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Admissions Some questions about double degrees and graduate admissions (in Mathematics)

  1. Apr 1, 2012 #1

    Here is some (more or less) relevant information:

    So I'm majoring in Philosophy and Logic, and I recently found out that if I do about an extra year of undergrad work, I can get a second bachelor's degree (In Mathmatics!)

    So I'm thinking: Since graduate school in Philosophy is pretty hard to get into (if you care about the competence of your advisor: think 200-400 applicants and 3-8 people getting accepted), and I doubt that I'll be able to get into a graduate program at a mathematics department without that extra degree*, taking that extra year seems like a pretty good way to make my chances of getting, if not a PhD, then at least a paid job, somewhat higher.

    *(The mathy courses I've taken so far are: Set theory, Logic I, Logic II (Metalogic I), Proof Theory, Computability Theory, Modal Logic. Each worth ca. 4.5 credit hours.)

    The questions

    Does anyone know/want to guess how/if staying an extra year to get an extra degree will affect my chances of getting into graduate school as a mathematician?

    Will it look suspicious?

    If I get into a Master program in Philosophy and then can't get into a PhD program, will it look even more suspicious if I apply for a math program?

    Is the acceptance rate higher for PhD programs in Mathematics than in Philosophy?

    Why do questions about the future take up so much of my time? (You're welcome to try to answer this one as well!)

    Would you have taken that extra year?

  2. jcsd
  3. Apr 1, 2012 #2
    Do I understand correctly that the ONLY math classes that you have taken are the ones you have listed? If so, you haven't taken near enough math classes and most of those shouldn't really be considered math classes, at least with respect to getting into grad school.

    You need 3 years of calculus and differential equations to begin with. You will need some Analysis and some Algebra (that is Abstract Algebra) at the very least. What other math classes do you plan on taking between now and when you graduate?

    I should also mention that one of my favorite mathematicians, Paul Halmos, was a philosophy undgrad. He started a philosophy Ph.D. but flunked out and switched to math.
  4. Apr 1, 2012 #3
    Great. I wrote a really long reply and got logged out, and it was lost in the process... :mad:


    If I chose to do that extra year, I'll have at least the following math courses in addition to the ones I mentioned (Don't dis logic :frown: ):

    Calculus I-III (Mandatory)
    Linear Algebra I-II (Mandatory)
    Discrete Mathematics I (Mandatory)
    Abstract Algebra I-II
    Analysis I
    a Bachelors thesis in mathematics

    Do you think I should add anything to this? Remove something? Change something?

    Could you say something about the minimum number of credits in math courses that a math major takes wherever you are from? Three years doesn't say that much, since I'm probably not from wherever you are. For example, it is custom for students to cover Calculus I-III, Linear Algebra I-II and Discrete Mathematics I and some additional topic within two semesters here; It's not uncommon at my university that people cover somewhere around the equivalence of 40 US credits in pure math courses in one year.

    Saying that I need three years of math, in order to get into a graduate program, sounds bizarre to me.

    Does anyone have any thoughts about this?
    Last edited: Apr 1, 2012
  5. Apr 1, 2012 #4

    I mis-spoke (er mis-typed).

    I mean to say that you needed calc 1 calc 2 and calc 3. For some reason this came out as "three years."

    As for the courses you have listed. These are probably enough to get you into grad school but someone else might know better. However I would take out the crypto class and add another analysis class. At my school analysis I is mostly just lays the groundwork for analysis II which is where you do differentiation and integration.

    As for the minimum number of courses we have to take many more. Here is a list:
    Calc 1 - 3
    Abstract Vector Spaces (kind of like a really abstract linear algebra)
    Intro to Prob/Stat
    Applied Combinatorics
    Algebra I
    Analysis I
    Analysis II
    Numerical Analysis
    Complex Analysis

    Plus 5 Math "upper level" math courses. I have taken:
    Number Theory
    Algebra II
    Mathematical Stats
    Linear Algebra (more on this in a bit)
    Combinatorial Analysis

    We have a very accelerated calc sequence where I go. For example linear algebra is taught with calc II and as a result calc I goes pretty fast. (At least faster than what I know other schools do.)

