class.</p>
<p>This guy in my grade is going it - he’s taken BC equivalent, Lin Alg, DiffEQ, Multi, Complex Analysis before this. </p>
<p>YOU ARE THE .5%, according to my school. Or better.</p>
<p>You’re probably at the top of a strong school. It’s not possible to pass judgement in a broader sense because “I took abstract in HS” doesn’t really mean anything since not all classes are created equal.</p>
<p>pfft Algebra, I took that in middle school</p>
<p>The thing with having “college level courses” taught at a high school is that each high school will of course teach it with a different difficulty level. While algebra might look impressive on paper, if the only people in the class couldn’t even score a 5 on calc AB, then I highly doubt how much algebra is actually taught in the course, especially since there doesn’t appear to be any prerequisites. At my school, one of the prerequisites to algebra 1 is an analysis course that requires a 5 on calc BC to take. In addition to that, half the class usually drops this analysis course (all of whom scored a 5 on BC), and even fewer make it to algebra. </p>
<p>As for the implied meaning of your question, which is likely asking how impressive it is to colleges, I believe it wouldn’t be very impressive. As noted before, “college level courses” are taught at wildly different difficulty levels, and colleges will have clues as to the difficulty of your course: your score in calc AB, lack of other math courses, etc.</p>
<p>The elementary abstract algebra course at my school is at the 4000-level and requires linear algebra and an intro to proofs course, which in turn requires at least calculus 2. If your course doesn’t have prereqs other than calc AB I don’t know how rigorous it will be…</p>
<p>You should consider Harvard. They have an awesome, very rigorous abstract algebra course here, Math 55, that would definitely build very much upon the course you’re describing. I have too many disparate academic interests to commit 40 hours a week to math problem sets, so I’m not taking it. However, I’m friends with several of the people taking it, and the proofs I’ve talked with them about are beautiful, elegant, and not at all trivial. Building up, proof by proof, to subjects like Galois theory, from the Peano axioms, (in a semester!) would be seriously difficult for almost anyone, but if you appreciate the elegance of mathematical logic, I strongly recommend considering Harvard simply for Math 55 alone. </p>
<p>As for how rare that is, it is certainly very rare. I studied abstract algebra at an intro level independently over junior and senior years, but it was informal and leisurely in pace. Your background in application sounds decent as well. You will need to self-study multivariate and linear algebra over the summer, but other than that you’re very strong in mathematics.</p>
<p>Thanks for all the comments, they answer my question very thoroughly. To be honest though, I am not that good of a student and I do not go to an exceptional high school. I am not hardworking or studious. I get by on my wits. I see that the people who typically take Abstract Algebra are way more advanced and dedicated students than I am, and it is true that the course I am taking does not go at nearly the pace or the depth of the Abstract Algebra courses others are taking. My course is only just now about to finish set theory, intro to proofs etc., before starting abstract algebra for the last month of the semester. However, the class covers the same topics that would be taught elsewhere and I think that during the summer after the course I would know enough that I could learn any topics that we may not get a chance to cover in depth.</p>
<p>Abstract Algebra prerequisites are only to show that the student can think logically. On a case by case basis however, one may even find a high school student who is taking Algebra II for some reason in spite of a profound ability for logical thought, who would be able to comprehend a vast amount of topics in Abstract Algebra.</p>
<p>Both me and my boyfriend took Abstract Algebra in high school (him senior year, me the summer after sophomore year). I liked it a lot, it helped me learn to prove things and solidified my interest in math.</p>
<p>Abstract Algebra is a course that has about fifty different names that varies by institution. </p>
<p>Saying X took Abstract Algebra after he took Y math class, or I took Z in high school means little when you’re not talking about the same class.</p>
<p>See, some more advanced courses in abstract algebra introduce complex ideas to attain interesting, even more complex results-- often without explaining either the practical use or motivation for the original ideas. For example, I know that Math 55 brings up eigenvectors and uses the theory behind them in some very difficult proofs, assuming a previously-achieved and thorough understanding of them.</p>
<p>Here’s an example of the type of work expected in a college-level rigorous course in abstract algebra: <a href=“http://isites.harvard.edu/fs/docs/icb.topic92739.files/ps9.pdf[/url]”>http://isites.harvard.edu/fs/docs/icb.topic92739.files/ps9.pdf</a></p>
<p>Are you suggesting that Math 55 is a standard college-level rigorous course in Abstract Algebra… Really?</p>
<p>Yeah, lower div math is a joke</p>