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Undegraduate Tips (thanks for reading!)

  1. Aug 2, 2011 #1
    Hi,

    I'm a raising college sophomore. I took Calc I through IV in high school and I'm on track to major in a completely different field (non-science) which I also love at a fine arts school which doesn't have a math dept.

    After college, I want to get a PhD in Math. To gain admission and also because it would be very interesting, I would like to do some unpaid research for some professors at a nearby university but I'm not sure how to go about that. I've contacted one professor about research but he said he only worked for kids from his school. How could I increase my chances of getting such a position and what advice do you guys have on how to present myself in the best possible light given my background?

    I can take one math class a semester as an elective for the next 3 years. What 6 classes should I select to get into a good math grad school? I'll take Linera Algebra in the Fall, but then is it better to take "core classes" like Intro to Modern Analysis and Algebra or is it better to self-study the material and register for more advanced classes which have these classes as pre-requisites?

    Thanks a lot for your answers guys! I know this is super long and I appreciate your time.
    MathGeeko
     
  2. jcsd
  3. Aug 3, 2011 #2
    Without an undergrad degree in math don't expect to get accepted to any graduate school. While this may be harsh you need to find a different school that offers a math program.
     
  4. Aug 3, 2011 #3
    I suspect this is the case, too.
     
  5. Aug 3, 2011 #4
    I don't see how you can expect to get a PhD in math from a good school without taking many more (advanced) math classes than you will be taking. You may have to do an extra year of just math classes before applying to grad school. Why not go to a school with a math department, major in math, and minor or double major in the *completely different field*?
     
  6. Aug 3, 2011 #5

    micromass

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    You can't get into math grad school without majoring in mathematics. In your plan, you will have taken about 6 math courses in total. To go to grad school you'll need about 20-30 math courses. They really aren't going to accept anybody with just 6 courses...

    If you're ultimate dream is to do a math PhD, then major in math. Or at least do a double major!!
     
  7. Aug 3, 2011 #6
    Thanks a lot for your replies guys, I appreciate it!

    Actually I believe you need only 13-14 math courses (about 40 credits for a major at most schools, which is 13-14 classes worth 3 credits each).
    Since I've taken 4 already, if I take 6 more, I'll be at 10 which is a little more (about 3 classes) than a minor. I was thinking of taking the 3 or 4 remaing classes during the summer at a university or as a visiting student for a semester.
    I could also go to free grad school in my field, take 5-6 more math classes (total of 48 credits so far) as electives and then apply to math PhD? Does that make more sense?

    How much does the Putnam fellowship, chess prizes and GRE scores count?

    I choose my major because I hope I can do research which combines both. Few people have but there is interesting stuff to find there.
     
  8. Aug 3, 2011 #7

    micromass

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    Here are all the courses I took as an undergraduate:

    Discrete mathematics
    Linear algebra
    Affine and projective geometry
    Differential geometry I
    Differential geometry II
    Algebraic geometry
    Coding theory
    Stochastic Processes
    Analysis I
    Analysis II
    Functional Analysis
    Topology
    Complex Analysis
    Measure theory
    Probability theory
    Mathematical statistics
    Differential equations
    Logic
    Algebra I
    Algebra II
    Algebra III
    Numerical mathematics I
    Numerical mathematics II
    Bachelor project

    This amounts to 24 courses. I suppose that this is a typical undergraduate curriculum. In my country, they would not accept you at all with just 14 courses... But perhaps america is different.

    Anyway, the grad committees will find it pretty strange that you want to do a PhD in mathematics, while you did a major in something else. Be prepared to explain this.
     
  9. Aug 3, 2011 #8
    Which of these classes did you consider
    1. Most challenging
    2. Most essential to your sucess in grad school
    3. Most important to the long-term developpement of your math abilities ?

    Thanks a lot
     
  10. Aug 3, 2011 #9

    micromass

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    That would be measure theory and probability theory. It was quite difficult, but very fulfilling.

