Rising senior's math classes

Colleges & Universities A-Z Massachusetts Institute of Technology
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<p>Hey everyone I'm going to be a HS senior in the fall and I'm looking forward to apply to MIT and hopefully become a mathematics major. I have some quick questions about what classes you guys think would benefit me the most to enroll in, both to look good in my application and prepare me for the academic workload once/if I get accepted.</p>

<p>To start things off I currently attend a small private school where all the courses are taken at a large public university in Texas (The University of North Texas) so that should give you a bit of a gauge of how rigorous the courses are comparatively.</p>

<p>What I have taken already:</p>

<p>Pre-Calculus and Cal I - The Cal I class is the first in a three part series on calculus, so the course I've taken so far covers at least as much material as is on the AB test.</p>

<p>Real Analysis I - At UNT this course is both an introduction to real analysis as well as the first rigorous introduction to proof and logic within the math department.</p>

<p>What I plan to take:</p>

<p>Cal II and Cal III - These courses complete the calculus sequence, and cover the material within the BC test as well as multivariable with some introduction to vector thrown in as well. Cal III finishes with Green's and Stoke's Theorems as the most advanced subjects it includes.</p>

<p>Real Analysis II - Like I said earlier Real Analysis I is both an introduction to proof and logic as well as real analysis course, and thus it doesn't get very far in terms of real analysis topics (it does get through basic topology though). RA II builds on that to cover many of the topics in calculus, including series and sequences as well as pretty much all of the basic calculus theorems up through multivariable.</p>

<p>So my question is a toss up between two classes I could take in the fall:</p>

<p>Linear Algebra - From what I've heard from other students who've taken this course already it's a purely computation-based class, with little to no concern for the underlying theory. It covers pretty much all of the topics you'd expect in a LinAl class, and really is meant to be a class that's not too painful for non mathematicians to take. So on one hand I think it might be helpful to learn many of these computational techniques before going into MIT level math classes, but on the other I know that I'm probably going to be bored out of my mind taking the class.</p>

<p>Abstract Algebra - I don't know as much about this course, as it isn't always offered and nobody I know has taken it (although I will have two friends who'll be enrolling in it with me). What I do know is that it's focus will be on building our current system of algebra entirely from the fundamental axioms of mathematics. Since I really enjoy the more abstract and theoretical side of math (Real Analysis was my most enjoyable I've taken so far) I think that I'll love it. Also the instructor will be the head of the math department, and he's supposed to be one of the best teachers when it comes to really advanced, abstract courses. So I think that I'll love the class, but what I learn might not have as many direct applications as LinAl might.</p>

<p>So what do you guys think would be a better bet to take in the fall? Linear or Abstract Algebra? Thanks for taking the time to read through this.</p>

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<p>Take what you’ll enjoy - it sounds like both options are difficult classes, so don’t worry about that too much =D. I personally would take Abstract Algebra, since MIT offers Linear Algebra and as a math major you’ll end up taking that anyway =D. But it’s not going to make a difference in admissions decisions - assuming your grades are good, your load seems to show that you are capable of the courseload. That’s all they’re looking for as far as academics are concerned =).</p>

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<p>you’ll take abstract algebra as a math major.</p>

<p>I would take abstract algebra. Linear algebra is pretty dry. Abstract algebra is much deeper.</p>

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<p>i am in course 8 and 18 at MIT.</p>

<p>re: collegealum314:</p>

<p>linear algebra can be approached theoretically – the problem is that it’s extremely useful in a variety of engineering-ish fields to focus on matrix techniques instead of linear transformations in general. i’m a math/physics major, and i think linear algebra is pretty interesting from the more abstract perspective (“linear algebra done right” by axler is a good reference for this sort of approach)</p>

<p>probably the best course you can take to learn linear algebra “the right way” is an intermediate quantum mechanics course (e.g. 8.05 at MIT. no, you do not need to know 8.04 to understand and appreciate 8.05. even 8.321 maybe – i have some friends who took this as their first introduction to QM). the reason is that quantum mechanics typically requires vector spaces having uncountably many dimensions – by definition, in these sorts of spaces, you can’t talk about matrices at all, so you use the “real” methods.</p>

<p>my opinion about your choice:</p>

<p>linear algebra is cool, but abstract algebra is ten times cooler. i’m serious: galois theory is <strong>beautiful</strong>.</p>

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<p>“linear algebra can be approached theoretically – the problem is that it’s extremely useful in a variety of engineering-ish fields to focus on matrix techniques instead of linear transformations in general. i’m a math/physics major, and i think linear algebra is pretty interesting from the more abstract perspective (“linear algebra done right” by axler is a good reference for this sort of approach)”</p>

<p>I’m going to guess that University of North Texas doesn’t offer two versions of linear algebra like MIT does, so it’s probably geared toward the applied people. You can’t make abstract algebra boring, however. If given a choice, I’d take abstract algebra. </p>

<p>It probably would be easier to impress a faculty member for a rec with your prowess in abstract algebra assuming you can do it, because applied linear algebra is fairly straightforward.</p>

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<p>Thanks to everyone for their input so far. I think I’ll go with abstract, although I’m still open to hearing any other input members of this board might have.</p>