Taking Topology, Real Analysis and Abstract Algebra concurrently a good idea?

[PiAreSquared]

Hello all,

In the Fall I am planning on taking Real Analysis, Abstract Algebra and doing an independent study in something(my professor has yet to get back to me on what he is willing to do it in). My question is would it be too much of a workload to try and do another independent study in Topology, in addition to those three courses?

The courses in question are the only ones that I will be taking that term. I would like to have completed the entire sequence for Real Analysis, Abstract Algebra and Topology before graduating(I have only one year(two terms) left), as I plan on attended graduate school.

 

[Robert1986]

Are you going to grad school in math? I honestly don't see how you could even get in somewhere without algebra and analysis. Anyway, normally I would recommend taking a proof based math class before analysis. I took algebra one semester and analysis the next. (But where I go, we have this proof-based linear algebra class that all the math majors take before moving to the upper-level stuff.) But you only have a year left and you want to go to grad school, so you'll want this on your transcript, so I guess I would take them. What other math classes have you taken?

 

[PiAreSquared]

I have taken the multi-variable calculus, Linear Algebra, ODE's, Probability, Statistics, Intro to Proofs, and I am currently taking Number Theory. I plan on taking the full analysis and algebra sequences without a doubt.

 

[Robert1986]

Can you wait another year to graduate? I'd do that if I was in your position.

 

[PiAreSquared]

No not really. I'm not sure why that would be beneficial anyhow. Upon graduating, I will have had at least Real Analysis I and II, Abstract Algebra I and II, a second course in Linear Algebra, and either Numerical Analysis or Complex Analysis. I will also end up taking about two or three more math courses in addition to those because I have no other Gen. Ed. requirements left, I just haven't decided which ones I want take.

So if I waited another year to graduate, I would not have much else to take (my school does not have a graduate program, so taking graduate classes is not an option).

 

[Arsenic&Lace]

I did that exact same thing last semester and found it to be very challenging. Topology was quite difficult for me since I did not have a background in analysis and couldn't figure out the motivation for the material. From what I gather you do not have an analysis background? Also, it looks as though you've only taken one proofs course. Both real analysis and topology will be very proofs intensive. Abstract algebra was for me more conceptually easy but it's still quite a challenging course.

I took the risk and borked it (all B's). You might get off more easily, but those grades matter a lot!

 

[Robert1986]

Perhaps do topology the second semester? The reason is that topology is the generalisation of properties of real numbers, (really of R^n). It is amazing. I didn't take it as an undergrad (a mistake) but I've been working through a book and it is just marvelous. But, you won't really get to marvel if you don't make the connection that it is generalising euclidean spaces.

 

[deluks917]

I agree it make more sense to take topology after real analysis. Real and abstract together is good. I think you will be able to understand topology but it will make more intuitive sense after Real. If you are pressed for time though I think the plan is fine.

 

[Ivan92]

Perhaps do topology the second semester? The reason is that topology is the generalisation of properties of real numbers, (really of R^n). It is amazing. I didn't take it as an undergrad (a mistake) but I've been working through a book and it is just marvelous. But, you won't really get to marvel if you don't make the connection that it is generalising euclidean spaces.

Robert, may I ask what book you use for Topology?

 

[Robert1986]

Robert, may I ask what book you use for Topology?

This one:
https://www.amazon.com/dp/0387901256/?tag=pfamazon01-20

EDIT:
The reason I got this book is that someone around here recommended it (I think micromass, but I'm not sure.)

 

[deluks917]

^That is a fairly hard book in my opinion. I would recommend it for someone without a pretty strong background or a lot of time and motivation.

 

[Robert1986]

^That is a fairly hard book in my opinion. I would recommend it for someone without a pretty strong background or a lot of time and motivation.

Do you mean "wouldn't"?

I don't know enough to recommend or not to recommend any topology book. I just saw someone recommend it on these forums, and they happened to have it in my university's library. So I checked it out and it has been tough - but interesting. However, I had to return it a couple weeks ago but I plan on buying a copy.

Anyway, I wouldn't have been able to get through it if I hadn't had lots of experience working with the topology of R^n. So, I don't want it to seem that I was recommending this book for anyone.

 

[PiAreSquared]

Thanks for the input guys. I'll try to take Topology after I have had at least Analysis I.

Since I have room for another independent study, are there any topics/courses that any of you all have had (or wished that you would have had) as an undergraduate that really helped you out in graduate school? I could surely find something that seems interesting but I might as well find something that could be very beneficial in the long run. I don't know what area of math I would like to go into, so I realize that it may be too broad of a question.

Thanks for the input.

 

[deluks917]

Yeah meant to say wouldn't!