    I think most students would complete calc I-III and the other stuff in 1.5 to 2 years. Then the other stuff that I listed in about 2-2.5 years.

    Anyway, like I said, I think you have enough courses there to get into grad school. Especially when you consider the thesis you have to write. Also, it would help to do research with a professor (something I wish I had done.) Again, I'm not an expert, and others around here will have more to say, but I think you will be in good shape.

    Also, I wasn't dissing logic. The fact is, you may understand logic very well and not know anything about math. Yes, in some sense math is "applied logic," but in a very weird sense. But to really understand this, you have to have a solid mathematical foundation, which you presently lack (but shouldn't after you graduate.)
  6. Apr 1, 2012 #5
    I would think getting into graduate school for mathematics is harder than philosophy. A lot of students who get excepted into the top schools already have publications. It is also necessary to have good recommendations from professors.

    If you are in the US it might be very hard to complete all those classes you have listed without schooling year round. Even then you will be compared to students who have participated in mathematics since the beginning of their university careers. I say this because I am very skeptical about geniuses. 99.9% of people need more time than just one year to develop their understanding of mathematics.

    If you are thinking about going for a PhD in mathematics just because it's too hard to get into a PhD program for philosophy, you have a lot of rethinking to do.

    I also include this in all posts where the OP asks for help on a decision about their decision. I am a firm believer that nothing is impossible. If you really do enjoy mathematics, then go for it. I am sure you will do great.
    Last edited: Apr 2, 2012
  7. Apr 1, 2012 #6
    An additional year of study is not sufficient to make up for your mathematical deficiencies. You need to start over again (i.e. spend four years studying math), if you want to apply to math programs.

    I really suggest you stick with philosophy.
  8. Apr 2, 2012 #7
    Well, maybe. The situation seems to to be pretty much the same from what you just said though. (I don't really care about "top programs" though...)
    I'm not in the US. I also think that you somehow misunderstood something. First of all, I'm not going to take all the courses I listed in one year; I'm going to stay an extra year to have time enough to complete all of them, and some more. I'll get some of them done before that. Also, I've been in contact with the departments and the people who award degrees, and they said that it's completely normal to get those courses done in the timeframe I have in mind.
    (I don't believe in geniuses either; I'm more of an DP/expertise guy.)

    That's not the point at all... I just thought the extra year would be a geneally good back up plan, and wanted to know if anyone knew what admission committees think of people with non-standard backgrounds.
    That's preposterous. But thanks. :smile:

    If I spent four years doing math at my school, that would amount to something like 160 US credit hours in only math courses. What you do in a semester, we often do in a month. If you do a semester course in a subject here, it most often means that you take a course package with classes in that subject only, and most of the time courses are done one at a time. So for example: If you take semester course on Logic, you do ONLY mathematical logic every day for a month, take an exam, and then you do only structural proof theory every day for a month, and so on. Sometimes we do them at a slower speed, but you would still be doing something like, say, Calculus II and Linear Algebra II simultaneously for two months, and then do two other math courses simultaneously for two months.

    Hmh, okay. It seems possible to change the cryptography course for a course in linear analysis or analytic functions... But I think that would make the schedule kind of tough though (timewise).
    Okay, thanks.

    I know that it'll be possible for me to get into a Master Program in my country at least (provided I don't do really bad...), so the number of courses wasn't really my concern. What I'm interested in is mainly what admission committees think of applicants with non-standard backgrounds. Maybe I should've been more clear about this.

    I wasn't very serious with that comment; I just think it sounds strange to not count mathematical logic as a form of mathematics.
  9. Apr 2, 2012 #8
    Well it might make sense to do the Master's first, then move on to the Ph.D. This is good for two reasons 1)You might have an easier time getting into a Master's Program (though, if you have done some research, have good letters of recommendation, take the courses you have taken and make good grades, it might be just as easy to get into a Ph.D. program. I think that the main difference between the two is that for the Ph.D. they want to make sure you can do research) and 2)the Ph.D. is a HUGE commitment; one that many people cannot complete. So, doing the Master's in Math is kind of like testing the waters before jumping into the Ph.D.

