Congrats to RacerX

Yeah, it reminds me of Back to the Future in that way.

The Star Trek series (which are more individual stories) found out that once every two years was to close together. I do like how Lord of the Rings is doing it (one a year) considering the story line. And Star Wars is matching the schedule that they used for the original three (though one every two years would have worked better in my opinion).
 
Hey Valrus,

So have you put much thought into an area of specialty yet? I started out as a physics major, so I was picky about the mathematics I was taking early on.

Are you planning on going to graduate school? Are you considering the U? I know quite a few good professors around the country in a number of fields, though I don't know that many professors at the U (Marden and McGehee, but I knew them through the Geometry Center). My favorite semi-non geometry professors would be Doyle (Dartmouth) and Conway (Princeton), both of which love probability and games (and Doyle worked under Conway as a student at Princeton as I recall).

So what is the math department at Macalester College like? I couldn't tell if they had a graduate program by my first look at their web site.

What classes are you planning on taking? I love taking classes, so I've taken a ton of extra courses that had slowed down my progress toward a degree, but was very helpful in my research. Here is a list of the ones I can remember:

  • Math 100A-C Modern Algebra (groups, rings, fields, vector spaces, Galois theory, etc.)
    Math 117 Geometry and the Imagination (introduction to topics in geometry, topology, knot theory)
    Math 140A-B Foundation in Analysis
    Math 150A Differential Geometry (classical differential geometry)
    Math 150B Calculus on Manifolds (techniques in differential forms)
    Math 151 Topic in Geometry (Lie Geometry)
    Math 151 Topic in Geometry (Clifford Algebras)
    Math 190 Introduction to Topology (geometric and point-set)
    Math 191 Topics in Topology (aspects of Homotopy theory)
    Math 200A Algebra (more of the same)
    Math 210A Mathematical Methods in Physics
    Math 250A Differentiable Manifolds
    Math 250B Riemannian Geometry
    Math 250C Integration on Manifolds
    Math 251A Lie Groups
    Math 251B Lie Algebras
    Physics 100A Electromagnetism
    Physics 110A-B Mechanics
    Physics 162 Galaxies and Cosmology
    Physics 225A General Relativity
That is not counting the courses I audited :D. And the ones I need to take (and probably should have by now):

  • Math 200B-C Algebra
    Math 240A-C Real Analysis
    Math 290A-C Topology
 
Well, I think I'm most interested in pure math, although I haven't really chosen an area of specialization within that yet. Algebraic Structures was fun but I think I want to get a taste of some of the other areas of higher-level math before I decide which to focus on. I have always kind of liked algebra though, and I do a lot of math competitions in which number theory and the like comes in handy.

I do think I'm going to go to grad school, but I haven't really thought about where yet. Macalester is only a college so it doesn't have a graduate program.

So far at Macalester I've taken Discrete Math, Multi-variable Calculus, Linear Algebra and Algebraic Structures, which may be roughly the equivalent of your Modern Algebra. Next semester I'm going to take Real Analysis, and then I hope to be studying abroad in Budapest the following semester. Maybe. I'd also like to take Combinatorics sometime, either in Budapest or my senior year (next year I'm a junior). I don't have my course catalog or major plan handy, so I can't tell you what else is on it. :D But I'm also pusuing a CS major, so I'm working on some stuff in that direction as well.

Wow, man. You've taken a lot of courses! Are you doing research at a grad school? Do you teach? Actually, if I keep asking questions like this I'll just reveal the depth of my ignorance in this area, so I'll just be blunt: What happens after you graduate from college? :D I really haven't given much thought to my post-Macalester plans, partly because I don't know what my options are, and partly because as far as the options I do know about (i.e. grad school), I don't know what they entail.

-the valrus
 
Wow, Budapest sounds like fun. And I had some friends that were doubling as CS majors. I hadn't thought much about computers when I was in school because there was so little that computers could do to help with the type of math that I do. I wasted a great opportunity at the Geometry Center in 1994 because my research didn't require the use of any of the vast computer resources they had (I was doing research on tight immersions and embeddings of both smooth and polyhedral manifolds). I could kick myself now though.

As for my current standing... limbo would best describe it. About five years ago I had a number of events happen (any one of which would be considered life altering) which brought everything I was working on to a complete halt. I am only now getting back to the point where I could pick up where I left off. This is mostly do to the fact that I'm much happier now than I have been in a number of years, and one of my professors (who is like a father to me) retired and moved here. Having him near is very inspiring.

The direction that I planned on (and hope to resume) would have me going to do post-doc work for two to four years after grad school (which I have about two to three years left of once I restart), and then trying to find a tenure-track position at a university some where. My love is research (trying to answer the many questions I have), so I'm more than willing to trade teaching for the ability to follow my passions freely.

I have two research projects (maybe three, but the third is more physics than mathematics) that I could use for my doctoral thesis, so it really is more passing the qualifying exams in Algebra, Real Analysis and Topology that I need for getting a Ph.D. Oh, and that stupid Bachelors which I also don't have yet :( . I need two quarters of Muir Writing, a quarter of visual arts, a quarter of US History, and a cultural diversity course to finish my Bachelors degree (as you can probably guess, I was having way to much fun taking math and physics classes to be bothered with my lower division requirements :D ). I'll mix those classes in with my remaining math courses. Who knows, maybe I'll get both my Ph.D. and Bachelors within a year of each other. :rolleyes: Then it would look like I finished graduate school in less than a year! :D

I've never been a good student. I've always done what made me happy in school versus what would get me through the fastest. And I've been very lucky. I have had some great mathematicians go out of their way to work with me even with all of my very obvious faults.
 
