<p>I am majoring in math, so I obviously have certain requirements to fulfill for my major (plenty of analysis, algebra, etc.). But I also get to choose many of my major classes. Are there any classes in particular that competitive grad schools are looking for? (Keep in mind that my school's math department has a mix of theoretical and applied math classes that I can choose from.)</p>
<p>I suppose it depends what kind of grad school you are looking for (i.e. Applied or Pure). In either case, however, more pure math classes can never hurt. I’ve heard Complex Analysis is really fun. Much more than Real Analysis, anyways.</p>
<p>But really, grad schools don’t really care as long as you cover the essentials: Analysis and Algebra, and usually something Topology-ish.</p>
<p>Thanks!</p>
<p>Also, which is more important: a slightly higher GPA with fewer math classes, or a slightly lower GPA with more math classes? (And by more, I mean more advanced. Not, like, taking high school calculus classes over again.)</p>
<p>How many math classes per semester would you recommend I take before graduation?</p>
<p>My professors recommended the following as preparation for pure math:</p>
<p>Highly recommended:
2 semesters of real analysis
2 semesters of abstract algebra
1-2 semesters of topology</p>
<p>Recommended for a good general math background:
complex analysis
partial differential equations
differential geometry
number theory
combinatorics</p>
<p>Recommended to get your feet wet and demonstrate interest as well as aptitude:
a few graduate courses in your primary area of interest</p>
<p>I would also highly recommend a programming class or two. My programming background has helped me again and again.</p>
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If you are aiming for graduate school, you primary focus should be to learn math. Only take as much math as you can comprehend and retain. If your grades suffer, you are probably not on top of the material.</p>
<p>Thanks!</p>
<p>How would this differ for applied math? Does it depend on which specific area you want to focus on? Is it drastically different from the pure math track?</p>
<p>Applied math is such a general term that it is impossible to give you a general answer. Statistics entails very different classes from numerical analysis/scientific computing, for example. Many applied math programs won’t need abstract algebra or number theory, but if you wanted to go into cryptology, these might be the single most important courses on your transcript. Topology is usually considered pure math, but there are applied topologists out there that would recommend you take as much geometry and topology courses as available to you.</p>
<p>In short, there’s no general answer. If you know what you are interested in, you can ask your professors or experts in that field for advice. If you are not sure yet (and most college freshmen are not), just take whatever math classes sound the most appealing to you and see where that path leads you.</p>
<p>Thanks! That was my plan–to take as many courses as possible and see which ones I’m drawn to, and go from there. I just wanted to make sure there weren’t any all-important classes that everyone who goes to grad school for any type of math should have taken, aside from the major requirements. So again, thanks!</p>
<p>I have to second what Barium said in both posts. It is really important that you take a programming class. My grad program isn’t called “applied math” but it is an area of applied math and I can’t tell you how glad I am that I took a couple programming classes back in the day. CS classes have probably been the most helpful/important out of major classes I have taken.</p>
<p>How much programming would you recommend? I am still in high school, but my school doesn’t offer any computer science or programming courses. So I’ll have to start from intro courses. How far should I go?</p>
<p>I would recommend Intro and Data Structures. After Data Structures computer science becomes more technical. You would learn how to build a processor, how to implement a programming language, how an operating system works, etc. Interesting stuff but not relevant to math.</p>
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<p>Especially to an algebraist and/or geometer, because complex analysis involves lots of invariants using some geometry where you can determine data at a point easily. I can’t see it NOT being fun, but plenty like real analysis by itself. I am not one of them.</p>
<p>As for coursework, I’d concentrate on learning, but not sacrifice too much just to get perfect grades. Make sure you’re challenging yourself and doing good stuff. Make sure you actually like some areas of math a lot, so that when you apply to graduate school, you have SOME idea of what you want to do.</p>
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<p>I think everyone ideally should know some algebra, real analysis, complex analysis, and some topology. Besides that, if with applied interests, be sure to take the programming suggested above (up to data structures), and take some numerical analysis and ODEs and PDEs, and you really have a good foundation.</p>