Math Major - Grad School vs. Job Dilemma

College Majors
1

<p>Hi, I'm a first year math major at UCLA, and I'm somewhat concerned about the differences in the course schedule I would take if I were going to get a job with a BS or if I were planning to go to grad school (for reference: UCLA</a> Math courses). In terms of jobs, I would probably like something relating to economics, maybe as an actuary or quantitative finance. I would also maybe be interested in something relating to programming, though it seems like it would be harder to get a job without being a CS major. On the other hand, I'm also interested in mathematical logic (where UCLA apparently has a top-notch program) and might be interested in studying it in grad school. The problem is that these all seem to have differing course requirements and I'd like to be able to keep all my options open.</p>

<p>Here's what I've taken so far (or signed up for):
Differential Multivariable
Integral Multivariable
Linear Algebra
Lower Div Diff Eq's (at a CC)
Probability Theory I
Probability Theory II
Upper Div Linear Algebra (w/ intro to Proofs)
Introduction to C++</p>

<p>Actuarial Math Requirements:
Intro Financial Math (Math 172A)
Actuarial Models I (Math 172B)
Actuarial Models II (Math 172C)
Real Analysis I (Math 131)
Mathematics of Finance (Math 174)
Mathematical Finance A (Econ 141A)
Mathematical Finance B (Econ 141B)
Intro Mathematical Statistics (Stat 100B)
Linear Models (Stat 100C)</p>

<p>If I take all these (plus General Ed stuff) I'd have about 69 units available, with most classes being 4 units (a few are 5). Which classes would probably be most useful for keeping grad school options open, whether for Mathematical Logic, general Math PhD or some type of MFE type program? I've put asterisks by the ones required for Pure Math majors, since that might be an indication:</p>

<p>Real Analysis II (Math 131B)*
Complex Analysis (Math 132)*
Abstract Algebra I (Math 110A)*
Abstract Algebra II (Math 110B)*
Mathematical Logic (Math 114L)
Computability Theory (Math 114C)
Set Theory (Math 114S)
Linear/Nonlinear Systems of Differential Eq's (Math 134)
Ordinary Diff Eq's (Math 135)
Partial Diff Eq's (Math 136)
Intro Topology (Math 121)
Differential Geometry (Math 120A)*
Applied Numerical Methods (Math 151AB)
PDE Numerical Solutions (Math 153)
Intermediate C++
Advanced C++
Discrete Structures (Math 61)
Combinatorics (Math 180)
Upper Div Lin Algebra II (Math 115B)
Number Theory (Math 111)
Metalogic (Phil 135)
Modal Logic (Phil 136)
Philosophy of Math (Phil 128AB)</p>

<p>I was also curious about general math jobs. I've heard about the NSA and how they have a prett in-depth training process. Would that mean that if you were trying to get a job in say cryptology, you wouldn't necessarily need to have course experience in Number Theory? Anyway, if you've read this far down thanks for bearing with me - I know it's a long post. It's also probably somewhat incoherent given that I had my wisdom teeth removed at the beginning of spring break and I've been taking painkillers and stuff. The math department website has also been giving me problems, so I've written down a lot of the lists just from memory. Hopefully I can clear some of this up later. Thanks for the help.</p>

2

<p>I think I would make a few fundamental changes to how you think about your concerns, and you’ll be much happier! </p>

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<p>I would not approach it in the sense of keeping options open over all of undergrad. It is best to really reflect on what you will likely do, as you’ll likely want to go in one direction or the other starting the beginning of your junior year. Whether it be employers or graduate schools you’re trying to apply to, you need to be able to convince them you know what you want at least to a basic extent when you do apply. Else, serious a student as you may be, they would feel shaky about taking you. </p>

<p>If you’re considering logic, you should definitely sample some logic, set theory, etc. Keep in mind that becoming a researcher in a field often involves a long job search of moving from university to university in not very well paid postdoctoral positions prior to your gaining the expertise necessary to become valued by a university. This is the path you’d set yourself on if you went to grad school. </p>

<p>Else, if you are simply interested in the logic, you could take a few classes and concentrate on things like economics, programming skills, and your career options would be open. If you’re strong at CS and a math major, obviously one place to consider a job at would be Google. </p>

