<p>What classes do I need to take to be a competitive candidate for math graduate school?</p>
<p>I'm just finishing my first year of classes now, but I hope to have taken the following classes during my undergraduate career:</p>
<p>Calc 1,2,3
Discrete Mathematics 1 & 2
Linear Algebra
Differential Equations
Number Theory
Algebra 1 & 2
Real Analysis 1 & 2
Complex Analysis
Topology
Differential Geometry
Probability
Advanced Linear Algebra</p>
<p>(I will also hopefully have 2 REUs and a senior thesis)</p>
<p>Is there anything else I need to take? I'm doing BSM, and I could possibly fit classes like Commutative Algebra, Algebraic Number Theory, Partial Differential Equations, etc. into my schedule, but how important is it to have taken those classes?</p>
<p>It depends on what field you want to go into in math. Make sure you take 4 years of a foreign language, in order to keep your options open (many grad schools, including their respective math departments, require foreign language proficiency in an “academic language”; i.e. French, Russian, or German. ) I’d also recommend at least 1 programming class.</p>
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<p>Bachelors of Science in Management, BS/MS. . . ?</p>
<p>If you’re looking at top math programs, your research will be important. Don’t overload yourself by taking too many classes though, you need the time to really think about the material, and sometimes, to play around with it a little. There’s a difference between real understanding and an “A.”</p>
<p>Thanks for your responses guys!
BSM=Budapest Semester in Mathematics</p>
<p>I’ve already taken one programming class, and I have comp sci credit from high school too. As for the language requirement, I’m fluent in spanish and proficient in Chinese, but unfortunately those won’t help too much for math grad school. Do you really think I need 4 years of the language though? I know a lot of grad programs have 2-semester reading courses to help grad students pass language exams.</p>
<p>I think 4 years of a foreign language is an overkill for the purposes of a math PhD. I wouldn’t take more than a single year of a foreign language just for the purposes of the language exam, or more likely just postpone it until I enroll at a specific graduate school and see what their requirements are. You are not expected to be fluent in a foreign language at the time you apply!</p>
<p>Did you talk to your professors about your proposed course sequence? Here is some advice I got, but that may not apply to your college or personal situation:</p>
<ul>
<li><p>There might be a lot of overlap between Discrete Math I + II on the one hand and Elementary Number Theory + Probability on the other. I would only take one of the two sequences at my own college.</p></li>
<li><p>I was advised to skip Differential Equations and go straight to Partial Differential Equations. It worked fine for me (although I did occasionally have to ask for help on ODE stuff). </p></li>
<li><p>Consider taking a graduate-level class if you have the chance. What you describe is the “standard” background for an undergraduate math major applying to graduate school. That is solid preparation for sure, but it might be beneficial to get your feet wet early.</p></li>
</ul>
<p>Yeah that’s kinda what I was thinking about the language lol.</p>
<p>The Number Theory course is technically a “graduate level” course, but it’s a grad course at a liberal arts college, and from reading the course description there is definitely some overlap…but oh well. It still covers some other good material (diophantine equations, etc). The probability class is required for the math major, and it has some overlap as well.</p>
<p>That’s interesting that you were able to skip ODE and go straight into PDE. Our college offers PDE this upcoming spring, so I’ll ask my professors what they would recommend.</p>
<p>As for taking graduate courses, I go to TCU and they have a weird system. All of my upper division courses are actually graduate courses (we get thrown in with the masters students) but they assign us a different course number, because TCU has a policy that no undergrad can take graduate courses. So I’m taking graduate Algebra1&2, Real Analysis1&2, Linear2, Number Theory, etc. (I’m planning on taking Topology, Complex Analysis, Probability, and maybe Differential Geometry in the Budapest Semester in Mathematics).</p>
<p>What is your opinion on taking courses beyond this? I’ve noticed a lot of students who are admitted into top-tier programs also have courses like Algebraic/Analytic Number Theory, Topology II, Commutative Algebra, and other “post-qual” courses under their belt.</p>
<p>Obviously it helps to have taken these courses, but how helpful is it for graduate admissions to have taken such courses? I’m trying to decide whether I want to cram all of my coursework together to facilitate room for courses like this (to have an edge on grad admissions) or if I should just stick with the courses listed above and focus on getting good grades without a jam-packed schedule.</p>
<p>I am not the best person to ask for advice because I am still an undergraduate student myself.</p>
<p>What I can tell you is that the more selective graduate programs will consider all of the classes on your list to be undergraduate classes. It is interesting that they are considered graduate level at TCU. Your number theory class, for example, seems to work exclusively with modular arithmetic and would be considered a lower-division undergraduate class at many colleges. Upper-division undergraduate classes refer to real analysis, abstract algebra, topology, PDEs, differential geometry of curves and surfaces, a first course in algebraic number theory or a second course in linear algebra. </p>