    Its not that it isn't a form of math, it just isn't something that will get you into grad school. You could take all the math logic you want and not know anything about math, other than (perhaps) the very fundamental grounding of math in logic. Obviously this is important, but if you can't even do a derivative, then you aren't of much use to a math department, you know? It doesn't really make any difference whether or not you know that mathematical theorems are "correct" if you don't know what the theorems are. So, I'm not saying that math logic is not important, it is very important, nor am I saying that math logic is not a branch of math (actually, it might be more accurate to say math is a branch of logic, but anyway).
  10. Apr 2, 2012 #9
    If your interests are in mathematical logic, then going into philosophy isn't a bad idea at all. Also, your whole plan doesn't make any sense. The entire undergraduate math curricula can't be digested in one or two years. Seeing that you don't even know math at the level of a typical first year student in the US (yes, English and Art majors probably know more math than you), you need to devote four more years of study. I could care less how your semesters work. You need four years to learn and understand the necessary math. Sorry if I sound harsh. I'm just giving you a dose of reality.
  11. Apr 2, 2012 #10
    Is there a placement test? If you ace it you might be able to skip Calc I-II (the single variable stuff) all together. In fact, I wouldn't suggest doing this unless you do ace the placement test...pure mathematics IMHO is a hard abstract branch of academia which only a few select people find interesting...

    If you really insist on this, what you could do is instead of getting a BS in Math, you get a BA in Math. Then you can skip a lot of the theory/proof based classes and just choose the computational classes (which is a lot easier and lot more useful IMO)

    And to everyone ragging on him for being a Philosophy Major, a lot of genius mathematicians were philosophers.
  12. Apr 2, 2012 #11
    No. This is completely insane. What he is trying to do is hard enough as it is. Not taking calculus is just asking for disaster. To be able to pass the placement exam is going to require the same amount of time as it would to take the class, and he's not going to know near enough.

    Who is ragging on him for being a Philosophy Major? I don't think anyone is. In fact, I mentioned a mathematician who was a Philosophy Major as an undergrad. So, to what exactly are you referring?
  13. Apr 2, 2012 #12
    I take it that you would like to do something logic related?? Be aware that there aren't many people out there studying logic (as compared to more popular branches such as abstract algebra), so you'll have to do very well.

    I like this schedule. Perhaps it's missing some analysis. Also complex variables is something that should be seen.

    This schedule you're proposing isn't easy by far. Expect to spend quite some time on it. You should finish calculus as soon as possible as the other courses depend on that.
  14. Apr 2, 2012 #13
    I'm beginning to agree more and more with this.

    I think you are going to need 4 more years. I took calc I-III in my first year of college, in essence. I have now had three years of proof-based upper level math coursework. It is hard to explain, but the more math you do, the better you will be able to quickly understand other math stuff, even in unrelated fields. For example, I took Algebra I before Analysis I. I had a hard time getting through lots of proofs in Algebra I. In Analysis I, not as difficult. It isn't that the stuff in Analysis is easy, I was just more accustomed to proof-reading. Then, I took Algebra II and Analysis II the same semester, same thing again. And it continues.

    Now, it is not because I am a genius, it is because I have just been doing this upper-level math for more than 3 years now and more and more stuff starts to "click." This is very exciting to me because I know the more and more time I spend doing math, the more and more it will "click." Its kind of like growing exponentially.

    There is no way to do what you want with out spending the time to do it. It doesn't matter how much money you give an unpregnant woman, she can't give birth in 3 months no matter how hard she tries. There is a similar situation with you. It doesn't matter how much you want to do this, I just don't think it can be done. And if you are able to do it, my prediction is that you will be vastly unprepared for graduate studies in math.