Aaaaaahhhh, don't let this thread sink RacerX! I'm not done with you!

First off, blah blah, congrats for 1000 posts since I don't think I ever said that, but who gives a crap because that's not the important thing. So instead I'll say congratulations, really, for being one of the people I most respect on this board. Usually a good measure of whether or not a thread is worthwhile is whether you've posted in it. :D

Also, good luck with your classes etc. I think doing what makes you happy in school is more important than getting good grades. I get good grades becuase I seem to have some kind of irrational work ethic which makes me feel like a chump if I don't do my work, so being happy and getting good grades tend to coincide. :rolleyes:

You didn't really answer my question: What happens after college? I'm genuinely curious, since the end of college is approaching kind of rapidly for me. How does getting into grad school go? What kind of jobs can you get as a math major?

I don't mean to be pushy, so tell me if I am. I'm just starting to get a little concerned about the fact that I don't have the slightest idea where I'm going to be in two years. :D

-the valrus
 
Gosh, thanks!

Let me see if I can shed any more light on those questions. I'll keep working on them after this post (which I am writing while being quite worn out, so I'm sure I am forgetting stuff), but I'll need a little more time. For now I can try and relate some of my experiences to the questions.

Graduate school (and other positions like what I did at the Geometry Center) seem to revolve (for me) around letters of recommendation. Because I was already taking graduate courses at UCSD very early on as a undergrad, continuing on with my graduate studies there was easy (and expected by most of the faculty). The position at the Geometry Center was more like what I would expect getting into a good graduate school would be like. The summer I was there, they had 20 positions that were being paid for by a combination NSF and DoE funding. There were over 250 applications for those positions, and the only reason I was one of the applicants selected was because I had some very nice letters of recommendation. The director of that program, Professor Phillips, told me that he really wanted to meet me after reading those letters (and even went on to supervise a number of my projects even after I returned to UCSD and he went back to Stony Brook).

So another thing is networking. While you are taking courses at Macalester, run over to the U and take (audit, actually) some courses that would interest you (I am actually thinking about doing this next year also). This gives you the chance to get to know faculty at the U and possibly get a letter of recommendation from someone at an outside institution. I would point out that these classes could be just as important as any that you would get a grade in because they could help you get into a good graduate school. And professors love students that go out of their way for their subject.

Another thing to think about, research. Many undergrad programs don't require you to do independent research, but this can be both very helpful and very fun. My first extended project was on the subject of vector displacement and Levi-Civita's connections via developable surfaces (not all that different from connections on tangent bundles, but predating those techniques by many decades). I did this in my very first upper division course (Math 150A, Differential Geometry), and even though it was not creating a new solution or method, it was recreating work that had been lost and ideas that had been over generalized. Even though my other projects generated unique material, the techniques used in that first one gave me my first taste of real mathematics. I was very honored to find out that 10 years later my professor was still using my paper as a reference in the classroom for that course.

I hadn't actually put too much thought into the job market. All my plans for the future revolved around sustaining my research habit. My cousin who has a graduate degree works as a teacher at a small college, and he is still interested in doing research (he got interested in Clifford Algebras after we had talked about them, and we worked on geometric techniques in Minkowski space using circular geometry). I guess I had always thought about trading teaching at some school for being able to do research. The nice thing is that mathematics is easier to get funding for than any of the other sciences (like physics or chemistry, both of which can be big budget science). From what I saw, the average NSF grant usually wasn't more than a few thousand dollars (mainly to cover equipment and pay for assistants, which was usually a computer or two and a few grad students).

On a number of occasions I have been asked to solve applied problems. We would get engineers and the like coming to our department asking for help, and some of my professors pointed them in my direction if the problem looked like something I was specializing in. It was only a few hundred dollars here and there, but it gave me a little taste of what someone would do with applied mathematics. Part of my problem is that I specialize in a type of mathematics that has very few applications. I have been able to apply my type of math to some areas of theoretical physics, but even then, it was pretty far from any real world applications. I'll ask around to see what types of other options are out there, I just haven't thought that much about it once I set myself on the path I had chosen.

I’ll add some more after I get some sleep.
 
I think netowrking (the non-compuiter kind) is grande ;) -- If you have a job on campus it is infinitelly easier to network (depending on the job that is) because you will interact with faculty. Then you can get the inside track on classes, courses offered, materials and such. Not only that, you can also enter into classes which are otherwise full :)
 
Something about the subject of networking (the computer kind):

I love freaking people out with Apple Events. And it's easy to do!

I will teach the people that don't know if there are any... :D
 
Thanks a lot, Racer! I'd write a longer reply but I'm fast approaching bedtime. I'm back to getting up at 6:00 to go to work at GEICO...

I will say, though, that auditing classes at the U might be a little bit out of my reach, because of transportation considerations etc. If I find out that it's easier than I think it will be though, I'll definitely try to do it my senior year!

-the valrus
 
The last four days has been quite sad for me. :(

Take care my friends...

:rolleyes:

see ya on the other side. :D
 
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