<p>The undergraduate students at my own college who go on to top-20 graduate math programs routinely take courses like algebraic and differential topology, algebraic number theory, measure theory, etc in their junior and senior year. I don’t know if it is necessary to have this background to be a competitive applicant, but it certainly helps. I also think it is beneficial to take a few of these classes before you make a commitment to attend graduate school because they give a first taste of what higher math is really like. You cannot do any interesting math until you have real analysis, abstract algebra and basic topology under your belt.</p>
<p>Yeah the Number Theory course isn’t too intensive. (Then again, neither is TCU’s graduate program…) I can’t really tell how legitimate their abstract algebra, real analysis, etc. courses are since I don’t really know much about the terminology in the course descriptions anyways, but I’m pretty sure they’re comparable to two semesters in undergraduate algebra and analysis (I can’t really imagine them being comparable to a top-20 graduate course).</p>
<p>Right now I think I’m on track to take all of the courses listed above, plus some extra courses like Commutative Algebra and possibly Algebraic Number Theory in Budapest during the fall of my senior year. I guess I’ll be able to take courses beyond that during the spring of my senior year, but I don’t think grad schools will really even see that since applications are due by January.</p>
<p>We don’t have too many math majors going to grad school here, since TCU is a big liberal arts university, but I know the one kid who graduated last year followed basically the same path (minus the commutative algebra and alg. number theory), graduated with good in-major grades, phi beta kappa, and he ended up getting into Rice’s Ph.D program.</p>
<p>My goal school right now is UIUC, which is ranked a bit higher than Rice, so I’m doing everything I can to be competitive for graduate school admissions :)</p>
<p>I’m planning to do Budapest the fall of my senior year, which would mean that I’d be taking the GRE and Math Subject Test in Budapest (they have a testing center there).</p>
<p>For applications, I’ll be filling out and submitting applications from Budapest, with a lot of correspondence via email with my advisor and professors during the application process, of course. I’ll be able to submit my peripherals (transcripts) from the United States.</p>
<p>Batllo brings up a good point. It is certainly possible to apply to graduate school from Budapest but it might be less than ideal. </p>
<p>Most graduate school applicants do a lot of soul searching in their fall semester senior year. What exactly do you want to study in graduate school? (e.g. which specialty in math? or maybe some field of applied math?) What do you want to do with your graduate degree afterwards? What sort of environment would you strive in? (small and close-knit vs large and diverse, high vs low pressure, etc) </p>
<p>All of these questions should factor into your decision which graduate programs to apply to. Fall semester senior year is the best time to have these discussions with your professors because your perspective will inevitably change over the summer as you gather more experience.</p>
<p>Also keep in mind that the program in Budapest is very intense. You might have the energy to adjust to a new social environment, keep up with academics and focus on graduate school applications at the same time. I wouldn’t.</p>
<p>Yeah, it would obviously be more ideal to not be out of the country when applying for grad school. But the way that TCU and Budapest’s schedules work out, the only real good time (coursewise) would be senior year. I’m planning to take Algebra 1&2 and Real Analysis 1&2 during my junior year, and Budapest doesn’t (to the best of my knowledge) offer any Abstract Algebra.</p>
<p>As far as what I want to study, right now I think Number Theory and Algebraic Number Theory look interesting…Complex Analysis looks interesting too (maybe Analytic Number Theory?). But I know very little about those subjects right now since I haven’t taken any graduate courses on them…so it will be a while (until my senior year) until I can really figure out what I want to study.</p>
<p>Afterwards, I would like to teach at the college level. What kind of environment would I strive in? (small and close-knit vs large and diverse, high vs low pressure, etc)…I’m definitely a high-pressure guy (have you noticed? I’m posting about graduate school as a freshman. haha) I think I would prefer a larger program, but who knows.</p>
<p>I’m looking forward to Budapest a lot if I end up going. I don’t know how much of the city I’ll get to see with juggling, like you said, a new environment, intense academics, gre’s and grad school applications, etc. but I’m willing to give it a try. I’ll definitely look at this Budapest plan with discretion, especially since I’m away from my professors, but at the same time I feel like I would rather go to Budapest and have a more competitive application as a result, and deal with communication difficulties (not being able to meet in person with professors).</p>
<p>Budapest offers tons of Abstract Algebra! From their current course list: Intro to Abstract Algebra, Advanced Abstract Algebra, Commutative Algebra, Galois Theory, Finite Simple Groups, Representation Theory of Finite Groups, etc. They also offer real analysis: Intro to Analysis, Real Functions and Measures, Functional Analysis.</p>
