<p>I am currently a 4th year student at Penn State, and I am looking to try to apply for a graduate program in Mathematics. My Cumulative GPA is 3.62, and my in-major math GPA is 3.77. I also have a minor in economics
I want to pursue a graduate degree because I feel as if I want to learn more mathematics, and that my undergraduate curriculum has not satisfied my thirst for it. There are a few problems although:
1. My parents don't really approve. They would prefer me going down a more applied field like engineering (not a problem that we can really fix...just throwing it out there).
2. I feel I have not taken enough undergraduate math courses. I am rather worried if I can stretch out another year of debt just to take these courses here at Penn State as an Undergrad. I am an out of state student, and I would probably prefer if I had to stay in undergrad status to move to an university in my state. The courses I really feel like I am missing and are super essential are: Analysis II, Abstract Algebra, Toplogy. Would it be extremely difficult to get into a program with missing these courses? I have taken the general calc sequence, Honors Diff Equations, The standard linear algebra course and the advanced one aswell. I have also taken 2 semesters of analysis, probability theory, Discrete Mathematics and Mathematical Game theory.
I am planning on taking my regular GRE's sometime later this year, and possible the Math GRE's aswell. I am sure those would have an heavy impact.<br>
The one thing that really scares me is my lack of graduate studies based courses, and the time and money I would loose staying another year taking them as an undergrad.</p>
<p>I would think algebra and analysis are almost a must… I don’t know if your past courses were really proof based (they seem more like applied math), but make sure you have a lot of exposure to that before grad school</p>
<p>Let this be your guiding question: what do you want to do with your PhD in math?</p>
<p>There are a number of PhD programs that admit students with significant gaps in their undergraduate math preparation. However, a degree from one of those might limit your job opportunities significantly. (You’d probably be down to teaching jobs. Graduates of these programs rarely qualify for research positions, and industry will judge you by the prestige of the program you graduated from.)</p>
<p>If you really wanted to be a research mathematician, you’d probably want to get a much stronger foundation (including a few graduate courses plus more in-depth exposure to one specialty) and then apply to the top 20 PhD programs. There are three ways of doing that:
a) Stay another 1-2 years as an undergraduate.
b) Get a terminal Master’s degree before you apply to PhD programs.
c) Graduate as planned, get a job and study math on the side.</p>
<p>If you just want to take a few more math courses but have no interest in academia, I share the concerns of your parents. Why not choose a graduate program that combines the math you love with an area of application, to prepare you better for the job market? (Here at Stanford, for example, it is not rare for engineering students to take “pure” classes in the math department such as algebra or topology. A few engineers even venture into the graduate math curriculum.) </p>
<p>You don’t need to limit yourself to engineering either. I’ve had math major friends go into fields as diverse as biostatistics and management science. What could you see yourself doing for a living?</p>
<p>First of all thank you all for the responses and feedback, @eaglesfan- I understand what you are saying. I did take a few proof based math courses. For example the two semesters of analysis (real and classical analysis) were proof based, as well as discrete math and the advanced linear algebra course.
At this point, I applied for the penn state MASS program, to take a few more rigorous courses. If I get accepted, in the fall I would take a course in Polynomials, Brownian motion, and Geometric Topology. Also this program would help pay for my tuition as well and help me afford another year maybe of college. If not, I am planning on just taking one more semester of classes in topology, abstract algebra, and Analysis II. Hopefully that will all fit in perfectly, and maybe I will take it non-degree seeking somewhere near home.</p>
<p>@Barlum- I understand what you are saying. I am heavily interested in academia although, and all of the applied fields I tried do not interest me. The idea of engineering bores me, and business/economics isn’t the most interesting but manageable. I love the purity of math, and I could see myself in academia. I want to see myself in math, not that other opportunities don’t appeal to me, but it is what I enjoy the most out of school currently. Thank you for the good advice although, it is very helpful in deciding.</p>
<p>Depending on where you want to go, you simply will not stand out (or perhaps even be determined as ready) without a second semester of analysis, and abstract algebra. I wouldn’t say topology is particularly necessary (and you may get a bit of that in analysis depending on your instructor) but analysis and algebra make up the core of most pure math graduate programs.</p>
<p>Is there any reason you just want to work in academia? Do you enjoy teaching that much, or just want a posting where you can “do math” and maybe teach a class or two on the side?</p>
<p>@ANDS!- Thank you for the response and advice. I feel a full 3 credit topology course would be more helpful. A professor once told me the core to a math grad program are these 4 courses: Functional Analysis, Abstract Algebra, Linear Algebra, Topology.
Regardless, the max I would wish to stay in 1 year, maybe even one semester (if I could fit it all in- might be tough but well worth the challenge).
Would there be any hope if I took some courses as a non-degree student at another university maybe even? Would any programs anywhere accept my curriculum at the moment?</p>
<p>I like doing and learning math. I want to learn more, and research further. I don’t mind teaching, I have nothing against it or for it. I guess easiest to say, I have no feelings for teaching…</p>
<p>I think that a point-set topology class will be tremendously useful, even though it may not be absolutely necessary for admission. Both your graduate functional analysis class and first-year graduate algebraic/differential topology will be MUCH easier if you are comfortable with point-set topology, and many of the better graduate programs do not include it their standard graduate curriculum because most students have seen it before.</p>
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Yes, you can do that. Auditing might be fine, even. I audited 6 graduate classes before I applied to PhD programs in math. These courses did not appear on any transcript, but I did get letters of recommendations from two of the instructors (who I was also working with outside of the classroom). My graduate applications turned out fine.</p>
<p>I learned a good amount about point set topology (not a whole course, but a satisfying introduction) in Classical analysis I. Although I understand a good full introduction course in point set topology may be more useful.</p>
<p>A question regarding auditing courses: You stated you audited 6 courses. How did you let grad schools even know that you taken these courses other than the letters of recs from the prof and proof of outside research? I have auditing a course on Math Stats and Stochastic Modeling. I don’t have much proof to show for it though…</p>
<p>Letters of recommendation saying I did all of the work for the classes were enough for the people reading my application, I guess. A few programs also asked for a separate list of all math courses I had taken; I included my audited courses in that list. </p>
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You really want to know how to work with topologies in the absence of a metric. (In other words, if you defined open sets in terms of balls, or if you defined closedness/compactness in terms of convergent sequences, your story is not as general as you’ll need it for functional analysis.) If you haven’t seen point-set topology in full generality yet, I’d encourage you to take a class or at least work through the basic framework on your own before you start grad school. Gaps in point-set topology were the #1 reason why grad students failed their qualifying exam in analysis in my year.</p>