    All of these classes have helped me in one way or another, but the most important classes would include

    Linear algebra
    Affine and projective geometry
    Differential geometry I
    Differential geometry II
    Algebraic geometry
    Analysis I
    Analysis II
    Functional Analysis
    Topology
    Complex Analysis
    Measure theory
    Algebra I
    Algebra II
    Algebra III

    All of them. Seriously. There isn't one class that I regret taking. Not all classes are useful to me know, but I'm very glad I know something about it anyway.
     
  11. Aug 3, 2011 #10
    Thanks a lot! So if I took:

    Linear Algebra, Honors Complex Variables, Ordinary Differential Equations (S), Partial Differential Equations, Analytic Number Theory, Algebraic Number Theory, Probability (S), Logic (S), Knot Theory.

    S stands for Summer Class and Modern Analysis and Algebra are self-studied. Would I have a shot?
     
  12. Aug 3, 2011 #11
    I highly doubt it.

    There's still the problem of not having a degree in math. The graduate admissions committe is going to see you have a degree in "unrelated field" and strongly question your reasons for applying. They will definitely put someone with an actual degree in math infront of you.
     
  13. Aug 3, 2011 #12
    I really have to disagree with Clever-Name, streeters, and to a lesser extent micromass (since he lives in Belgium). Many, if not the majority, of graduate schools in the US do not have 'a bachelors degree in mathematics' as one of their requirements. Furthermore I am skeptical that they would automatically "put someone with an actual degree in math in front of you", considering what their primary motivations are for taking on and funding graduate students. You will however need to be competitive with those who do have math degrees, which will be difficult if you are majoring in something else.
     
  14. Aug 3, 2011 #13

    jbunniii

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    I agree with the philosophy behind this remark and strongly echo the recommendation, but it's not literally true. I got into a top-20 math PhD program (in the US) with an EE undergraduate degree plus some extra coursework. Fine arts would be a different story, though!
     
  15. Aug 3, 2011 #14

    micromass

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    OK, I was wrong with my comment :smile: But just for curiosity, how much extra coursework are we talking about??
     
  16. Aug 3, 2011 #15
    I would think it would be best to ask the grad school which you wish to go to! Find out what the entry requirements to the program are. Talk to an admissions counselor. That would seem to be the best way to know what you need to do.
     
  17. Aug 3, 2011 #16

    Pengwuino

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    You can get into a math PHD program without a math degree. HOWEVER, there are no hard and fast rules to getting into phd programs other than the fact that you are competing with other people to get into the schools. They're almost all going to have degrees in math, more classes than you, probably better math GRE and GRE scores than you and their application will look better. So all that matters is how does your application look versus everyone elses. Also, no, chess stuff doesn't matter for graduate school. Your GRE is important but the subject GRE is the more important one. It's assumed you'll do nearly perfect if not perfect on the math portion of the GRE and at least decently on the rest of the GRE.

    Getting into a fine arts PHD program, taking a bunch of math courses, and transferring seems highly suspect, although I'll leave this for people with more experience in the area. Also, self-studying is meaningless when it comes to looking like you know math on your application. If you say you studied X, Y, and Z courses, that's pretty much meaningless to them. They have to see transcripts with actual grades. Sure it helps you to actually know the material, but it doesn't make you look better on an application.

    I have no idea why you're doing a fine arts BA. Why don't you transfer to a university with a math BS? If you do a math PHD, your fine arts degree is going to be just for show, I really don't understand this.

    But whatever your reason is, just remember that at the end of the day, your application is going to get 15 minutes to prove to the admissions committee why they should allow you in compared to everyone else that applies. Any oddity or missing component to your application will only work against you.
     
  18. Aug 3, 2011 #17

    jbunniii

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    During my undergraduate degree, the standard calculus 1,2,3, a couple of differential equations courses, linear algebra, real analysis (Baby Rudin), complex analysis, real analysis (Lebesgue/measure theory). Plus a bunch of probability and stochastic processes.