<p>I am sorry if my previous posts sounded judgmental. I sometimes do that without really realizing it. I am sure BSM would be a great experience and add to your resume regardless of when you go. It might indeed be better to finish the real analysis and abstract algebra sequences at TCU before going abroad; or it might be possible to go abroad early and use BSM as a chance for acceleration, so that you can take more higher-level courses at TCU after you return. </p>
<p>If you have not already, talk to a faculty adviser about your study abroad and graduate school plans before you sign up for classes for next semester. They might have a few surprising recommendations for you! </p>
<p>Each semester in college I thought that I knew what I should be taking based on the catalog descriptions of the courses and the chains of prerequisites, but my professors often had other suggestions. I ended up taking a lot of courses out of sequence and was effectively accelerated by a year as a result. I ended up: taking abstract algebra concurrently with calc 3, skipping ODEs, and ignoring the real analysis prerequisite of topology, among other things.</p>
<p>b@r!um:
Oh wow they do offer abstract algebra…and it’s right at the top of the page. Fail on my part…
I knew they had all those classes with functions and analysis in the name, but I wasn’t sure which ones were equivalent to Real Analysis 1&2.</p>
<p>I talked to my advisor today and she did say that it would be preferred for me to take Algebra1&2 and Real1&2 with the same teacher in order–like you just mentioned–since they would know exactly where to start off second semester, as opposed to taking one class in Hungary and one class in the U.S., where material may be skipped or overlapped. Also it would allow the professor who taught both semesters to better assess my ability in algebra/analysis. She also seemed surprisingly okay with me going the fall of my senior year, saying that we could communicate via telephone and email…</p>
<p>Ideally I could go the spring of my sophomore year too…but I don’t know how that works with prerequisites, etc. My main concern (and my advisor’s concern as well) would be taking courses like Topology in Budapest (which I heard from a participant really requires a good amount of real analysis) without having taken analysis. (Then again, you took a lot of classes out of order and did fine, so who knows…) The main issue with scheduling classes is TCU’s unintense grad program and brand new Ph.D program only allow algebra1, real1 in the fall and algebra2/real2 in the spring, and only offer classes like Topology, Linear 2, Diff. Geometry, Complex Analysis once every 4 semesters, so it requires a lot of maneuvering to fit everything correctly.</p>
<p>Dont worry about sounding judgmental–it’s math. Mathematicians have to be critical </p>
<p>trout:
Yeah I hear getting into REUs are tough. I’m going to apply for one for the next summer (between sophomore and junior year) when I’ll have Calc sequence, DiffEQ, Linear, Advanced Linear, Number Theory and maybe Statistics or Differential Geometry under my belt.</p>
<p>You mentioned a backup plan if I don’t get into REUs–what would you recommend as a backup plan? Right now my backup plan is…getting good grades and applying to a ton of REUs. lol.</p>
<p>I am a sophomore right now, and applied to 5 reus. I have been rejected from 3 of them. I don’t have the best GPA mostly because I didn’t do well in my school’s honors calc sequence, but I did pretty good first semester this year and almost got all As, didn’t take many math classes, but I did take linear algebra, got a b, and analysis, got an a-.</p>
<p>As for a backup plan, i have no clue as well. I’m rapidly trying to come up with one but the professor I talked to today said he didn’t have anything going on this summer.</p>
<p>Another question–do grad schools see what courses you’re taking second semester of your senior year at all?</p>
<p>I know they obviously wouldn’t see the grades…but since transcripts only show your completed grades (from the past 7 semesters), how do graduate schools know what you’re taking during your last semester?</p>
<p>I don’t know about official transcripts, but the unofficial one at my school shows courses without grades. Like the courses i’m currently taking are on it, and after I register for next semester’s courses those will be on it as well. It is under a courses in progress section.</p>
<p>Yeah I confirmed that with my advisor today. She said that they’ll see that you’re taking the courses from second semester. Whether or not they see your current grades…probably not.</p>
<p>So, the course list for next semester was released today. There is only 1 math class I can take next semester. Modern algebra. I was thinking about retaking honors calc i because of that. I don’t know if it would be worth it though. </p>
<p>My school is apart of a consortium so I can take classes at a bunch of other schools, but the classes I was interested in taking at another school (differential geometry, and complex analysis) were already offered this year and supposedly are only offered every other year. The other school hasn’t released a course listing for the fall yet though. </p>
<p>If there are no other options, maybe you could get a professor to let you do an independent study of a course? It wouldn’t be ideal, but you could certainly manage it if you’re only taking one other course.</p>
<p>My school is exactly the same as this–next spring they only offer number theory :/</p>
<p>As for retaking honors calc 1, I would do it just for the gpa boost. I’m pretty sure that grad schools see both grades, and I don’t think they’ll care too much about calc 1, but it certainly couldn’t hurt. You’ll obviously breeze through the course, boost your gpa and in-major gpa, and it won’t cost you much time since you’ve taken the course before.</p>
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