Yet another which math course to take? thread

[PieceOfPi]

Yet another "which math course to take?" thread

Dear PF members,

First, I would like to apologize in advance for asking this type of question repeatedly. I just haven't made my mind yet, and I just think getting another advice from PF members might be helpful.

So, I'm going to be a junior, a math major, and it looks like I can take two math classes on next time. I am planning to take mathematical statistics for my first slot--this course might be good since the course is mainly targeted for math majors (i.e. no science/CS/econ majors unless they have taken Calc III and linear algebra), and I don't know much about statistics and probability, even though I realize that it's an important subject. For the other space, I'm trying to choose from 1) analysis (baby Rudin), 2) topology (Munkres), 3) algebra (Beachy/Blair), or 4) Numerical Analysis (Warner/Kincaid).

I don't know what to do after graduation yet, but which one(s) would be the best choice if I want to

(A) go to a graduate school in mathematics.
(B) go to a graduate school in applied mathematics.
(C) go to a graduate school in computer science.
(D) study computational science.
(E) get the hell out of academics and get a job.

As you can see, my interests lie somewhere in-between math and CS and a little bit of science.

Personally, algebra might fit my interest the most since the math course I liked include linear algebra (both intro and abstract) and combinatorics & graph theory. But the order of the qualities of the instructors, on average, seem to be topology => analysis > numerical analysis => algebra, according to the course evaluation report at my school and ratemyprofessors.com. I've had analysis and numerical analysis profs before. I liked the guy who is teaching analysis quite a bit, and I thought the guy who is teaching numerical analysis was just ok. I've heard bad stuff about the prof who's teaching algebra... but most of those complaints came from business calculus students, so that doesn't prove much! But the other complaints came from linear algebra students, so that's not a good news... Should I depend on picking my course by the reviews of instructors?

Feel free to ask question if you have any.

Thanks

 

[rubrix]

Here, Analysis and Abstract Algebra (both 1 and 2) are mandatory courses, usually we take 'em in our junior year. For first semester Analysis 1 and Abstract Algebra 1 and then sequence 2 of both courses for next semester. So yeah, imo those two courses should be in your list.

As per Numerical Analysis, i asked about that in this forum before, and it is highly recommended subject, in Mathematical Computer Science itself as well as in Physics.

seeing that you are interested in applied mathematics...incase your college provides Partial Differential Equations (PDE) course for Undergrad, don't miss it!

 

[PieceOfPi]

Here, Analysis and Abstract Algebra (both 1 and 2) are mandatory courses, usually we take 'em in our junior year. For first semester Analysis 1 and Abstract Algebra 1 and then sequence 2 of both courses for next semester. So yeah, imo those two courses should be in your list.

As per Numerical Analysis, i asked about that in this forum before, and it is highly recommended subject, in Mathematical Computer Science itself as well as in Physics.

seeing that you are interested in applied mathematics...incase your college provides Partial Differential Equations (PDE) course for Undergrad, don't miss it!

Thanks. Looks like the only option you wouldn't consider is topology, as I've heard from others that getting done with analysis or algebra is more important.

Unfortunately, I won't be able to take PDE this year, due to schedule conflicts. I'm hoping that I can take that next year.

Analysis vs. algebra is a hard choice... I took analysis last year, but somehow I felt like I couldn't get my brain to really understand the materials, so I ended up taking the course Pass/No Pass (I passed it though). I guess I can give analysis one more chance (with a professor who I think is better than the guy who taught it last year), but I wonder if I should choose this option over algebra (which I'm more interested, but I'm also scared about the professor). Maybe I could take both (instead of taking stat), but I wonder if that would be an overkill.

 

[mrb]

I can only speak to pure math: at least one decently ranked grad school (I forget which one) says you should regard two courses in analysis, two in algebra, and one in topology as pretty much the bare minimum to apply. This seems to be comparable to other places, although some are probably more flexible.

Mathematical statistics is fine but much less important.

If you felt like you didn't really grasp analysis, that is definitely something you will have to rectify at some point.

 

[rubrix]

Looks like the only option you wouldn't consider is topology

actually i don't know much about topology hence i said nothing. That does not mean you shouldn't consider it.

edit: I'm just looking over MS program for pure mathematics at some universities here and (like mrb said) analysis, abstract algebra, and topology are pretty much mandatory. Our university however, gives one an option to swamp topology requirement with complex analysis course or a much higher analysis or algebra course.

 

[PieceOfPi]

Thanks for your comments,

I can only speak to pure math: at least one decently ranked grad school (I forget which one) says you should regard two courses in analysis, two in algebra, and one in topology as pretty much the bare minimum to apply. This seems to be comparable to other places, although some are probably more flexible.

Mathematical statistics is fine but much less important.

If you felt like you didn't really grasp analysis, that is definitely something you will have to rectify at some point.

Now that I have abstract linear algebra under my belt, I guess I can try analysis again... but I don't know. Personally I find algebra more interesting than analysis, but analysis professor seems to be better than the algebra professor for this school year. Oh well. The school hasn't even started yet, so once it started, I'll just go to the both lectures during the first week to see which I would like to stay more.

actually i don't know much about topology hence i said nothing. That does not mean you shouldn't consider it.

edit: I'm just looking over MS program for pure mathematics at some universities here and (like mrb said) analysis, abstract algebra, and topology are pretty much mandatory. Our university however, gives one an option to swamp topology requirement with complex analysis course or a much higher analysis or algebra course.

Thanks. From what I've heard, topology is usually taken after either analysis or algebra is taken, but I've also heard it doesn't necessarily have to be that way.



Which one of analysis, algebra, and analysis would be more helpful if I decided to study applied math? Computer science?

 

[rubrix]

Among analysis and algebra, analysis ought to be more helpful for applied mathematics. But you don't need it for MS.