    How about this: Take the extra year as you planned and take lots of math classes. Get a MA in Philosophy and take lots of Math classes in grad school (like some upper-level undergrad courses and a bunch of grad courses). Then perhaps you can apply to Math Ph.D. programs and get in, and succeed.
  15. Apr 2, 2012 #14
    Agreed. You don't need 3 years to actually learn everything. Rather, you need 3 years to develop mathematical maturity. Once you're used to reading math texts, then your schedule can be completed in less than a year. But it's getting used to abstract math that will take your time.
  16. Apr 3, 2012 #15
    I don't think there's any such distinction where I'm at really.

    Well, I'm not completely sure I'd be going into logic. The topics I've enjoyed the most so far are model theory and set theory, and I've also enjoyed categorical logic quite a bit. So maybe something similar. I don't know. I don't really care what I do as long as it's interesting and challenging (and not too practically relevant!).
    I'd also like to stress that I'm not even sure that I would be trying to pursue a graduate degree in mathematics, were I to get a bachelor in it. As I mentioned in the original post, a bachelor in mathematics will probably get me a better job than a bachelor in philosophy will. I think that's a good enough reason to do it.

    Well, there are also courses in complex analysis and linear analysis and analytic functions at that level, but because of the "strange" scheduling here, it's hard to fit more of them in. It's probably possible to take one of those instead of cryptography though.

    I think I know what you mean with the "click", and I think it's the same with most topics; similar things have happened to me in philosophy for example. Similar things happend when I learned to play musical instruments and music theory as well.
    I guess the point is: One has to practice in order to become good, and doing a lot very intensely over a shorter time frame isn't a good subsitute for doing the same over a longer time frame? This is a valid point, but I really don't expect to develop the same expertise in half the time. I know it's going to be really hard and time-consuming, but again, I would be completing the material within the standard timeframe at my university, so I don't think I would be at a disadvantage if I would chose to continue my education here.

    About my interstes:
    My interests are in intellectual development and trying to understand things. Doing mathematical logic is just something I found to be a good way to increase certain abilities which are relevant for those interests. The same goes for philosophy. And I also think that you're wrong. It's hard to find a job in a philosophy department in general, and especially if one wants to specialize in mathematical logic. The chances that one will be allowed to specialize in mathematical logic in a PhD-program for philosophers is virtually nil; they want you to take philosophy courses and write on philosophy. If one is interested in logic, then one has to work on topics that are philosophically relevant, which most of mainstream mathematical logic isn't. It's also very hard to find a job if your AOS is mathematical logic. Most philosophy departments don't need to hire logicians; they need people who can teach the courses that more than five people take. And tbh, most universities don't even offer mathematical logic to their philosophy students. Most often there is one mandatory logic course, which is based on translating between First-Order logic and natural language, and doing simple proofs and deductions using natural deduction or semantic tableaux, and if you're lucky you'll see completeness and soundness theorems.
    About humanities majors: I don't really get your point.
    About time: I hope you understand that many, if not most, places outside of the US don't even have 4 year long undergraduate programs, so I have a hard time taking the literal content of what you're saying as true. American majors don't really seem much more accomplished than others, but if what you say is true, then large portions of the world would have been graduating tons of sub-par scientists and mathematicians for a long time. The timeframe I have in mind is, I say it again, standard here. There have been enough scientists and mathematicians educated in this system for me to believe that it works better than good enough. Also, I'm not going to do "the entire undergraduate curricula" (I think you mean curriculum, as curricula is the plural form) in one or two years.

    How would you say that reading a math text and a logic text differs? Admittedly, I'm not really sure where the line goes between logic and mathematics. The only book I've worked through that I'm sure shouldn't be counted as a logic book is a calculus book. On the other hand I've worked through books like Goldblatt's Topoi: The Categorical Analysis of Logic and Manzano's Model Theory which I'm not sure if it's meaningful to classify as one or the other.

    Thanks for your replies everyone.
    I'm not really sure what kind of answers I was expecting but it sure wasn't this kind.
  17. Apr 3, 2012 #16
    Don't listen to these guys about the 4 year figure. That makes no sense. An entire degree normally takes 4 years, and that includes a load of extra classes unrelated to the major. Why on earth would it take you 4 extra years if you are just taking the core classes? Just study hard, take as many classes as your school lets you, and make great grades. I believe in you.
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