mathsuxhard said:
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)
I don't think there's any such distinction where I'm at really.
micromass said:
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.
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.
Robert1986 said:
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 without 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.
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 happened 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.
inknit said:
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.
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.
micromass said:
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.
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.
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