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<p>Cryptography research can be grounded in number theory, but it really depends what kind of stuff you want to do. Chances are, if they have an in depth training program, any specific course isn’t going to help you immensely. Classes in college are one way of getting a real feel for what that material is like, but if you really wanted to go deep into such a field (which takes reflection and some trial and error to be able to say), you would probably have to do your own reading, to be realistic. </p>

<p>If you would like to head down the finance track (MFE), be sure to take some stochastic processes, statistics, know some basic programming, learn basic real analysis up through what’s taught in a second course (on measure theory) very well, and eventually since the MFE programs are competitive to say the least, you’d better gather some work experience and convince them you really want to attend their programs. Having good coursework probably is far from enough to do that. I think either graduate training in relevant topics or work experience would be important for those.</p>

<p>Bottom line – for graduate school, the best preparation is engaging solidly in the material of the flavor you want to learn more about, and figure out some basic idea of what you’d actually study, so you can show you have an idea what you want. For work in industry, you should gather practical experience (internships), and get a broad foundation in programming, statistics, etc, and eventually specialize in a few subjects, but again, don’t underestimate that much of what you’ll learn is through practical experience – you kind of have to go out there and work to figure that stuff out.</p>

<p>Any more questions, I’ll be happy to answer. If I forget to check this thread, you can PM me.</p>

3

<p>Thanks for the response. It seems like I should take a more general path for the next couple quarters until I know more specifically what I want to do. Does something similar to the following look ok?</p>

<p>Fall
Math 131A (Real Analysis)
Phil 135 (Metalogic)
Phil 7 (Phil of Mind - GE)
Econ 1 (Microecon)</p>

<p>Winter
Math 131B (Real Analysis)
Math 115B (Linear Alg)
Math 114C (Computability Theory)
PIC 10B (Intermed C++)</p>

<p>Spring
Math 132 (Complex Analysis)
PIC 10C (Adv C++)
Math 121 (Topology)
Some GE</p>

<p>To be honest, I’m taking PIC 10A in the summer, so I’m not really sure if the more advanced programming classes would be something for me. If I decided to go with the grad school path, I would be able to apply for the BS/MA program and also the Logic Summer Program at UCLA. On the other hand, if I went with more of a focus on finance, I could substitute in another econ class and also Stochastic Processes or a statistics class.</p>

<p>I was also curious about the importance of Diff Eq’s. As I said in the OP, I took lower div Diff Eq’s at a CC, so my background isn’t as strong as it might be. I was glancing at the UCLA grad school admissions suggestions, and it seemed to say that you should have taken an upper div class, but that’s not part of the pure math graduation requirements. I also noticed on MFE websites that it stresses the importance of PDE’s. Would it be really looked down upon in terms of grad school to not take those upper div courses? And would it be difficult to get through a PDE class without taking the classes on ODE’s and systems first? Thanks.</p>

4

<p>There are better authorities than me, but everybody I’ve ever known who has been in your situation has, when given the choice, taken the courses of interest to them, rather than the ones they thought would have some other benefit. If you don’t have much interest in DiffEq, for instance, no sense taking more courses in it, particularly if you already have a background in that area. You say you might want to do mathematical logic in graduate school, and if that is the case, I’d say forget about DiffEq… take more logic, discrete math, and possibly rigorous theoretical CS courses dealing with the topics you’re interested in. No sense being a generalist in grad school.</p>

5

<p>As Auburn hints, you should always sample classes first and see if you want to go farther with them. Sit in on some of the classes (like Diff Eq), and check if they’re for you. </p>

<p>Ultimately, if you DO want to go into the financial mathematics setting, stochastic processes, basic programming, basic linear algebra and multivariable calculus, basic real analysis, and ODE’s/PDE’s are all you need for even the master’s degree in MFE with regards to maths courses. Beyond that, it’s specific to the type of financial courses you want. </p>

<p>If you don’t like Diff-Eqs at all, see if you can learn to like them if you really like other aspects of careers that involve them.</p>

<p>For graduate school, if you’re not doing something in Diff Eqs itself, you are fine not taking the class, to be perfectly honest. </p>

<p>The classes you list are fine, they seem like you’re sampling good stuff, and not totally closing any doors. Figure out what you like and then try to be more focused in junior year. Then apply to schools and/or jobs, and you can do whatever you want (possibly just get even more specialized) in your senior year.</p>

6

<p>OK, thanks a lot for all the help.</p>