Take Intro to Topology or Intro to Analysis?

[andyroo]

I'm about to take my higher upper division classes to complete my mathematics major. I've decided that I'd like to take either Intro to Topology or Intro to Analysis as my topics of choice, along with the required Linear Algebra course that most graduate schools are looking for in applicants. I know what each type of study is about and that it's likely that they'd both interest me, however, I'm not sure which one I would truly enjoy the most.

As far as classes go, I enjoyed vector calculus but not so much multi-variable calculus, I enjoyed elementary analysis to an extent (meaning I can only take so much analysis homework before I become bored), and lastly, elementary differential equations was a favorite class of mine as well. I have yet to take elementary linear algebra, but will this summer before my fall term. Going off this information is there anyway someone could give me an idea about which sequence I should take out of either Intro to Topology or Intro to Analysis? Thanks for your advice.

 

[MathWarrior]

I would take intro to analysis I think its more interesting, and probably has more application areas.

 

[AlephZero]

As a general answer, I would agree with "into to analysis".

But I suppose if you were totally committed to specialising in algebra or geometry, and were only interested in algebraic topology and not analytic, then you could argue the other way.

 

[andyroo]

Thanks for the thoughts! I'll probably register for analysis then

 

[Newtime]

Why not both?

 

[hitmeoff]

Analysis is usually a minimum core class for just about any grad program (linear algebra and abstract algebra being the other two core sequences). So if you can take only one, and you are considering grad school, Analysis is it.

The other thing to consider/ask is: how "Intro" is this Topology class? Topology draws a lot of ideas from analysis, and usually (but not always), at least one course of Analysis is a pre-req to an Intro to Topology course. Also, Topology at my school is noooooo joke, much more difficult than an Intro to Analysis course, and would be even harder without the Analysis experience.

You also said this will be your first higher lever math class? By that do you mean your first real "Proof" based class? Again, depending on the level they are teaching the topology and analysis, you may want to consider taking Analysis as a first real rigorous math course (actually, junior/senior level Linear Algebra is probably the kindest "first" course in rigorous, proof based math, but Analysis would probably be the next after).

Having said all that, personally I find Analysis to be EXTREMELY BORING. Though Topology is very similar in style, for whatever reason I find it much more interesting and fun. Definitely harder, definitely consuming more of my time, but just more enjoyable. So my opinion is that if you just need a class to fill up your schedule and your school does not require Analysis as pre-req to Topology and either Grad School isn't your future or you have time to take Analysis some other time, maybe consider taking Topology first...only because I think it would be more interesting and should prepare you for Analysis in the future.