    Some years later when I decided to apply to graduate programs, I took an honors-level abstract algebra sequence and a couple of other courses. I think I got in largely on the strength of letters of recommendation from the professors of those later courses. After I started the graduate program, I would say I was about middle of the pack or a bit higher in terms of preparation. I was fairly strong in algebra and analysis, very weak in topology, and of course missed out on stuff most of my peers had done, like REU's. I knew next to nothing about number theory. So it's possible with an unconventional background, but not the most efficient or recommended path!
     
  19. Aug 4, 2011 #18

    chiro

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    Hey mathgeeko and welcome to the forums.

    I don't know about you, but in my experience you really have to be constantly doing and thinking about math to have any success in it.

    I couldn't picture a PhD student having a half-hearted view of math. I don't know if the "all or nothing" principle is accurate of this, but in my short experience, I think this the case.

    Micromasses class list is a good list and I want to emphasize that math is not just analysis, or statistics, or number theory, its the whole kit and kaboodle. Knowing a bit of everything adds to your toolkit of knowledge and seeing the sum of its parts in my opinion, really makes a difference between someone that just wants to know about math, to someone who wants to do and practice math.

    I consider myself an average mathematician (I'm still studying), but from observations about other students (undergraduate or graduate), lecturers, or professors, it really is a full time endeavor and then some.
     
  20. Aug 4, 2011 #19
    I'll agree with Pengiuno that it's not impossible to gain acceptance... but rather that to gain admission to a program, you need to be in the top portion of the pool of applicants whose stack of applications sits in front of the admissions committee at that time. So conditions for acceptance can vary from year to year, although there are trends that admissions counselors (or the departments administrative assistants) may be able to provide to help you.

    Generally, a degree in the field is helpful.... but if you don't have a degree and nonetheless demonstrate aptitude in upper-level coursework you might be moved up in the stack. The degree, however, will help, because most departments will have qualifying exams, core coursework, and perhaps comprehensive exams over that core coursework before you can pursue research fully. The committee will want to know the you will be able to jump these hurdles successfully. They don't want to accept someone who can't... and the undergraduate degree is considered good preparation for these hurdles, but sometimes acceptance occurs with a degree in a related field and strong coursework in upper-level classes in the field.

    Although I've served on graduate admissions committees, my field is physics (not math).. so I'm not sure how much the subject GRE matters for math (it generally matters quite a bit for physics). Getting a very high mathematics GRE score may also sufficiently demonstrate aptitude for some departments. Again, however, the mathematics major at universities is designed to help prepare a student for that... and your score will be compared with those of the other applicants who probably had that preparation for the test.

    Doing some research will help (in my experience the committee definitely looked for this). It will show that you know what getting a Ph.D. is about, and are truly interested... not just thinking it sounds cool, or not just facing bleak post-undergraduate job prospects. Warning: Unfortunately, bleak job prospects is the case for many students now... and will increase the pool of applicants for graduate programs as graduating students try to increase their chances by applying to both jobs and graduate programs.

    All that said... you ask this:

    Do you have a list of generally offered coursework? Some may be slow to give advice without this (since your school doesn't have the degree program they may think offerings are scarce).
     
  21. Aug 4, 2011 #20
    Thanks again for your replies guys.

    @physics girl phd: My school has an agreement with a nearby research university (an Ivy League school with a serious math dept) which enables me to register for the same classes as any college student. Sorry I wasn't clear about that. I can also register for graduate level classes and I am somewhat free to go around pre-requisites.
    Given that I can take these classes, which ones do you think I should select? What skills and knowledge does an unpaid undergraduate research assistant usually needs to have and how hard is it usually to get such a position?

    @chiro: Thank you for your welcoming words. I do think that math occupies a big place in my life, whether it is reading a lot about it, making up my own problems or trying to find patterns in series of number I randomly encounter. What more could you suggest for me to get a more "mathematician-like" way of thinking about math?
     
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